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Mean-square exponential stability of stochastic Volterra systems in infinite dimensions

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Science China(Information Sciences) 2024年第10期67卷 298-314页

作者： Lin FU Shiguo PENG feiqi deng Quanxin ZHU School of Automation Guangdong University of Technology School of Automation Science and Engineering South China University of Technology Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal University

Over the past decade, the study of stability theory in integro-differential systems has grown significantly owing to their relevance in solving physical and engineering problems, such as viscoelasticity and thermo-viscoelasticity in materials with memory properties. This paper concentrates on a class of infinite-dimensional stochastic integro-differential systems. We establish the well-posedness of the system and identify mild solutions to the system and an abstract stochastic Cauchy problem. This identification is identified by employing a semigroup approach combined with Yosida approximation. We derive sufficient conditions that ensure the mean-square exponential stability of mild solutions to the system boils down to the boundedness of a certain function and a norm estimate for the stochastic part. These conditions are implemented through the semigroup approach and the composition operator method. Illustrative examples are provided and the obtained theoretical results are validated by numerical simulations.

关键词： stochastic integro-differential equations mean-square exponential stability stochastic distributed parameter systems Hardy space composition operators

Hybrid stochastic control strategy by two-layer networks for dissipating urban traffic congestion

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Science China(Information Sciences) 2024年第4期67卷 40-41页

作者： Xiaojing ZHONG Bin PANG feiqi deng Xueyan ZHAO School of Mechanical and Electrical Engineering Guangzhou University School of Automation Science and Engineering South China University of Technology

With the rapid development of mobile devices and geographic information systems, social network data have become part of the traffic condition dissemination system,thereby influencing traffic conditions. Current research has indicated that the dissemination of traffic congestion information can partially alleviate congestion problems and thus enhance road transportation efficiency [1].

关键词： Traffic congestion

Solution of the HJI equations for nonlinear H_∞ control design by state-dependent Riccati equations approach

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Journal of Systems Engineering and Electronics 2011年第4期22卷 654-660页

作者： Xueyan Zhao feiqi deng Institute of Systems Engineering South China University of Technology Guangzhou 510640 E R. China

The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.

关键词： nonlinear system robust control Hamilton-Jacobi-Isaacs (HJI) equation state-dependent Riccati equation (SDRE),global stabilization optimal control.

Asymptotic and stable properties of general stochastic functional differential equations

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Journal of Systems Engineering and Electronics 2014年第1期25卷 138-143页

作者： Xiaojing Zhong feiqi deng College of Automation Science and Engineering South China University of Technology

The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.

关键词： stochastic functional differential equations Lyapunov functions LaSalle asymptotic properties stability semi-martingale convergence theorem.

Equilibrium solution of two enterprises cooperative game

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Journal of Systems Engineering and Electronics 2007年第2期18卷 270-274页

作者： Li Ling deng feiqi Inst. of Systems Engineering South China Univ. of Technology Guangzhou 510640 P. R. China

Based on the actual experience of cooperation in the supply chain, the Nash solution of two enterprises cooperative games is given. Not only is the solution unique, but it is also stable, and neither side has the capability to deviate the allocation of interests from the equilibrium point. If some firm tries to withdraw from cooperation or threaten to use other particular strategy, the negotiations are likely to achieve the distribution by the threat game; The calculating method of the choice of the optimal bargaining base point and the corresponding optimal pay-off vector are given.

关键词： Enterprises cooperation Supply chain Cooperative game Bargaining base point Optimal pay-off vector.

Stability of stochastic switched epidemic systems with discrete or distributed time delay

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Journal of Systems Engineering and Electronics 2014年第4期25卷 660-670页

作者： Xiaoying Meng feiqi deng Institute of Systems Engineering South China University of Technology School of Statistics and Mathematics Zhongnan University of Economics and Law

Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.

关键词： stochastic switched epidemic system discrete timedelay distributed time delay stochastically stable Lyapunov functional.

Delay-dependent dissipative filtering for nonlinear stochastic singular systems with time-varying delays

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Science China(Information Sciences) 2017年第12期60卷 93-110页

作者： Shuangyun XING feiqi deng Systems Engineering Institute South China University of Technology College of Science Shenyang Jianzhu University

This paper concentrates on studying the delay-dependent dissipative filtering problem for nonlinear stochastic singular systems with time-varying delays via a Takagi-Sugeno(T-S) fuzzy control approach. The T-S fuzzy model is employed to represent a nonlinear stochastic singular system with unknown or partially unknown membership functions. Firstly, based on an auxiliary vector function, by utilizing an integral inequality and the free-weighting-matrix approach, a delay-dependent sufficient condition is derived to enable the considered filtering error system with time-varying delays to be stochastically admissible and dissipative. Furthermore,on the basis of the derived condition, by using a new type of candidate Lyapunov-Krasovskii function, the solvability conditions of the dissipative filter are addressed, and the corresponding fuzzy filter parameters can be obtained by solving a set of linear matrix inequalities. And then, we deduce the solving method for the H∞filter. The delay-dependent sufficient conditions are proposed to guarantee the systems to be regular, impulsefree, stochastically stable and to achieve a prescribed performance index ?γ. Finally, some simulation examples are proposed to manifest the effectiveness and merits of the filter design methodology developed in the paper.

关键词： nonlinear stochastic singular systems dissipative filtering unknown membership functions stochastic admissibility time-varying delays

Event-Triggered Sampled-Data Consensus of Nonlinear Multi-Agent Systems with Control Input Losses

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Journal of Systems Science & Complexity 2018年第6期31卷 1469-1497页

作者： XING Mali deng feiqi Department of Automation Science and Engineering South China University of Technology

This paper investigates the leader-following consensus problem for multi-agent systems with event-triggered mechanism and control packet *** on the local synchronization error, event-triggered mechanisms are proposed in order to reduce the number of controller *** control packet may lose due to unreliability of communication *** the assumption that once the packet loss happens the controller will be set to zero,sufficient consensus criteria for multi-agent system with event-triggered mechanism and control packet losses is *** is also shown that the interplay among the allowable packet loss rate,event-triggered mechanism and sampling *** illustrative example is given to demonstrate the effectiveness of the theoretical results.

关键词： Consensus control packet losses event-triggered mechanism multi-agent systems

Stability for discrete-time uncertain systems with infinite Markov jump and time-delay

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Science China(Information Sciences) 2021年第5期64卷 100-110页

作者： Ting HOU Yueying LIU feiqi deng School of Mathematics and Statistics Shandong Normal University College of Mathematics and Systems Science Shandong University of Science and Technology School of Automation Science and Engineering South China University of Technology

In this paper, we developed a stability analysis for discrete-time uncertain time-delay systems governed by an infinite-state Markov chain(DUTSs-IMC). Some sufficient conditions for the considered systems to be exponential stability in mean square with conditioning(ESMS-C) are derived via linear matrix inequalities(LMIs), which can be examined conveniently. Under novel sufficient conditions, the equivalence among asymptotical stability in mean square(ASMS), stochastic stability(SS), exponential stability in mean square(ESMS), and ESMS-C has been established. Besides, numerical simulations are employed in result validation.

关键词： infinite jump time-delay parametric uncertainties exponential stability in mean square with conditioning stochastic stability