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Exact controllability of rational expectations model with multiplicative noise and input delay

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Journal of Automation and Intelligence 2024年第1期3卷 19-25页

作者： Wenjing Wang Juanjuan Xu huanshui zhang Minyue Fu School of Control Science and Engineering Shandong UniversityJinan 250061China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China School of System Design and Intelligent Manufacturing Southern University of Science and TechnologyShenzhen 518055China

This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future *** main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations *** particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free *** key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

关键词： Rational expectations model Exact controllability Exactly null controllability Multiplicative noise Input delay

Time-inconsistent stochastic linear quadratic control for discrete-time systems

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Science China(Information Sciences) 2017年第12期60卷 44-56页

作者： Qingyuan QI huanshui zhang School of Control Science and Engineering Shandong University

This paper is mainly concerned with the time-inconsistent stochastic linear quadratic(LQ) control problem in a more general formulation for discrete-time systems. The time-inconsistency arises from three aspects: the coefficient matrices depending on the initial pair, the terminal of the cost function involving the initial pair together with the nonlinear terms of the conditional expectation. The main contributions are: firstly,the maximum principle is derived by using variational methods, which forms a flow of forward and backward stochastic difference equations(FBSDE); secondly, in the case of the system state being one-dimensional, the equilibrium control is obtained by solving the FBSDE with feedback gain based on several nonsymmetric Riccati equations; finally, the necessary and sufficient solvability condition for the time-inconsistent LQ control problem is presented explicitly. The key techniques adopted are the maximum principle and the solution to the FBSDE developed in this paper.

关键词： time-inconsistency open-loop equilibrium control maximum principle FBSDE nonsymmetric Riccati equations

Stabilization for Discrete-Time Stochastic Systems with Multiple Input Delays

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Journal of Systems Science & Complexity 2023年第5期36卷 1961-1980页

作者： LI Lin zhang huanshui College of Mechanical and Electronic Engineering Shandong Agricultural UniversityTaian 271018China School of Information Science and Engineering Shandong Agricultural UniversityTaian 271018China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China

A stabilization problem for stochastic systems with multiple input delays is investigated herein.A new method to construct an optimal control problem with input constraints is adopted.A sufficient stabilization condition is established via Riccati-type equations,whose verification is computationally simple because the variable dimension of the equations does not increase with regard to the delay.A stabilization controller is proposed,and it is a feedback of the state and a history *** controller uses less history information than those with distributed *** numerical examples illustrate the effectiveness of the obtained results.

关键词： Riccati-type equations stabilization stochastic systems time-delay systems

Optimal control with irregular performance

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Science China(Information Sciences) 2019年第9期62卷 116-129页

作者： huanshui zhang Juanjuan XU School of Control Science and Engineering Shandong University

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 *** show that irregular LQ control is totally different from regular control as the irregular controller must guarantee the terminal state constraint of P1（T）x（T） = 0.

关键词： irregular LQ control Riccati equation stabilization

Achievable delay margin using LTI control for plants with unstable complex poles

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Science China(Information Sciences) 2018年第9期61卷 182-189页

作者： Peijun JU huanshui zhang School of Control Science and Engineering Shandong University School of Mathematics and Statistics Taishan University

We consider the achievable delay margin of a real rational and strictly proper plant, with unstable complex poles, by a linear time-invariant(LTI) controller. The delay margin is defined as the largest time delay such that, for any delay less than this value, the closed-loop stability is maintained. Drawing upon a frequency domain method, particularly a bilinear transform technique, we provide an upper bound of the delay margin, which requires computing the maximum of a one-variable function. Finally, the effectiveness of the theoretical results is demonstrated through a numerical example.

关键词： delay margin systems with time-delay time-invariant systems unstable complex poles frequency domain method

On Stabilization of It Stochastic Time-Varying Systems

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Journal of Systems Science & Complexity 2017年第4期30卷 818-827页

作者： GAO Rong zhang huanshui School of Control Science and Engineering Shandong UniversityJinan 250061China School of Mathematics and Statistics Science Ludong UniversityYantai 264025China

The stabilization with receding horizon control （RHC） of It5 stochastic time-varying systems is studied in this paper. Based on monotonically non-increasing of optimal cost and stochastic Lyapunov stability theory, a necessary and sufficient stabilization condition on the terminal weighting matrix is proposed, which guarantees the mean-square stability of the closed-loop system. The explicit receding horizon controller is obtained by employing stochastic maximum principle. Simulations demonstrate the effectiveness of the proposed method.

关键词： Mean-square stability receding horizon control stochastic time-varying system.

H_∞ FILTERING FOR CONTINUOUS-TIME SYSTEMS WITH POINTWISE TIME-VARYING DELAY

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Journal of Systems Science & Complexity 2012年第1期25卷 90-104页

作者： Wei WANG huanshui zhang School of Control Science and Engineering Shandong University

The problem of H∞ filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper. By applying an innovation analysis in Krein space, a necessary and sufficient condition for the existence of an H∞ filter is derived in two methods： One is the partial differential equation approach, the other is the reorganized innovation analysis approach. The former gives a solution to the proposed H∞ filtering problem in terms of the solution of a partial differential equation with boundary conditions. The later gives an analytical solution to the proposed H∞ filtering problem in terms of the solutions of Riccati and matrix differential equations.

关键词： Continuous-time systems H∞ filtering partial differential equations pointwise timevarying delay reorganized innovation analysis Riccati differential equations.

Distributed Design of Approximately Optimal Controller for Identical Discrete-Time Multi-Agent Systems

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Journal of Systems Science & Complexity 2016年第3期29卷 629-641页

作者： zhang Fangfang WANG Wei zhang huanshui School of Electrical Engineering Zhengzhou University School of Control Science and Engineering Shandong University

This paper considers the distributed control of the LQR problem for discrete-time multiagent *** controllers are designed based on the solutions of centralized optimal control and the topological structure of the *** mild conditions,it is shown that the distributed controller can approximate to the centralized optimal *** the states of the closed-loop systems of the distributed control exponentially converge to the states of the closed-loop systems of the centralized optimal *** examples are given to show effectiveness of the proposed results.

关键词： Approximately optimal controller centralized optimal control distributed controller multi-agent systems.

Stabilization analysis for Markov jump systems with multiplicative noise and indefinite weight costs

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Science China(Information Sciences) 2021年第5期64卷 111-120页

作者： Hongdan LI Chunyan HAN huanshui zhang School of Control Science and Engineering Shandong University School of Electrical Engineering University of Jinan

This paper mainly discusses the stabilization problem for discrete-time Markov jump linear systems(MJLSs) involving multiplicative noise with an infinite horizon. The cost weighting matrices are generalized to be indefinite. To the best of our knowledge, this paper is novel and unlike most previous studies, it provides the necessary and sufficient conditions that stabilize the MJLSs in the mean square sense with indefinite weighting matrices.

关键词： stabilization indefinite multiplicative noise Markov jump linear system