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Systems and Control

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preprint2016arXiv

Optimal control for a robotic exploration, pick-up and delivery problem

This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or drop-off of an object. The objects are modeled by point masses with a-priori unknown locations in a bounded two-dimensional space that may contain unknown obstacles. For this hybrid system, an Optimal Control Problem (OCP) is approximately solved by a receding horizon scheme, where the derived lower bound for the cost-to-go is evaluated for the worst and for a probabilistic case, assuming a uniform distribution of the objects. First, a time-driven approximate solution based on time and position space discretization and mixed integer programming is presented. Due to the high computational cost of this solution, an alternative event-driven approximate approach based on a suitable motion parameterization and gradient-based optimization is proposed. The solutions are compared in a numerical example, suggesting that the latter approach offers a significant computational advantage while yielding similar qualitative results compared to the former. The methods are particularly relevant for various robotic applications like automated cleaning, search and rescue, harvesting or manufacturing.

preprint2015arXiv

Global results on reset-induced periodic trajectories of planar systems

We study the existence of asymptotically stable periodic trajectories induced by reset feedback. The analysis is developed for a planar system. Casting the problem into the hybrid setting, we show that a periodic orbit arises from the balance between the energy dissipated during flows and the energy restored by resets, at jumps. The stability of the periodic orbit is studied with hybrid Lyapunov tools. The satisfaction of the so-called hybrid basic conditions ensures the robustness of the asymptotic stability. Extensions of the approach to more general mechanical systems are discussed.

preprint2016arXiv

Model-based versus model-free control designs for improving microalgae growth in a closed photobioreactor: Some preliminary comparisons

Controlling microalgae cultivation, i.e., a crucial industrial topic today, is a challenging task since the corresponding modeling is complex, highly uncertain and time-varying. A model-free control setting is therefore introduced in order to ensure a high growth of microalgae in a continuous closed photobioreactor. Computer simulations are displayed in order to compare this design to an input-output feedback linearizing control strategy, which is widely used in the academic literature on photobioreactors. They assess the superiority of the model-free standpoint both in terms of performances and implementation simplicity.

preprint2018arXiv

On Redundant Observability: From Security Index to Attack Detection and Resilient State Estimation

The security of control systems under sensor attacks is investigated. Redundant observability is introduced, explaining existing security notions including the security index, attack detectability, and observability under attacks. Equivalent conditions between redundant observability and existing notions are presented. Based on a bank of partial observers utilizing Kalman decomposition and a decoder exploiting redundancy, an estimator design algorithm is proposed enhancing the resilience of control systems. This scheme substantially improves computational efficiency utilizing far less memory.

preprint2016arXiv

A Stochastic Global Identification Framework for Aerospace Vehicles Operating Under Varying Flight States

In this work, a novel data-based stochastic global identification framework is introduced for air vehicles operating under varying flight states and uncertainty. In this context, the term global refers to the identification of a model that is capable of representing the system dynamics under any admissible flight state based on data recorded from sample states. The proposed framework is based on stochastic time-series models for representing the system dynamics and aeroelastic response under multiple flight states, with each state characterized by several variables, such as the airspeed and angle of attack, forming a flight state vector. The method's cornerstone lies in the new class of Vector-dependent Functionally Pooled (VFP) models which allow the explicit analytical inclusion of the flight state vector into the model parameters and, hence, system dynamics. The experimental evaluation is based on a prototype bio-inspired self-sensing composite wing that is subjected to a series of wind tunnel experiments. Distributed micro-sensors in the form of stretchable sensor networks are embedded in the composite layup of the wing to provide the sensing capabilities. Data collected from piezoelectric sensors are employed for the identification of a stochastic global VFP model. The estimated VFP model parameters constitute two-dimensional functions of the flight state vector defined by the airspeed and angle of attack. The identified model is able to successfully represent the aeroelastic response of the wing under the admissible flight states via a minimum number of estimated parameters compared to standard identification approaches. The obtained results demonstrate the high accuracy and effectiveness of the proposed global identification framework, thus constituting a first step towards the next generation of fly-by-feel aerospace vehicles with state awareness capabilities.

preprint2018arXiv

On stochastic imitation dynamics in large-scale networks

We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game structure: they only know their own current utility and the one of neighbor players contacted through pairwise interactions in a network. In response to this information, players update their state according to some stochastic rules. For potential population games and complete interaction networks, we prove convergence and long-lasting permanence close to the evolutionary stable strategies of the game. These results refine and extend the ones known for deterministic imitation dynamics as they account for new emerging behaviors including meta-stability of the equilibria. Finally, we discuss extensions of our results beyond the fully mixed case, studying imitation dynamics where agents interact on complex communication networks.

