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Published work

37 published item(s)

preprint2026arXiv

DORA: A Scalable Asynchronous Reinforcement Learning System for Language Model Training

Reinforcement learning (RL) has become a critical paradigm for LLM post-training, yet the rollout phase -- accounting for 50--80% of total step time -- is bottlenecked by skewed generation: long-tailed trajectories indispensable for model performance block the entire training pipeline. Asynchronous training offers a natural remedy by overlapping generation with training, but introduces a fundamental tension between efficiency and algorithmic correctness. We identify three constraints in asynchronous training to preserve convergence: intra-trajectory policy consistency, data integrity, and bounded staleness. Existing approaches fail to intrinsically address the long-tailed trajectory problem, which is further exacerbated by the imbalance characteristic of Mix-of-Experts models, or deviate from the standard RL training formulation, thereby hindering model convergence. Therefore, we propose DORA (Dynamic ORchestration for Asynchronous Rollout), which addresses this challenge through algorithm-system co-design. DORA introduces multi-version streaming rollout, a novel asynchronous paradigm that maintains multiple policy versions concurrently -- simultaneously achieving full bubble elimination without compromising algorithmic constraints. Experimental results demonstrate that our DORA system achieves substantial improvements in throughput -- up to 2--3 times higher than state-of-the-art systems on open-source benchmarks -- without compromising convergence. Furthermore, in large-scale industrial applications with tens of thousands of accelerators, DORA accelerates RL training by 2--4 times compared to synchronous training across various scenarios. The resultant open-source models, LongCat-Flash-Thinking, exhibit competitive performance on complex reasoning benchmarks, matching the capability of most advanced LLMs.

preprint2026arXiv

Image Restoration via Diffusion Models with Dynamic Resolution

Diffusion models (DMs) have exhibited remarkable efficacy in various image restoration tasks. However, existing approaches typically operate within the high-dimensional pixel space, resulting in high computational overhead. While methods based on latent DMs seek to alleviate this issue by utilizing the compressed latent space of a variational autoencoder, they require repeated encoder-decoder inference. This introduces significant additional computational burdens, often resulting in runtime performance that is even inferior to that of their pixel-space counterparts. To mitigate the computational inefficiency, this work proposes projecting data into lower-dimensional subspaces using dynamic resolution DMs to accelerate the inference process. We first fine-tune pre-trained DMs for dynamic resolution priors and adapt DPS and DAPS, which are two widely used pixel-space methods for general image restoration tasks, into the proposed framework, yielding methods we refer to as SubDPS and SubDAPS, respectively. Given the favorable inference speed and reconstruction fidelity of SubDAPS, we introduce an enhanced variant termed SubDAPS++ to further boost both reconstruction efficiency and quality. Empirical evaluations across diverse image datasets and various restoration tasks demonstrate that the proposed methods outperform recent DM-based approaches in the majority of experimental scenarios. The code is available at https://github.com/StarNextDay/SubDAPS.git.

preprint2026arXiv

Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squares

We study online prediction for marginally stable, partially observed linear dynamical systems under nonstochastic disturbances. Our objective is to minimize the cumulative squared prediction loss and compete with the best-in-hindsight Luenberger predictor. Standard online learning methods typically rely on bounded domains/gradients, and thus their guarantees may fail to deal with potentially unbounded trajectories in marginally stable systems. In this paper, we introduce an unconstrained online least squares method that stabilizes the learning process via tailored predictive hints. With model knowledge, we prove that hints constructed from any stabilizing Luenberger predictor render the hint residuals uniformly bounded, achieving logarithmic regret despite unbounded trajectory growth. We also discuss model-free prediction and introduce a simple universal hint for symmetric systems, under which logarithmic regret is maintained without model knowledge. Our results provide an adaptive, instance-wise optimal online predictor compared to classical fixed-gain observers under nonstochastic disturbances.

preprint2026arXiv

Outlier-Robust Diffusion Solvers for Inverse Problems

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this work, to tackle IPs with outliers, we first refine the measurement via explicit noise estimation to mitigate the effect of noise. Subsequently, we formulate an iteratively reweighted least squares objective based on the Huber loss to address the outliers. We propose a method utilizing gradient descent to approximately solve the corresponding optimization problem for the robust objective. To avoid delicate tuning of the learning rate required by the gradient descent method, we further employ the conjugate gradient method with an efficient strategy for updating. Extensive experiments on multiple image datasets for linear and nonlinear tasks under various conditions demonstrate that our proposed methods exhibit robustness to outliers and outperform recent DM-based methods in most cases.

