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Hongchao Zhang

Hongchao Zhang appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.OCastro-ph.COeess.SYMachine LearningArtificial Intelligencegr-qcLogic in Computer ScienceSystems and Control

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Published work

9 published item(s)

preprint2026arXiv

k-Inductive Neural Barrier Certificates for Unknown Nonlinear Dynamics

While conventional (k=1) discrete-time barrier certificate conditions impose strict safety constraints by requiring the function to be non-increasing at every step, k-inductive barrier certificates relax this by allowing a temporary increase -- up to k-1 times, each within a threshold $ε$ -- while maintaining overall safety, and improving flexibility. This paper leverages neural networks and constructs k-inductive neural barrier certificates (k-NBCs) for (partially) unknown nonlinear systems. While neural networks offer scalability in the design process, they lack formal guarantees, requiring additional approaches such as counterexample-guided inductive synthesis (CEGIS) with satisfiability modulo theories (SMT) for verification. However, the CEGIS-SMT framework requires knowledge of system dynamics, which is unavailable in practical settings. To address this, we leverage the generalization of the Willems et al.'s fundamental lemma, using a single state trajectory, to construct a data-driven representation of (partially) unknown models for SMT verification without sacrificing accuracy. Additionally, CEGIS-SMT further removes the constraint of restricting barrier certificates to specific function classes, such as sum-of-squares, enabling greater flexibility in their design. We validate our approach on three nonlinear case studies with (partially) unknown dynamics.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Barrier Certificate based Safe Control for LiDAR-based Systems under Sensor Faults and Attacks

Autonomous Cyber-Physical Systems (CPS) fuse proprioceptive sensors such as GPS and exteroceptive sensors including Light Detection and Ranging (LiDAR) and cameras for state estimation and environmental observation. It has been shown that both types of sensors can be compromised by malicious attacks, leading to unacceptable safety violations. We study the problem of safety-critical control of a LiDAR-based system under sensor faults and attacks. We propose a framework consisting of fault tolerant estimation and fault tolerant control. The former reconstructs a LiDAR scan with state estimations, and excludes the possible faulty estimations that are not aligned with LiDAR measurements. We also verify the correctness of LiDAR scans by comparing them with the reconstructed ones and removing the possibly compromised sector in the scan. Fault tolerant control computes a control signal with the remaining estimations at each time step. We prove that the synthesized control input guarantees system safety using control barrier certificates. We validate our proposed framework using a UAV delivery system in an urban environment. We show that our proposed approach guarantees safety for the UAV whereas a baseline fails.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Testing the effect of $H_0$ on $fσ_8$ tension using a Gaussian Process method

Using the $fσ_8(z)$ redshift space distortion (RSD) data, the $σ_8^0-Ω_m^0$ tension is studied utilizing a parameterization of growth rate $f(z) = Ω_m(z)^γ$. Here, $f(z)$ is derived from the expansion history $H(z)$ which is reconstructed from the observational Hubble data applying the Gaussian Process method. It is found that different priors of $H_0$ have great influences on the evolution curve of $H(z)$ and the constraint of $σ_8^0-Ω_m^0$. When using a larger $H_0$ prior, the low redshifts $H(z)$ deviate significantly from that of the $Λ$CDM model, which indicates that a dark energy model different from the cosmological constant can help to relax the $H_0$ tension problem. The tension between our best-fit values of $σ_8^0-Ω_m^0$ and that of the \textit{Planck} 2018 $Λ$CDM (PLA) will disappear (less than $1σ$) when taking a prior for $H_0$ obtained from PLA. Moreover, the tension exceeds $2σ$ level when applying the prior $H_0 = 73.52 \pm 1.62$ km/s/Mpc resulted from the Hubble Space Telescope photometry. By comparing the $S_8 -Ω_m^0$ planes of our method with the results from KV450+DES-Y1, we find that using our method and applying the RSD data may be helpful to break the parameter degeneracies.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On the acceleration of the Barzilai-Borwein method

The Barzilai-Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to the modest accuracy and has a great advantage of being easily extended to solve a wide class of constrained optimization problems. In this paper, we propose a new stepsize to accelerate the BB method by requiring finite termination for minimizing two-dimensional strongly convex quadratic function. Combing with this new stepsize, we develop gradient methods which adaptively take the nonmonotone BB stepsizes and certain monotone stepsizes for minimizing general strongly convex quadratic function. Furthermore, by incorporating nonmonotone line searches and gradient projection techniques, we extend these new gradient methods to solve general smooth unconstrained and bound constrained optimization. Extensive numerical experiments show that our strategies of properly inserting monotone gradient steps into the nonmonotone BB method could significantly improve its performance and the new resulted methods can outperform the most successful gradient decent methods developed in the recent literature.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

An Active Set Algorithm for Nonlinear Optimization with Polyhedral Constraints

A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Distinguish three time-dependent dark energy models using statefinder pairs with error bars and Bayesian evidence

In this work, two completely different approaches, statefinder with error bars and Bayesian evidence, are used to distinguish and judge three time-dependent dark energy models. The parameters constrain for the three dark energy models are given using the current cosmic observational data sets : $Planck$ 2015, SNIa, BAO and OHD. Using the statefinder pairs with error bars, we find that the error region of the dark energy model, whose equation of state parameter is given by $w(a) = w_0+w_3\frac{1-a}{a^2+(1-a)^2}$, is relativity compact than the other two models during the all the evolving history. Meanwhile, the Bayesian evidence also provide that this model is significantly better than the other two models and the other two models are inconclusive. Then, there are reasons for believing that this model is a preferential candidate in dark energy investigation rather than the other two.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Inexact alternating direction multiplier methods for separable convex optimization

Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach involves linearized subproblems, a back substitution step, and either gradient or accelerated gradient techniques. Global convergence is established. The methods are particularly useful when the ADMM subproblems do not have closed form solution or when the solution of the subproblems is expensive. Numerical experiments based on image reconstruction problems show the effectiveness of the proposed methods.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Generalized Uniformly Optimal Methods for Nonlinear Programming

In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search step (gradient descent or Quasi-Newton iteration) into these uniformly optimal convex programming methods, and then enforce a monotone decreasing property of the function values computed along the trajectory. Algorithms of these types will then achieve the best known complexity for nonconvex problems, and the optimal complexity for convex ones without requiring any problem parameters. As a consequence, we can have a unified treatment for a general class of nonlinear programming problems regardless of their convexity and smoothness level. In particular, we show that the accelerated gradient and level methods, both originally designed for solving convex optimization problems only, can be used for solving both convex and nonconvex problems uniformly. In a similar vein, we show that some well-studied techniques for nonlinear programming, e.g., Quasi-Newton iteration, can be embedded into optimal convex optimization algorithms to possibly further enhance their numerical performance. Our theoretical and algorithmic developments are complemented by some promising numerical results obtained for solving a few important nonconvex and nonlinear data analysis problems in the literature.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization

This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but convex) component. In order to solve these problems, we propose a randomized stochastic projected gradient (RSPG) algorithm, in which proper mini-batch of samples are taken at each iteration depending on the total budget of stochastic samples allowed. The RSPG algorithm also employs a general distance function to allow taking advantage of the geometry of the feasible region. Complexity of this algorithm is established in a unified setting, which shows nearly optimal complexity of the algorithm for convex stochastic programming. A post-optimization phase is also proposed to significantly reduce the variance of the solutions returned by the algorithm. In addition, based on the RSPG algorithm, a stochastic gradient free algorithm, which only uses the stochastic zeroth-order information, has been also discussed. Some preliminary numerical results are also provided.

0 citations0 reviewsNo code linkedOpen access