preprint2018arXiv

Deux améliorations concurrentes des PID

In today's literature "Model-Free Control," or MFC, and "Active Disturbance Rejection Control," or ADRC, are the most prominent approaches in order to keep the benefits of PID controllers, that are so popular in the industrial world, and in the same time for attenuating their severe shortcomings. After a brief review of MFC and ADRC, several examples show the superiority of MFC, which permits to tackle most easily a much wider class of systems.

preprint2017arXiv

On imitation dynamics in potential population games

Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics - that encompass the replicator equation as well as other models previously considered in evolutionary biology - players have no global information about the game structure, and all they know is their own current utility and the one of fellow players contacted through pairwise interactions. For potential population games, global asymptotic stability of the set of Nash equilibria of the sub-game restricted to the support of the initial population configuration is proved. These results strengthen (from local to global asymptotic stability) existing ones and generalize them to a broader class of dynamics. The developed techniques highlight a certain structure of the problem and suggest possible generalizations from the fully mixed population case to imitation dynamics whereby agents interact on complex communication networks.

preprint2017arXiv

Transitivity of Commutativity for Linear Time-Varying Analog Systems

In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and without initial conditions. On the base of impulse response function, transitivity of commutation property is formulated for any triplet of commutative linear time-varying relaxed systems. Transitivity proves are given for some special combinations of first and second-order linear time-varying systems which are initially relaxed.

preprint2018arXiv

Detection of Sensor Attack and Resilient State Estimation for Uniformly Observable Nonlinear Systems having Redundant Sensors

This paper presents a detection algorithm for sensor attacks and a resilient state estimation scheme for a class of uniformly observable nonlinear systems. An adversary is supposed to corrupt a subset of sensors with the possibly unbounded signals, while the system has sensor redundancy. We design an individual high-gain observer for each measurement output so that only the observable portion of the system state is obtained. Then, a nonlinear error correcting problem is solved by collecting all the information from those partial observers and exploiting redundancy. A computationally efficient, on-line monitoring scheme is presented for attack detection. Based on the attack detection scheme, an algorithm for resilient state estimation is provided. The simulation results demonstrate the effectiveness of the proposed algorithm.

preprint2019arXiv

Contingency Model Predictive Control for Automated Vehicles

We present Contingency Model Predictive Control (CMPC), a novel and implementable control framework which tracks a desired path while simultaneously maintaining a contingency plan -- an alternate trajectory to avert an identified potential emergency. In this way, CMPC anticipates events that might take place, instead of reacting when emergencies occur. We accomplish this by adding an additional prediction horizon in parallel to the classical receding MPC horizon. The contingency horizon is constrained to maintain a feasible avoidance solution; as such, CMPC is selectively robust to this emergency while tracking the desired path as closely as possible. After defining the framework mathematically, we demonstrate its effectiveness experimentally by comparing its performance to a state-of-the-art deterministic MPC. The controllers drive an automated research platform through a left-hand turn which may be covered by ice. Contingency MPC prepares for the potential loss of friction by purposefully and intuitively deviating from the prescribed path to approach the turn more conservatively; this deviation significantly mitigates the consequence of encountering ice.

preprint2018arXiv

On Structural Controllability of Symmetric (Brain) Networks

The question of controllability of natural and man-made network systems has recently received considerable attention. In the context of the human brain, the study of controllability may not only shed light into the organization and function of different neural circuits, but also inform the design and implementation of minimally invasive yet effective intervention protocols to treat neurological disorders. While the characterization of brain controllability is still in its infancy, some results have recently appeared and given rise to scientific debate. Among these, [1] has numerically shown that a class of brain networks constructed from DSI/DTI imaging data are controllable from one brain region. That is, a single brain region is theoretically capable of moving the whole brain network towards any desired target state. In this note we provide evidence supporting controllability of brain networks from a single region as discussed in [1], thus contradicting the main conclusion and methods developed in [2].

preprint2019arXiv

A Hybrid Controller for Obstacle Avoidance in an n-dimensional Euclidean Space

For a vehicle moving in an $n$-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded spherical region. The proposed hybrid control algorithm switches between two modes of operation: stabilization (motion-to-goal) and avoidance (boundary-following). The geometric construction of the flow and jump sets of the hybrid controller, exploiting a hysteresis region, guarantees robust switching (chattering-free) between the stabilization and avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for a 3-dimensional scenario.

preprint2019arXiv

Bullwhip effect attenuation in supply chain management via control-theoretic tools and short-term forecasts: A preliminary study with an application to perishable inventories