preprint2024arXiv

On equivalence relations induced by Polish groups

The motivation of this article is to introduce a kind of orbit equivalence relations which can well describe structures and properties of Polish groups from the perspective of Borel reducibility. Given a Polish group $G$, let $E(G)$ be the right coset equivalence relation $G^ω/c(G)$, where $c(G)$ is the group of all convergent sequences in $G$. Let $G$ be a Polish group. (1) $G$ is a discrete countable group containing at least two elements iff $E(G)\sim_BE_0$; (2) if $G$ is TSI uncountable non-archimedean, then $E(G)\sim_BE_0^ω$; (3) $G$ is non-archimedean iff $E(G)\le_B=^+$; (4) if $H$ is a CLI Polish group but $G$ is not, then $E(G)\not\le_BE(H)$; (5) if $H$ is a non-archimedean Polish group but $G$ is not, then $E(G)\not\le_BE(H)$. The notion of $α$-l.m.-unbalanced Polish group for $α<ω_1$ is introduced. Let $G,H$ be Polish groups, $0<α<ω_1$. If $G$ is $α$-l.m.-unbalanced but $H$ is not, then $E(G)\not\le_B E(H)$. For TSI Polish groups, the existence of Borel reduction is transformed into the existence of a well-behaved continuous mapping between topological groups. As its applications, for any Polish group $G$, let $G_0$ be the connected component of the identity element $1_G$. Let $G$ and $H$ be two separable TSI Lie groups. If $E(G)\le_BE(H)$, then there exists a continuous locally injective map $S:G_0\to H_0$. Moreover, if $G_0,H_0$ are abelian, $S$ is a group homomorphism. In particular, for $c_0,e_0,c_1,e_1\in{\mathbb N}$, $E({\mathbb R}^{c_0}\times{\mathbb T}^{e_0})\le_BE({\mathbb R}^{c_1}\times{\mathbb T}^{e_1})$ iff $e_0\le e_1$ and $c_0+e_0\le c_1+e_1$.

preprint2023arXiv

Robust TOA-based Localization with Inaccurate Anchors for MANET

Accurate node localization is vital for mobile ad hoc networks (MANETs). Current methods like Time of Arrival (TOA) can estimate node positions using imprecise baseplates and achieve the Cramér-Rao lower bound (CRLB) accuracy. In multi-hop MANETs, some nodes lack direct links to base anchors, depending on neighbor nodes as dynamic anchors for chain localization. However, the dynamic nature of MANETs challenges TOA&#39;s robustness due to the availability and accuracy of base anchors, coupled with ranging errors. To address the issue of cascading positioning error divergence, we first derive the CRLB for any primary node in MANETs as a metric to tackle localization error in cascading scenarios. Second, we propose an advanced two-step TOA method based on CRLB which is able to approximate target node&#39;s CRLB with only local neighbor information. Finally, simulation results confirm the robustness of our algorithm, achieving CRLB-level accuracy for small ranging errors and maintaining precision for larger errors compared to existing TOA methods.

preprint2022arXiv

6D Camera Relocalization in Visually Ambiguous Extreme Environments

We propose a novel method to reliably estimate the pose of a camera given a sequence of images acquired in extreme environments such as deep seas or extraterrestrial terrains. Data acquired under these challenging conditions are corrupted by textureless surfaces, image degradation, and presence of repetitive and highly ambiguous structures. When naively deployed, the state-of-the-art methods can fail in those scenarios as confirmed by our empirical analysis. In this paper, we attempt to make camera relocalization work in these extreme situations. To this end, we propose: (i) a hierarchical localization system, where we leverage temporal information and (ii) a novel environment-aware image enhancement method to boost the robustness and accuracy. Our extensive experimental results demonstrate superior performance in favor of our method under two extreme settings: localizing an autonomous underwater vehicle and localizing a planetary rover in a Mars-like desert. In addition, our method achieves comparable performance with state-of-the-art methods on the indoor benchmark (7-Scenes dataset) using only 20% training data.

preprint2022arXiv

Block Factor-width-two Matrices and Their Applications to Semidefinite and Sum-of-squares Optimization

Semidefinite and sum-of-squares (SOS) optimization are fundamental computational tools in many areas, including linear and nonlinear systems theory. However, the scale of problems that can be addressed reliably and efficiently is still limited. In this paper, we introduce a new notion of block factor-width-two matrices and build a new hierarchy of inner and outer approximations of the cone of positive semidefinite (PSD) matrices. This notion is a block extension of the standard factor-width-two matrices, and allows for an improved inner-approximation of the PSD cone. In the context of SOS optimization, this leads to a block extension of the scaled diagonally dominant sum-of-squares (SDSOS) polynomials. By varying a matrix partition, the notion of block factor-width-two matrices can balance a trade-off between the computation scalability and solution quality for solving semidefinite and SOS optimization problems. Numerical experiments on a range of large-scale instances confirm our theoretical findings.

