arXiv subjects

Huanshui Zhang

Publications and source records attributed to Huanshui Zhang.

At least 55 records · Page 3Linked to original sources

arXiv2020

Mean Field Linear Quadratic Control: Uniform Stabilization and Social Optimality

This paper is concerned with uniform stabilization and social optimality for general mean field linear quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the definiteness condition. For the finite-horizon problem, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback-type control by decoupling the FBSDEs. For the infinite-horizon problem, by using solutions to two Riccati equations, we design a set of decentralized control laws, which is further proved to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems in different cases, respectively. Finally, the proposed decentralized controls are compared to the asymptotic optimal strategies in previous works.

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arXiv2020

The Difference and Unity of Irregular LQ Control and Standard LQ Control and Its Solution

Irregular linear quadratic control (LQ, was called Singular LQ) has been a long-standing problem since 1970s. This paper will show that an irregular LQ control (deterministic) is solvable (for arbitrary initial value) if and only if the LQ cost can be rewritten as a regular one by changing the terminal cost $x'(T)Hx(T)$ to $x'(T)[H+P_1(T)]x(T)$, while the optimal controller can achieve $P_1(T)x(T)=0$ at the same time. In other words, the irregular controller (if exists) needs to do two things at the same time, one thing is to minimize the cost and the other is to achieve the terminal constraint $P_1(T)x(T)=0$, which clarifies the essential difference of irregular LQ from the standard LQ control where the controller is to minimize the cost only. With this breakthrough, we further study the irregular LQ control for stochastic systems with multiplicative noise. A sufficient solving condition and the optimal controller is presented based on Riccati equations.

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arXiv2019

Optimal Decentralized Control with Asymmetric Partial Information Sharing

This paper considers the optimal decentralized control for networked control systems (NCSs) with asymmetric partial information sharing between two controllers. In this NCSs model, the controller 2 (C2) shares its observations and part of its historical control inputs with the controller 1 (C1), whereas C2 cannot obtain the information of C1 due to network constraints. We present the optimal estimators for C1 and C2 respectively based on asymmetric observations. Since the information for C1 and C2 are asymmetric, the estimation error covariance (EEC) is coupled with the controller which means that the classical separation principle fails. By applying the Pontryagin's maximum principle, we obtain a solution to the forward and backward stochastic difference equations. Based on this solution, we derive the optimal controllers to minimize a quadratic cost function. Combining the optimal controllers with the EEC, the controller C1 is decoupled from the ECC. It should be emphasized that the control gain is dependent on the estimation gain. What's more, the estimation gain satisfies the forward Riccati equation and the control gain satisfies the backward Riccati equation which makes the problem more challenging. We propose iterative solutions to the Riccati equations and give a suboptimal solution to the optimal decentralized control problem.

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arXiv2019

Optimal Control and Stabilization for Networked Control Systems with Asymmetric Information

This paper considers the optimal control and stabilization problems for networked control systems (NCSs) with asymmetric information. In this NCSs model, the remote controller can receive packet-dropout states of the plant, and the available information for the embedded controller are observations of states and packet-dropout states sent from the remote controller. The two controllers operate the plant simultaneously to make the quadratic performance minimized and stabilize the linear plant. For the finite-horizon case, since states of the plant cannot be obtained perfectly, we develop the optimal estimators for the embedded and remote controllers based on asymmetric information respectively. Then we give the necessary and sufficient condition for the optimal control based on the solution to the forward-backward stochastic difference equations (FBSDEs). For the infinite-horizon case, on one hand, the necessary and sufficient condition is given for the stabilization in the mean-square sense of the system without the additive noise. On the other hand, it is shown that the system with the additive noise is bounded in the mean-square sense if and only if there exist the solutions to the two coupled algebraic Riccati equations. Numerical examples on the unmanned underwater vehicle are presented to show the effectiveness of the given algorithm.

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arXiv2019

Stabilization Control for ItO Stochastic System with Indefinite State and Control Weight Costs

In standard linear quadratic (LQ) control, the first step in investigating infinite-horizon optimal control is to derive the stabilization condition with the optimal LQ controller. This paper focuses on the stabilization of an Ito stochastic system with indefinite control and state weighting matrices in the cost functional. A generalized algebraic Riccati equation (GARE) is obtained via the convergence of the generalized differential Riccati equation (GDRE) in the finite-horizon case. More importantly, the necessary and sufficient stabilization conditions for indefinite stochastic control are obtained. One of the key techniques is that the solution of the GARE is decomposed into a positive semi-definite matrix that satisfies the singular algebraic Riccati equation (SARE) and a constant matrix that is an element of the set satisfying certain linear matrix inequality conditions. Using the equivalence between the GARE and SARE, we reduce the stabilization of the general indefinite case to that of the definite case, in which the stabilization is studied using a Lyapunov functional defined by the optimal cost functional subject to the SARE.