Supply chain management and inventory control provide most exciting examples of control systems with delays. Here, Smith predictors, model-free control and new time series forecasting techniques are mixed in order to derive an efficient control synthesis. Perishable inventories are also taken into account. The most intriguing "bullwhip effect" is explained and attenuated, at least in some important situations. Numerous convincing computer simulations are presented and discussed.

preprint2019arXiv

An Adaptive Groundtrack Maintenance Scheme for Spacecraft with Electric Propulsion

In this paper, the repeat-groundtrack orbit maintenance problem is addressed for spacecraft driven by electric propulsion. An adaptive solution is proposed, which combines an hysteresis controller and a recursive least squares filter. The controller provides a pulse-width modulated command to the thruster, in compliance with the peculiarities of the electric propulsion technology. The filter takes care of estimating a set of environmental disturbance parameters, from inertial position and velocity measurements. The resulting control scheme is able to compensate for the groundtrack drift due to atmospheric drag, in a fully autonomous manner. A numerical study of a low Earth orbit mission confirms the effectiveness of the proposed method.

preprint2019arXiv

A Scalable Max-Consensus Protocol For Noisy Ultra-Dense Networks

We introduce \emph{ScalableMax}, a novel communication scheme for achieving max-consensus in a network of multiple agents which harnesses the interference in the wireless channel as well as its multicast capabilities. In a sufficiently dense network, the amount of communication resources required grows logarithmically with the number of nodes, while in state-of-the-art approaches, this growth is at least linear. ScalableMax can handle additive noise and works well in a high SNR regime. For medium and low SNR, we propose the \emph{ScalableMax-EC} scheme, which extends the ideas of ScalableMax by introducing a novel error correction scheme. It achieves lower error rates at the cost of using more channel resources. However, it preserves the logarithmic growth with the number of agents in the system.

preprint2018arXiv

Optimal Energy Distribution with Energy Packet Networks

We use Energy Packet Network paradigms to investigate energy distribution problems in a computer system with energy harvesting and storages units. Our goal is to minimize both the overall average response time of jobs at workstations and the total rate of energy lost in the network. Energy is lost when it arrives at idle workstations which are empty. Energy is also lost in storage leakages. We assume that the total rate of energy harvesting and the rate of jobs arriving at workstations are known. We also consider a special case in which the total rate of energy harvesting is sufficiently large so that workstations are less busy. In this case, energy is more likely to be sent to an idle workstation. Optimal solutions are obtained which minimize both the overall response time and energy loss under the constraint of a fixed energy harvesting rate.

preprint2019arXiv

Comprehensive Introduction to Fully Homomorphic Encryption for Dynamic Feedback Controller via LWE-based Cryptosystem

The cryptosystem based on the Learning-with-Errors (LWE) problem is considered as a post-quantum cryptosystem, because it is not based on the factoring problem with large primes which is easily solved by a quantum computer. Moreover, the LWE-based cryptosystem allows fully homomorphic arithmetics so that two encrypted variables can be added and multiplied without decrypting them. This chapter provides a comprehensive introduction to the LWE-based cryptosystem with examples. A key to the security of the LWE-based cryptosystem is the injection of random errors in the ciphertexts, which however hinders unlimited recursive operation of homomorphic arithmetics on ciphertexts due to the growth of the error. We show that this limitation can be overcome when the cryptosystem is used for a dynamic feedback controller that guarantees stability of the closed-loop system. Finally, we illustrate through MATLAB codes how the LWE-based cryptosystem can be customized to build a secure feedback control system. This chapter is written for the control engineers who do not have background on cryptosystems.

preprint2018arXiv

Initialization-free Privacy-guaranteed Distributed Algorithm for Economic Dispatch Problem

This paper considers the economic dispatch problem for a network of power generators and customers. In particular, our aim is to minimize the total generation cost under the power supply-demand balance and the individual generation capacity constraints. This problem is solved in a distributed manner, i.e., a dual gradient-based continuous-time distributed algorithm is proposed in which only a single dual variable is communicated with the neighbors and no private information of the node is disclosed. The proposed algorithm is simple and no specific initialization is necessary, and this in turn allows on-line change of network structure, demand, generation constraints, and even the participating nodes. The algorithm also exhibits a special behavior when the problem becomes infeasible so that each node can detect over-demand or under-demand situation of the power network. Simulation results on IEEE 118 bus system confirm robustness against variations in power grids.