preprint2022arXiv

Convex Parameterization of Stabilizing Controllers and its LMI-based Computation via Filtering

Various new implicit parameterizations for stabilizing controllers that allow one to impose structural constraints on the controller have been proposed lately. They are convex but infinite-dimensional, formulated in the frequency domain with no available efficient methods for computation. In this paper, we introduce a kernel version of the Youla parameterization to characterize the set of stabilizing controllers. It features a single affine constraint, which allows us to recast the controller parameterization as a novel robust filtering problem. This makes it possible to derive the first efficient Linear Matrix Inequality (LMI) implicit parametrization of stabilizing controllers. Our LMI characterization not only admits efficient numerical computation, but also guarantees a full-order stabilizing dynamical controller that is efficient for practical deployment. Numerical experiments demonstrate that our LMI can be orders of magnitude faster to solve than the existing closed-loop parameterizations.

preprint2022arXiv

Cooperative Formation of Autonomous Vehicles in Mixed Traffic Flow: Beyond Platooning

Cooperative formation and control of autonomous vehicles (AVs) promise increased efficiency and safety on public roads. In mixed traffic flow consisting of AVs and human-driven vehicles (HDVs), the prevailing platooning of multiple AVs is not the only choice for cooperative formation. In this paper, we investigate how different formations of AVs impact traffic performance from a set-function optimization perspective. We first reveal a stability invariance property and a diminishing improvement property of noncooperative formation when AVs adopt typical Adaptive Cruise Control (ACC) strategies. Then, we focus on the case of cooperative formation where the AV controllers are cooperatively designed %redesign the control strategies of AVs in different formations and investigate the optimal formation of multiple AVs using set-function optimization. Two predominant optimal formations, i.e., uniform distribution and platoon formation, emerge from extensive numerical experiments. Interestingly, platooning might have the least potential to improve traffic performance when HDVs have poor string stability behavior. These results suggest more opportunities for cooperative formation of AVs, beyond platooning, in practical mixed traffic flow.

preprint2022arXiv

Data-Driven Predictive Control for Connected and Autonomous Vehicles in Mixed Traffic

Cooperative control of Connected and Autonomous Vehicles (CAVs) promises great benefits for mixed traffic. Most existing research focuses on model-based control strategies, assuming that car-following dynamics of human-driven vehicles are explicitly known. In this paper, instead of relying on a parametric car-following model, we introduce a data-driven predictive control strategy to achieve safe and optimal control for CAVs in mixed traffic. We first present a linearized dynamical model for mixed traffic systems, and investigate its controllability and observability. Based on these control-theoretic properties, we then propose a novel DeeP-LCC (Data-EnablEd Predictive Leading Cruise Control) strategy for CAVs based on measurable driving data to smooth mixed traffic. Our method is implemented in a receding horizon manner, in which input/output constraints are incorporated to achieve collision-free guarantees. Nonlinear traffic simulations reveal its saving of up to 24.96% fuel consumption during a braking scenario of Extra-Urban Driving Cycle while ensuring safety.

preprint2022arXiv

Escaping High-order Saddles in Policy Optimization for Linear Quadratic Gaussian (LQG) Control

First order policy optimization has been widely used in reinforcement learning. It guarantees to find the optimal policy for the state-feedback linear quadratic regulator (LQR). However, the performance of policy optimization remains unclear for the linear quadratic Gaussian (LQG) control where the LQG cost has spurious suboptimal stationary points. In this paper, we introduce a novel perturbed policy gradient (PGD) method to escape a large class of bad stationary points (including high-order saddles). In particular, based on the specific structure of LQG, we introduce a novel reparameterization procedure which converts the iterate from a high-order saddle to a strict saddle, from which standard random perturbations in PGD can escape efficiently. We further characterize the high-order saddles that can be escaped by our algorithm.

preprint2022arXiv

GIMO: Gaze-Informed Human Motion Prediction in Context

Predicting human motion is critical for assistive robots and AR/VR applications, where the interaction with humans needs to be safe and comfortable. Meanwhile, an accurate prediction depends on understanding both the scene context and human intentions. Even though many works study scene-aware human motion prediction, the latter is largely underexplored due to the lack of ego-centric views that disclose human intent and the limited diversity in motion and scenes. To reduce the gap, we propose a large-scale human motion dataset that delivers high-quality body pose sequences, scene scans, as well as ego-centric views with the eye gaze that serves as a surrogate for inferring human intent. By employing inertial sensors for motion capture, our data collection is not tied to specific scenes, which further boosts the motion dynamics observed from our subjects. We perform an extensive study of the benefits of leveraging the eye gaze for ego-centric human motion prediction with various state-of-the-art architectures. Moreover, to realize the full potential of the gaze, we propose a novel network architecture that enables bidirectional communication between the gaze and motion branches. Our network achieves the top performance in human motion prediction on the proposed dataset, thanks to the intent information from eye gaze and the denoised gaze feature modulated by the motion. Code and data can be found at https://github.com/y-zheng18/GIMO.