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arXiv2019

Optimal Control Problem for Discrete-Time Systems with Colored Multiplicative Noise

The optimal control problem for discrete-time systems with colored multiplicative noise is discussed in this paper. The problem will be more difficult to deal with than the case of white noise due to the correlation of the adjoining state. By solving the forward and backward stochastic difference equations (FBSDEs), the necessary and sufficient conditions for the solvability of the optimal control problems in both delay-free and one-step input delay case are given.

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arXiv2019

Mean Field Games for Multi-agent Systems with Multiplicative Noises

This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal control problem subject to consistent mean field approximations. The set of decentralized strategies is further shown to be an $\varepsilon$-Nash equilibrium. For the integrator multiagent systems, we design a set of $\varepsilon$-Nash strategies by exploiting the convexity property of the limiting problem. It is shown that under the mild conditions all the agents achieve mean-square consensus.

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arXiv2019

Output Feedback Control for Irregular LQ Problem

In this paper, we study the irregular output feedback linear quadratic (LQ) control problem, which is a continuous work of previous works for irregular LQ control [33] where the state is assumed to be exactly known priori. Different from the classic output feedback LQ control problem, the cost function must be modified to guarantee the solvability. In the framework of the modified cost function, it is shown that the separation principle holds and the explicitly optimal controller is given in the feedback form of the Kalman filtering. In particular, the feedback gain is calculated by two Riccati equations independently of the Kalman filtering. The key technique is the "two-layer optimization" approach. We also emphasize that the optimal controller at the terminal time is required to be deterministic.

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arXiv2019

Mean Field Linear Quadratic Control: FBSDE and Riccati Equation Approaches

This paper studies social optima and Nash games for mean field linear quadratic control systems, where subsystems are coupled via dynamics and individual costs. For the social control problem, we first obtain a set of forward-backward stochastic differential equations (FBSDE) from variational analysis, and construct a feedback-type control by decoupling the FBSDE. By using solutions of two Riccati equations, we design a set of decentralized control laws, which is further proved to be asymptotically social optimal. Two equivalent conditions are given for uniform stabilization of the systems in different cases. For the game problem, we first design a set of decentralized control from variational analysis, and then show that such set of decentralized control constitute an asymptotic Nash equilibrium by exploiting the stabilizing solution of a nonsymmetric Riccati equation. It is verified that the proposed decentralized control laws are equivalent to the feedback strategies of mean field control in previous works. This may illustrate the relationship between open-loop and feedback solutions of mean field control (games).

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arXiv2019

Deterministic Optimal Control of Ito Stochastic Systems with Random Coefficients

This paper is concerned with the deterministic optimal control of Ito stochastic systems with random coefficients. The necessary and sufficient conditions for the unique solvability of the optimal control problem with random coefficients are derived via the solution to the coupled stochastic Riccati-type equations. An explicit expression of the deterministic optimal controller for this problem is given. The presented results include the case of deterministic coefficient [14] as special case.

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arXiv2019

Optimal Stabilization Control for Discrete-time Markov Jump Linear System with Control Input Delay

This paper will investigate the infinite horizon optimal control and stabilization problems for the Markov jump linear system (MJLS) subject to control input delay. Different from previous works, for the first time, the necessary and sufficient stabilization conditions are explored under explicit expressions, and the optimal controller for infinite horizon is designed with a coupled algebraic Riccati equation. By introducing a new type of Lyapunov equation, we show that under the exact observability assumption, the MJLS with control input delay is stabilizable in the mean square sense with the optimal controller if and only if a coupled algebraic Riccati equation has a unique positive definite solution. The presented results are parallel to the optimal control and stabilization for standard system with input delay.

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arXiv2018

Integrated Stabilization Policy over a Software Defined Network

In this paper, we mainly investigate an integrated system operating under a software defined network (SDN) protocol. SDN is a new networking paradigm in which network intelligence is centrally administered and data is communicated via channels that are physically separated from those conveying user data. Under the SDN architecture, it is feasible to set up multiple flows for transmitting control signals to an actuator with high priority for each individual application. While each flow may suffer random transmission delay, we focus on the stabilization problem under the joint design of the event-driven strategy in actuator and the control policy in decision-maker. By introducing a predefined application time, the integrated system can be reformulated as the form of stochastic system with input delay and multiplicative noise. For such system, we propose a set of necessary and sufficient stabilization conditions. Specifically, for the scalar system, we derive the allowable sampling period bound that can guarantee stabilization in terms of the probability distributions of the random transmission delays. A simple example is included to show the performance of our theoretic results.

