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Multicriteria optimization problems of finite horizon stochastic cooperative linear-quadratic difference games

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Science China(Information Sciences) 2022年第7期65卷 197-209页

作者： Chenchen PENG weihai zhang College of Electrical Engineering and Automation Shandong University of Science and Technology

This paper investigates the Pareto optimality of the regular and the indefinite stochastic cooperative linear-quadratic difference games in a finite time horizon. We derive a general form and a linear property of the solution to the linear stochastic difference system by defining several sequences of bounded and linear operators. The performance criteria's convexity can be guaranteed naturally under the weighted matrices' constraints for the regular cooperative game, and the weighting technique can well characterize the Pareto optimality. We also establish a novel convexity criterion for the cost functionals of the indefinite cooperative game, in which we find that the minimization of the performance criteria's weighted sum is equivalent to the Pareto optimal strategies. To derive all the Pareto optimal strategies and solutions, we present a computing algorithm using the weighted difference Riccati equation and the weighted difference Lyapunov equation for the regular and the indefinite cases. We present a practical example in the economy to validate the results.

关键词： multicriteria optimization problems Pareto optimality cooperative difference games discrete-time stochastic LQ theory the difference Riccati equation the difference Lyapunov equation

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PROPERTIES OF STORAGE FUNCTIONS AND APPLICATIONS TO NONLINEAR STOCHASTIC H∞ CONTROL

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Journal of Systems Science & Complexity 2011年第5期24卷 850-861页

作者： Qixia zhang weihai zhang School of Mathematics Shandong University Jinan 250100 China College of Information and Electrical Engineering Shandong University of Science and Technology Qingdao266510 China

This paper discusses the properties of the storage functions for a class of nonlinear stochastic systems. Some necessary and sufficient conditions for a function to be a storage function are derived. As applications, the finite and infinite horizon nonlinear stochastic H∞ controls for systems with state, control, and external disturbance dependent noise are investigated, which generalize the previous results.

关键词： Halmilton-Jacobi inequality H∞ control partial differential equation storage function viscosity solution.

On Observability and Detectability of Continuous-Time Stochastic Markov Jump Systems

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Journal of Systems Science & Complexity 2015年第4期28卷 830-847页

作者： TAN Cheng zhang weihai School of Control Science and Engineering Shandong University College of Electrical Engineering and Automation Shandong University of Science and Technology

This paper mainly studies observability and detectability for continuous-time stochastic Markov jump *** concepts called W-observability and W-detectability for such systems are introduced,which are shown to coincide with various notions of observability and detectability reported recently in literature,such as exact observability,exact detectability and ***,by introducing an accumulated energy function,some efficient criteria and interesting properties for both W-observability and W-detectability are obtained.

关键词： Continuous-time stochastic system detectability Markov jump observability.

Feedback Stackelberg Solution for Mean-Field Type Stochastic Systems with Multiple Followers

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Journal of Systems Science & Complexity 2023年第4期36卷 1519-1539页

作者： LIN Yaning zhang weihai School of Mathematics and Statistics Shandong University of TechnologyZibo 255000China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China

This paper discusses feedback Stackelberg strategies for the continuous-time mean-field type stochastic systems with multiple followers in infinite ***,optimal control problems of the followers are studied in the sense of Nash *** the help of a set of generalized algebraic Riccati equations(GAREs),sufficient conditions for the solvability are put ***,the leader faces a constrained optimal control problem by transforming the cost functional into a trace *** the Karush-Kuhn-Tucker(KKT)conditions,necessary conditions are presented in term of the solvability of the cross-coupled stochastic algebraic equations(CSAEs).Moreover,feedback Stackelberg strategies are obtained based on the solutions of the *** addition,an iterative scheme is introduced to obtain efficiently the solutions of the ***,an example is given to shed light on the effectiveness of the proposed results.

关键词： Feedback information structure generalized algebraic Riccati equations mean-field type stochastic systems Stackelberg strategy

Incentive Feedback Stackelberg Strategy in Mean-Field Type Stochastic Difference Games

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Journal of Systems Science & Complexity 2024年第4期37卷 1425-1445页

作者： GAO Wenhui LIN Yaning zhang weihai School of Mathematics and Statistics Shandong University of TechnologyZibo 255000China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China

This paper designs an incentive Stackelberg strategy for the discrete-time stochastic systems with mean-field *** conditions for the existence of such a design are ***,the incentive strategy is obtained as a feedback form including the deviation of the state and its mathematical ***,the stability analysis is *** is found that the stability can be guaranteed by the *** addition,the specific algorithm is proposed and its effectiveness is checked by two examples.