preprint2022arXiv

Learning 3D Mineral Prospectivity from 3D Geological Models Using Convolutional Neural Networks: Application to a Structure-controlled Hydrothermal Gold Deposit

The three-dimensional (3D) geological models are the typical and key data source in the 3D mineral prospecitivity modeling. Identifying prospectivity-informative predictor variables from the 3D geological models is a challenging and tedious task. Motivated by the ability of convolutional neural networks (CNNs) to learn the intrinsic features, in this paper, we present a novel method that leverages CNNs to learn 3D mineral prospectivity from the 3D geological models. By exploiting the learning ability of CNNs, the presented method allows for disentangling complex correlation to the mineralization and thus opens a door to circumvent the tedious work for designing the predictor variables. Specifically, to explore the unstructured 3D geological models with the CNNs whose input should be structured, we develop a 2D CNN framework in which the geometry of geological boundary is compiled and reorganized into multi-channel images and fed into the CNN. This ensures an effective and efficient training of CNNs while allowing the prospective model to approximate the ore-forming process. The presented method is applied to a typical structure-controlled hydrothermal deposit, the Dayingezhuang gold deposit, eastern China, in which the presented method was compared with the prospectivity modeling methods using hand-designed predictor variables. The results demonstrate the presented method capacitates a performance boost of the 3D prospectivity modeling and empowers us to decrease work-load and prospecting risk in prediction of deep-seated orebodies.

preprint2022arXiv

System-level, Input-output and New Parameterizations of Stabilizing Controllers, and Their Numerical Computation

It is known that the set of internally stabilizing controller $\mathcal{C}_{\text{stab}}$ is non-convex, but it admits convex characterizations using certain closed-loop maps: a classical result is the Youla parameterization, and two recent notions are the system-level parameterization (SLP) and the input-output parameterization (IOP). In this paper, we address the existence of new convex parameterizations and discuss potential tradeoffs of each parametrization in different scenarios. Our main contributions are: 1) We reveal that only four groups of stable closed-loop transfer matrices are equivalent to internal stability: one of them is used in the SLP, another one is used in the IOP, and the other two are new, leading to two new convex parameterizations of $\mathcal{C}_{\text{stab}}$. 2) We investigate the properties of these parameterizations after imposing the finite impulse response (FIR) approximation, revealing that the IOP has the best ability of approximating $\mathcal{C}_{\text{stab}}$ given FIR constraints. 3) These four parameterizations require no \emph{a priori} doubly-coprime factorization of the plant, but impose a set of equality constraints. However, these equality constraints will never be satisfied exactly in floating-point arithmetic computation and/or implementation. We prove that the IOP is numerically robust for open-loop stable plants, in the sense that small mismatches in the equality constraints do not compromise the closed-loop stability; but a direct IOP implementation will fail to stabilize open-loop unstable systems in practice. The SLP is known to enjoy numerical robustness in the state feedback case; here, we show that numerical robustness of the four-block SLP controller requires case-by-case analysis even the plant is open-loop stable.

preprint2021arXiv

Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control

This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: 1) connectivity of the set of stabilizing controllers $\mathcal{C}_n$; and 2) structure of stationary points. It is known that similarity transformations do not change the input-output behavior of a dynamical controller or LQG cost. This inherent symmetry by similarity transformations makes the landscape of LQG very rich. We show that 1) the set of stabilizing controllers $\mathcal{C}_n$ has at most two path-connected components and they are diffeomorphic under a mapping defined by a similarity transformation; 2) there might exist many \emph{strictly suboptimal stationary points} of the LQG cost function over $\mathcal{C}_n$ and these stationary points are always \emph{non-minimal}; 3) all \emph{minimal} stationary points are globally optimal and they are identical up to a similarity transformation. These results shed some light on the performance analysis of direct policy gradient methods for solving the LQG problem.