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arXiv2018

Optimal Control with Irregular Performance

In this paper, we solve the long-standing fundamental problem of irregular linear--quadratic (LQ) optimal control, which has received significant attention since the 1960s. We derive the optimal controllers via the key technique of finding the analytical solutions to two different forward and backward differential equations (FBDEs). We give a complete solution to the finite-horizon irregular LQ control problem using a new `two-layer optimization' approach. We also obtain the necessary and sufficient condition for the existence of optimal and stabilizing solutions in the infinite-horizon case in terms of solutions to two Riccati equations and the stabilization of one specific system. For the first time, we explore the essential differences between irregular and standard LQ control, making a fundamental contribution to classical LQ control theory. We show that irregular LQ control is totally different from regular control as the irregular controller must guarantee the terminal state constraint of $P_1(T)x(T)=0$.

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arXiv2018

Stabilization for Networked Control Systems with Simultaneous Input Delay and Markovian Packet Losses

The mean square stabilization problem for discrete-time networked control systems (NCSs) is investigated in this article. What the difference from most previous works is that input delay and packet losses occur simultaneously in the communication channel, moreover, the data packet dropout is modeled as a time-homogeneous Markov process which will bring some difficulties in solving the problem due to the temporal correlation. The contributions in this paper can be summarized as two points. Firstly, the equivalence condition for the solvability of linear quadratic optimal problem in finite horizon subject to the discrete-time NCSs is expressed by solving the forward and backward stochastic difference equations (FBSDEs-M) which is derived from the maximum principle involving Markov jump and delay. Secondly, under basic assumption, the necessary and sufficient condition of mean square stabilization is given by the solutions to the coupled algebraic Riccati equations with Markov jump (CAREs-M). To our best knowledge, the problems studied in this paper are new because most previous works mainly discussed the case of only delay or packet dropout in NCSs.

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arXiv2018

Optimal Control for Discrete-time Markov Jump Linear System with Control Input Delay

This paper deals with the finite horizon optimal control problem for discrete-time Markov jump linear system with input delay. The correlation among the jumping parameters and the input delay are considered simultaneously, which forms the basic difficulty of the design. one of the key techniques is to solve a delayed forward and backward jumping parameter difference equation which is obtained by an improved maximum principle, and the other is the introduction of a "d-step backward formula". Based on the proposed techniques, a necessary and sufficient condition for the existence of the optimal controller is given in an explicit form and an analytical solution to the optimal controller is supplied. The optimal controller is a linear function of the current time state and the historical time control input, where the feedback gains are a set of jumping parameter matrices derived by solving a new type of coupled difference Riccati equation. The key step in the derivation is to establish the relationship between the costate and the real state of the system. The result obtained in this paper can be viewed as a generalization of the standard case, in which there is only one mode of operation.

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arXiv2018

Exponential Stabilization for Ito Stochastic Systems with Multiple Input Delays

In this paper, we study the stabilization problem for the Ito systems with both multiplicative noise and multiple delays which exist widely in applications such as networked control systems. Sufficient and necessary conditions are obtained for the exponential stabilization problem of Ito stochastic systems with multiple delays. On one hand, we derive the solvability of the modified Riccati equation in case of the mean-square exponential stabilization. On the other hand, the mean-square exponential stabilization is guaranteed by the solvability of a modified Riccati equation. A novel stabilizing controller is shown in the feedback from of the conditional expectation in terms of the modified algebraic Riccati equation. The main technique is to reduce the original system with multiple delays to a pseudo delay-free system.

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arXiv2018

Consensusability of Multi-agent Systems with Delay and Packet Dropout Under Predictor-like Protocols

This paper considers the consensusability of multi-agent systems with delay and packet dropout. By proposing a kind of predictor-like protocol, sufficient and necessary conditions are given for the mean-square consensusability in terms of system matrices, time delay, communication graph and the packetdrop probability. Moreover, sufficient and necessary conditions are also obtained for the formationability of multi-agent systems.

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arXiv2018

Consensus Control of Multi-agent Systems with Optimal Performance

The consensus control with optimal cost remains major challenging although consensus control problems have been well studied in recent years. In this paper, we study the consensus control of multi-agent system associated with a given cost function. The main contribution is to present the distributed control protocol while minimizing the given cost function with positive semi-definite weighting matrix of control. The derived controller is composed of two parts: One part is the feedback of the individual state which minimizes the cost function and the other part is the feedback of the relative states between the neighbours which guarantees the consensus. The presented results are new to the best of our knowledge.

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