关键词： Discrete-time mean-field stochastic systems incentive strategy Stackelberg game teamoptimal solution

Discrete-Time Mean-Field Stochastic H_2/H_∞ Control

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Journal of Systems Science & Complexity 2017年第4期30卷 765-781页

作者： zhang weihai MA Limin zhang Tianliang College of Electrical Engineering and Automation Shandong University of Science and Technology Science and Information College Qingdao Agricultural University College of Information and Control Engineering China University of Petroleum (East China)

The finite horizon H_2/H_∞ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, the authors derive a mean-field stochastic bounded real lemma(SBRL). Secondly, a sufficient condition for the solvability of discrete-time mean-field stochastic linearquadratic(LQ) optimal control is presented. Thirdly, based on SBRL and LQ results, this paper establishes a sufficient condition for the existence of discrete-time stochastic H_2/H_∞ control of meanfield type via the solvability of coupled matrix-valued equations.

关键词： Discrete-time systems H2/H∞ control mean-field.

Global practical tracking for stochastic time-delay nonlinear systems with SISS-like inverse dynamics

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Science China(Information Sciences) 2017年第12期60卷 233-247页

作者： Lingrong XUE weihai zhang Xuejun XIE College of Electrical Engineering and Automation Shandong University of Science and Technology Institute of Automation Qufu Normal University

This paper investigates the practical tracking problem of stochastic delayed nonlinear systems. The powers of the nonlinear terms are relaxed to a certain interval rather than a precisely known point. Based on the Lyapunov-Krasovskii(L-K) functional method and the modified adding a power integrator technique,a new controller is constructed to render the solutions of the considered system to be bounded in probability,and furthermore, the tracking error in sense of the mean square can be made small enough by adjusting some designed parameters. A simulation example is provided to demonstrate the validity of the method in this paper.

关键词： nonlinear systems stochastic systems time-varying delay global practical tracking SISS-like inverse dynamics

Study on stability in probability of general discrete-time stochastic systems

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Science China(Information Sciences) 2020年第5期63卷 215-217页

作者： Tianliang zhang Feiqi DENG weihai zhang School of Automation Science and Engineering South China University of Technology College of Electrical Engineering and Automation Shandong University of Science and Technology

Dear editor,It is well-known that the stability should first be considered in system analysis and *** Lyapunov first initiated his stability theory regarding ordinary differential equations (ODEs)in 1892, Lyapunov’s stability theory has been an important research topic in both mathematics and control theory. Specifically, Lyapunov’s second method was soon generalized to the study of the stability of stochastic differential equa-

关键词： Study on stability in probability of general discrete-time stochastic systems

State and Output Feedback Finite-time Guaranteed Cost Control of Linear It Stochastic Systems

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Journal of Systems Science & Complexity 2015年第4期28卷 813-829页

作者： YAN Zhiguo zhang Guoshan WANG Jiankui zhang weihai School of Electrical Engineering and Automation Qilu University of Technology School of Electrical Engineering and Automation Tianjin University College of Electrical Engineering and Automation Shandong University of Science and Technology

The problem of guaranteed cost control based on finite-time stability for stochastic system is first investigated in this *** motivation of solving this problem arises from an observation that finite/infinite-horizon guaranteed cost control does not consider the transient performance of the closed-loop system,but guaranteed cost control based on finite-time stability involves this practical *** order to explain this problem explicitly,a concept of the stochastic finite-time guaranteed cost control is introduced,and then some new sufficient conditions for the existence of state and output feedback finite-time guaranteed cost controllers are derived,which guarantee finite-time stochastic stability of closed-loop systems and an upper bound of a quadratic cost ***,this problem is reduced to a convex optimization problem with matrix inequality constraints and a new solving algorithm is ***,an example is given to illustrate the effectiveness of the proposed method.

关键词： Finite-time stability guaranteed cost control matrix inequalities stochastic systems.