preprint2021arXiv

Decomposed Structured Subsets for Semidefinite and Sum-of-Squares Optimization

Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of matrix variables and the number of constraints increases. To improve scalability, SDPs can be approximated with lower and upper bounds through the use of structured subsets (e.g., diagonally-dominant and scaled-diagonally dominant matrices). Meanwhile, any underlying sparsity or symmetry structure may be leveraged to form an equivalent SDP with smaller positive semidefinite constraints. In this paper, we present a notion of decomposed structured subsets}to approximate an SDP with structured subsets after an equivalent conversion. The lower/upper bounds found by approximation after conversion become tighter than the bounds obtained by approximating the original SDP directly. We apply decomposed structured subsets to semidefinite and sum-of-squares optimization problems with examples of H-infinity norm estimation and constrained polynomial optimization. An existing basis pursuit method is adapted into this framework to iteratively refine bounds.

preprint2021arXiv

Leading Cruise Control in Mixed Traffic Flow: System Modeling, Controllability, and String Stability

Connected and autonomous vehicles (CAVs) have great potential to improve road transportation systems. Most existing strategies for CAVs&#39; longitudinal control focus on downstream traffic conditions, but neglect the impact of CAVs&#39; behaviors on upstream traffic flow. In this paper, we introduce a notion of Leading Cruise Control (LCC), in which the CAV maintains car-following operations adapting to the states of its preceding vehicles, and also aims to lead the motion of its following vehicles. Specifically, by controlling the CAV, LCC aims to attenuate downstream traffic perturbations and smooth upstream traffic flow actively. We first present the dynamical modeling of LCC, with a focus on three fundamental scenarios: car-following, free-driving, and Connected Cruise Control. Then, the analysis of controllability, observability, and head-to-tail string stability reveals the feasibility and potential of LCC in improving mixed traffic flow performance. Extensive numerical studies validate that the capability of CAVs in dissipating traffic perturbations is further strengthened when incorporating the information of the vehicles behind into the CAV&#39;s control.

preprint2020arXiv

An Input-Output Parametrization of Stabilizing Controllers: amidst Youla and System Level Synthesis

This paper proposes a novel input-output parametrization of the set of internally stabilizing output-feedback controllers for linear time-invariant (LTI) systems. Our underlying idea is to directly treat the closed-loop transfer matrices from disturbances to input and output signals as design parameters and exploit their affine relationships. This input-output perspective is particularly effective when a doubly-coprime factorization is difficult to compute, or an initial stabilizing controller is challenging to find; most previous work requires one of these pre-computation steps. Instead, our approach can bypass such pre-computations, in the sense that a stabilizing controller is computed by directly solving a linear program (LP). Furthermore, we show that the proposed input-output parametrization allows for computing norm-optimal controllers subject to quadratically invariant (QI) constraints using convex programming.

preprint2020arXiv

Automatic removal of false image stars in disk-resolved images of the Cassini Imaging Science Subsystem

Taking a large amount of images, the Cassini Imaging Science Subsystem (ISS) has been routinely used in astrometry. In ISS images, disk-resolved objects often lead to false detection of stars that disturb the camera pointing correction. The aim of this study was to develop an automated processing method to remove the false image stars in disk-resolved objects in ISS images. The method included the following steps: extracting edges, segmenting boundary arcs, fitting circles and excluding false image stars. The proposed method was tested using 200 ISS images. Preliminary experimental results show that it can remove the false image stars in more than 95% of ISS images with disk-resolved objects in a fully automatic manner, i.e. outperforming the traditional circle detection based on Circular Hough Transform (CHT) by 17%. In addition, its speed is more than twice as fast as that of the CHT method. It is also more robust (no manual parameter tuning is needed) when compared with CHT. The proposed method was also applied to a set of ISS images of Rhea to eliminate the mismatch in pointing correction in automatic procedure. Experiment results showed that the precision of final astrometry results can be improve by roughly 2 times than that of automatic procedure without the method. It proved that the proposed method is helpful in the astrometry of ISS images in fully automatic manner.

preprint2020arXiv

BI-MAML: Balanced Incremental Approach for Meta Learning

We present a novel Balanced Incremental Model Agnostic Meta Learning system (BI-MAML) for learning multiple tasks. Our method implements a meta-update rule to incrementally adapt its model to new tasks without forgetting old tasks. Such a capability is not possible in current state-of-the-art MAML approaches. These methods effectively adapt to new tasks, however, suffer from &#39;catastrophic forgetting&#39; phenomena, in which new tasks that are streamed into the model degrade the performance of the model on previously learned tasks. Our system performs the meta-updates with only a few-shots and can successfully accomplish them. Our key idea for achieving this is the design of balanced learning strategy for the baseline model. The strategy sets the baseline model to perform equally well on various tasks and incorporates time efficiency. The balanced learning strategy enables BI-MAML to both outperform other state-of-the-art models in terms of classification accuracy for existing tasks and also accomplish efficient adaption to similar new tasks with less required shots. We evaluate BI-MAML by conducting comparisons on two common benchmark datasets with multiple number of image classification tasks. BI-MAML performance demonstrates advantages in both accuracy and efficiency.