preprint2019arXiv

A gradient algorithm for Hamiltonian identification of open quantum systems

In this paper, we present a gradient algorithm for identifying unknown parameters in an open quantum system from the measurements of time traces of local observables. The open system dynamics is described by a general Markovian master equation based on which the Hamiltonian identification problem can be formulated as minimizing the distance between the real time traces of the observables and those predicted by the master equation. The unknown parameters can then be learned with a gradient descent algorithm from the measurement data. We verify the effectiveness of our algorithm in a circuit QED system described by a Jaynes-Cumming model whose Hamiltonian identification has been rarely considered. We also show that our gradient algorithm can learn the spectrum of a non-Markovian environment based on an augmented system model.

preprint2018arXiv

State Estimation and Tracking Control for Hybrid Systems by Gluing the Domains

We study the design problems of state observers and tracking controllers for a class of hybrid systems whose state jumps. The idea is to utilize the well-known method of gluing the jump set (a part of domain where the jumps take place) onto its image, which converts the hybrid system into a continuous-time system whose state does not jump. Sufficient conditions for this idea to be implemented are listed and discussed with a few concrete examples. In particular, we present a structural condition for an observer design, and, for tracking control, we introduce a feedback to compensate residual discontinuity in the vector field after gluing. The benefits of the proposed approach include that the observer design does not require detection of the state jumps, and that the tracking control does not require the plant state jumps when the reference jumps.

preprint2019arXiv

Robust Transmission Network Expansion Planning Problem Considering Storage Units

This paper addresses the transmission network expansion planning problem considering storage units under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby short- and long-term uncertainties are accounted for. This work differs from previously reported solutions in an important aspect, namely, we include binary recourse variables to avoid the simultaneous charging and discharging of storage units once uncertainty is revealed. Two-stage robust optimization with discrete recourse problems is a challenging task, so we propose using a nested column-and-constraint generation algorithm to solve the resulting problem. This algorithm guarantees convergence to the global optimum in a finite number of iterations. The performance of the proposed algorithm is illustrated using the Garver's test system.

preprint2019arXiv

Deep Reinforcement Learning Algorithm for Dynamic Pricing of Express Lanes with Multiple Access Locations

This article develops a deep reinforcement learning (Deep-RL) framework for dynamic pricing on managed lanes with multiple access locations and heterogeneity in travelers' value of time, origin, and destination. This framework relaxes assumptions in the literature by considering multiple origins and destinations, multiple access locations to the managed lane, en route diversion of travelers, partial observability of the sensor readings, and stochastic demand and observations. The problem is formulated as a partially observable Markov decision process (POMDP) and policy gradient methods are used to determine tolls as a function of real-time observations. Tolls are modeled as continuous and stochastic variables, and are determined using a feedforward neural network. The method is compared against a feedback control method used for dynamic pricing. We show that Deep-RL is effective in learning toll policies for maximizing revenue, minimizing total system travel time, and other joint weighted objectives, when tested on real-world transportation networks. The Deep-RL toll policies outperform the feedback control heuristic for the revenue maximization objective by generating revenues up to 9.5% higher than the heuristic and for the objective minimizing total system travel time (TSTT) by generating TSTT up to 10.4% lower than the heuristic. We also propose reward shaping methods for the POMDP to overcome the undesired behavior of toll policies, like the jam-and-harvest behavior of revenue-maximizing policies. Additionally, we test transferability of the algorithm trained on one set of inputs for new input distributions and offer recommendations on real-time implementations of Deep-RL algorithms. The source code for our experiments is available online at https://github.com/venktesh22/ExpressLanes_Deep-RL

preprint2019arXiv

ODE network model for nonlinear and complex agricultural nutrient solution system

In closed hydroponic systems, periodic readjustment of nutrient solution is necessary to continuously provide stable environment to plant roots because the interaction between plant and nutrient solution changes the rate of ions in it. The traditional method is to repeat supplying small amount of premade concentrated nutrient solution, measuring total electric conductivity and pH of the tank only. As it cannot control the collapse of ion rates, recent researches try to measure the concentration of individual components to provide insufficient ions only. However, those approaches use titrationlike heuristic approaches, which repeat adding small amount of components and measuring ion density a lot of times for a single control input. Both traditional and recent methods are not only time-consuming, but also cannot predict chemical reactions related with control inputs because the nutrient solution is a nonlinear complex system, including many precipitation reactions and complicated interactions. We present a continuous network model of the nutrient solution system, whose reactions are described as differential equations. The model predicts molar concentration of each chemical components and total dissolved solids with low error. This model also can calculate the amount of chemical compounds needed to produce a desired nutrient solution, by reverse calculation from dissolved ion concentrations.