preprint2020arXiv

Controllability Analysis and Optimal Control of Mixed Traffic Flow with Human-driven and Autonomous Vehicles

Connected and automated vehicles (CAVs) have a great potential to improve traffic efficiency in mixed traffic systems, which has been demonstrated by multiple numerical simulations and field experiments. However, some fundamental properties of mixed traffic flow, including controllability and stabilizability, have not been well understood. This paper analyzes the controllability of mixed traffic systems and designs a system-level optimal control strategy. Using the Popov-Belevitch-Hautus (PBH) criterion, we prove for the first time that a ring-road mixed traffic system with one CAV and multiple heterogeneous human-driven vehicles is not completely controllable, but is stabilizable under a very mild condition. Then, we formulate the design of a system-level control strategy for the CAV as a structured optimal control problem, where the CAV&#39;s communication ability is explicitly considered. Finally, we derive an upper bound for reachable traffic velocity via controlling the CAV. Extensive numerical experiments verify the effectiveness of our analytical results and the proposed control strategy. Our results validate the possibility of utilizing CAVs as mobile actuators to smooth traffic flow actively.

preprint2020arXiv

Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis, simulations and inverse method

A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non=invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use.

preprint2020arXiv

Impact of Disturbances on Mixed Traffic Control with Autonomous Vehicles

This paper investigates the impact of disturbances on controlling an autonomous vehicle to smooth mixed traffic flow in a ring road setup. By exploiting the ring structure of this system, it is shown that velocity perturbations impacting any vehicle on the ring enter an uncontrollable and marginally stable mode defined by the sum of relative vehicle spacings. These disturbances are then integrated up by the system and cannot be unwound via controlling the autonomous vehicle. In particular, if the velocity disturbances are zero-mean Gaussians, then the traffic flow on the ring will undergo a random walk with the variance growing indefinitely and independently of the control policy applied. In contrast, the impact of acceleration disturbances is benign as these disturbances do no enter the uncontrollable mode, meaning that they can be easily regulated using the autonomous vehicle. Our results support and complement the existing theoretic analysis and field experiments.

preprint2020arXiv

MNEW: Multi-domain Neighborhood Embedding and Weighting for Sparse Point Clouds Segmentation

Point clouds have been widely adopted in 3D semantic scene understanding. However, point clouds for typical tasks such as 3D shape segmentation or indoor scenario parsing are much denser than outdoor LiDAR sweeps for the application of autonomous driving perception. Due to the spatial property disparity, many successful methods designed for dense point clouds behave depreciated effectiveness on the sparse data. In this paper, we focus on the semantic segmentation task of sparse outdoor point clouds. We propose a new method called MNEW, including multi-domain neighborhood embedding, and attention weighting based on their geometry distance, feature similarity, and neighborhood sparsity. The network architecture inherits PointNet which directly process point clouds to capture pointwise details and global semantics, and is improved by involving multi-scale local neighborhoods in static geometry domain and dynamic feature space. The distance/similarity attention and sparsity-adapted weighting mechanism of MNEW enable its capability for a wide range of data sparsity distribution. With experiments conducted on virtual and real KITTI semantic datasets, MNEW achieves the top performance for sparse point clouds, which is important to the application of LiDAR-based automated driving perception.

preprint2020arXiv

Smoothing Traffic Flow via Control of Autonomous Vehicles

The emergence of autonomous vehicles is expected to revolutionize road transportation in the near future. Although large-scale numerical simulations and small-scale experiments have shown promising results, a comprehensive theoretical understanding to smooth traffic flow via autonomous vehicles is lacking. In this paper, from a control-theoretic perspective, we establish analytical results on the controllability, stabilizability, and reachability of a mixed traffic system consisting of human-driven vehicles and autonomous vehicles in a ring road. We show that the mixed traffic system is not completely controllable, but is stabilizable, indicating that autonomous vehicles can not only suppress unstable traffic waves but also guide the traffic flow to a higher speed. Accordingly, we establish the maximum traffic speed achievable via controlling autonomous vehicles. Numerical results show that the traffic speed can be increased by over 6% when there are only 5% autonomous vehicles. We also design an optimal control strategy for autonomous vehicles to actively dampen undesirable perturbations. These theoretical findings validate the high potential of autonomous vehicles to smooth traffic flow.

preprint2020arXiv

Sparsity Invariance for Convex Design of Distributed Controllers

We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure. This problem is NP-hard in general and motivates the development of tractable approximations. We characterize a class of convex restrictions based on a new notion of Sparsity Invariance (SI). The underlying idea of SI is to design sparsity patterns for transfer matrices Y(s) and X(s) such that any corresponding controller K(s)=Y(s)X(s)^-1 exhibits the desired sparsity pattern. For sparsity constraints, the approach of SI goes beyond the notion of Quadratic Invariance (QI): 1) the SI approach always yields a convex restriction; 2) the solution via the SI approach is guaranteed to be globally optimal when QI holds and performs at least as well as considering a nearest QI subset. Moreover, the notion of SI naturally applies to designing structured static controllers, while QI is not utilizable. Numerical examples show that even for non-QI cases, SI can recover solutions that are 1) globally optimal and 2) strictly more performing than previous methods.

preprint2019arXiv

Chordal decomposition in operator-splitting methods for sparse semidefinite programs

We employ chordal decomposition to reformulate a large and sparse semidefinite program (SDP), either in primal or dual standard form, into an equivalent SDP with smaller positive semidefinite (PSD) constraints. In contrast to previous approaches, the decomposed SDP is suitable for the application of first-order operator-splitting methods, enabling the development of efficient and scalable algorithms. In particular, we apply the alternating direction method of multipliers (ADMM) to solve decomposed primal- and dual-standard-form SDPs. Each iteration of such ADMM algorithms requires a projection onto an affine subspace, and a set of projections onto small PSD cones that can be computed in parallel. We also formulate the homogeneous self-dual embedding (HSDE) of a primal-dual pair of decomposed SDPs, and extend a recent ADMM-based algorithm to exploit the structure of our HSDE. The resulting HSDE algorithm has the same leading-order computational cost as those for the primal or dual problems only, with the advantage of being able to identify infeasible problems and produce an infeasibility certificate. All algorithms are implemented in the open-source MATLAB solver CDCS. Numerical experiments on a range of large-scale SDPs demonstrate the computational advantages of the proposed methods compared to common state-of-the-art solvers.

preprint2019arXiv

Chordal Decomposition in Rank Minimized Semidefinite Programs with Applications to Subspace Clustering

Semidefinite programs (SDPs) often arise in relaxations of some NP-hard problems, and if the solution of the SDP obeys certain rank constraints, the relaxation will be tight. Decomposition methods based on chordal sparsity have already been applied to speed up the solution of sparse SDPs, but methods for dealing with rank constraints are underdeveloped. This paper leverages a minimum rank completion result to decompose the rank constraint on a single large matrix into multiple rank constraints on a set of smaller matrices. The re-weighted heuristic is used as a proxy for rank, and the specific form of the heuristic preserves the sparsity pattern between iterations. Implementations of rank-minimized SDPs through interior-point and first-order algorithms are discussed. The problem of subspace clustering is used to demonstrate the computational improvement of the proposed method.

preprint2019arXiv

Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of multipliers (ADMM). We first apply a classical parameterization technique to restrict the optimal decentralized control into a convex problem that inherits the sparsity pattern of the original problem. The parameterization relies on a notion of strongly decentralized stabilization, and sufficient conditions are discussed to guarantee this notion. Then, chordal decomposition allows us to decompose the convex restriction into a problem with partially coupled constraints, and the framework of ADMM enables us to solve the decomposed problem in a distributed fashion. Consequently, the subsystems only need to share their model data with their direct neighbours, not needing a central computation. Numerical experiments demonstrate the effectiveness of the proposed method.

preprint2019arXiv

On the Equivalence of Youla, System-level and Input-output Parameterizations

A convex parameterization of internally stabilizing controllers is fundamental for many controller synthesis procedures. The celebrated Youla parameterization relies on a doubly-coprime factorization of the system, while the recent system-level and input-output characterizations require no doubly-coprime factorization but a set of equality constraints for achievable closed-loop responses. In this paper, we present explicit affine mappings among Youla, system-level and input-output parameterizations. Two direct implications of the affine mappings are 1) any convex problem in Youla, system level, or input-output parameters can be equivalently and convexly formulated in any other one of these frameworks, including the convex system-level synthesis (SLS); 2) the condition of quadratic invariance (QI) is sufficient and necessary for the classical distributed control problem to admit an equivalent convex reformulation in terms of Youla, system-level, or input-output parameters.

preprint2019arXiv

On the Existence of Block-Diagonal Solutions to Lyapunov and $\mathcal{H}_{\infty}$ Riccati Inequalities

In this paper, we describe sufficient conditions when block-diagonal solutions to Lyapunov and $\mathcal{H}_{\infty}$ Riccati inequalities exist. In order to derive our results, we define a new type of comparison systems, which are positive and are computed using the state-space matrices of the original (possibly nonpositive) systems. Computing the comparison system involves only the calculation of $\mathcal{H}_{\infty}$ norms of its subsystems. We show that the stability of this comparison system implies the existence of block-diagonal solutions to Lyapunov and Riccati inequalities. Furthermore, our proof is constructive and the overall framework allows the computation of block-diagonal solutions to these matrix inequalities with linear algebra and linear programming. Numerical examples illustrate our theoretical results.

preprint2018arXiv

Decomposition and Completion of Sum-of-Squares Matrices

This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices that are nonzero only on a principal submatrix. Also, the completion of an SOS matrix is equivalent to a set of SOS conditions on its principal submatrices and a consistency condition on the Gram representation of the principal submatrices. These results are partial extensions of chordal decomposition and completion of scalar matrices to matrices with polynomial entries. We apply the SOS decomposition result to exploit sparsity in matrix-valued SOS programs. Numerical results demonstrate the high potential of this approach for solving large-scale sparse matrix-valued SOS programs.

preprint2018arXiv

Fast ADMM for sum-of-squares programs using partial orthogonality

When sum-of-squares (SOS) programs are recast as semidefinite programs (SDPs) using the standard monomial basis, the constraint matrices in the SDP possess a structural property that we call \emph{partial orthogonality}. In this paper, we leverage partial orthogonality to develop a fast first-order method, based on the alternating direction method of multipliers (ADMM), for the solution of the homogeneous self-dual embedding of SDPs describing SOS programs. Precisely, we show how a &#34;diagonal plus low rank&#34; structure implied by partial orthogonality can be exploited to project efficiently the iterates of a recent ADMM algorithm for generic conic programs onto the set defined by the affine constraints of the SDP. The resulting algorithm, implemented as a new package in the solver CDCS, is tested on a range of large-scale SOS programs arising from constrained polynomial optimization problems and from Lyapunov stability analysis of polynomial dynamical systems. These numerical experiments demonstrate the effectiveness of our approach compared to common state-of-the-art solvers.

preprint2018arXiv

Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials

Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control. We investigate the relation between three tractable relaxations for optimizing over sparse non-negative polynomials: sparse sum-of-squares (SSOS) optimization, diagonally dominant sum-of-squares (DSOS) optimization, and scaled diagonally dominant sum-of-squares (SDSOS) optimization. We prove that the set of SSOS polynomials, an inner approximation of the cone of SOS polynomials, strictly contains the spaces of sparse DSOS/SDSOS polynomials. When applicable, therefore, SSOS optimization is less conservative than its DSOS/SDSOS counterparts. Numerical results for large-scale sparse polynomial optimization problems demonstrate this fact, and also that SSOS optimization can be faster than DSOS/SDSOS methods despite requiring the solution of semidefinite programs instead of less expensive linear/second-order cone programs.

preprint2017arXiv

Fast ADMM for Semidefinite Programs with Chordal Sparsity

Many problems in control theory can be formulated as semidefinite programs (SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity to improve the scalability. This paper develops efficient first-order methods to solve SDPs with chordal sparsity based on the alternating direction method of multipliers (ADMM). We show that chordal decomposition can be applied to either the primal or the dual standard form of a sparse SDP, resulting in scaled versions of ADMM algorithms with the same computational cost. Each iteration of our algorithms consists of a projection on the product of small positive semidefinite cones, followed by a projection on an affine set, both of which can be carried out efficiently. Our techniques are implemented in CDCS, an open source add-on to MATLAB. Numerical experiments on large-scale sparse problems in SDPLIB and random SDPs with block-arrow sparse patterns show speedups compared to some common state-of-the-art software packages.

preprint2017arXiv

Platooning of Connected Vehicles with Undirected Topologies: Robustness Analysis and Distributed H-infinity Controller Synthesis

This paper considers the robustness analysis and distributed $\mathcal{H}_{\infty}$ (H-infinity) controller synthesis for a platoon of connected vehicles with undirected topologies. We first formulate a unified model to describe the collective behavior of homogeneous platoons with external disturbances using graph theory. By exploiting the spectral decomposition of a symmetric matrix, the collective dynamics of a platoon is equivalently decomposed into a set of subsystems sharing the same size with one single vehicle. Then, we provide an explicit scaling trend of robustness measure $γ$-gain, and introduce a scalable multi-step procedure to synthesize a distributed $\mathcal{H}_{\infty}$ controller for large-scale platoons. It is shown that communication topology, especially the leader&#39;s information, exerts great influence on both robustness performance and controller synthesis. Further, an intuitive optimization problem is formulated to optimize an undirected topology for a platoon system, and the upper and lower bounds of the objective are explicitly analyzed, which hints us that coordination of multiple mini-platoons is one reasonable architecture to control large-scale platoons. Numerical simulations are conducted to illustrate our findings.