scholarly journals Nonlinear StochasticH∞Control with Markov Jumps and(x,u,v)-Dependent Noise: Finite and Infinite Horizon Cases

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Li Sheng ◽  
Meijun Zhu ◽  
Weihai Zhang ◽  
Yuhong Wang
Keyword(s):  
Design Method ◽  
External Disturbance ◽  
Infinite Horizon ◽  
State Control ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Numerical Examples ◽  
Inequality Techniques ◽  
Jump Systems ◽  
Control Designs

This paper is concerned with theH∞control problem for nonlinear stochastic Markov jump systems with state, control, and external disturbance-dependent noise. By means of inequality techniques and coupled Hamilton-Jacobi inequalities, both finite and infinite horizonH∞control designs of such systems are developed. Two numerical examples are provided to illustrate the effectiveness of the proposed design method.

scholarly journals H∞ Control for Nonlinear Infinite Markov Jump Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yueying Liu ◽  
Ting Hou
Keyword(s):  
Stochastic Systems ◽  
Design Method ◽  
Infinite Horizon ◽  
Mean Square ◽  
State Control ◽  
Markov Jump ◽  
Nonlinear Stochastic Systems ◽  
Markov Jump Systems ◽  
Jump Systems ◽  
Infinite State

In this paper, we discuss the infinite horizon H∞ control problem for a class of nonlinear stochastic systems with state, control, and disturbance dependent noise. The jumping parameters are modelled as an infinite-state Markov chain. Based on the solvability of a set of coupled Hamilton-Jacobi inequalities (HJIs), the exponential mean square H∞ controller for the considered nonlinear stochastic systems is obtained. A numerical example is given to show the effectiveness of the proposed design method.

An event-triggered approach to finite-time observer-based control for Markov jump systems with repeated scalar nonlinearities

2017 ◽  
Vol 40 (9) ◽  
pp. 2789-2797 ◽  
Author(s):  
Jingyu Li ◽  
Liang Shen ◽  
Fengqi Yao ◽  
Huanyu Zhao ◽  
Jing Wang
Keyword(s):  
Finite Time ◽  
Design Method ◽  
Function Technique ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Diagonally Dominant Matrix ◽  
Error System ◽  
Dominant Matrix ◽  
Jump Systems ◽  
Event Triggered

This paper studies the issue of finite-time observer-based control via an event-triggered scheme for Markov jump repeated scalar nonlinear systems. An observer-based controller via an event-triggered scheme is proposed, which can save the limited network communication bandwidth effectively, so that the resulting error system is stochastically finite-time bounded. Based on the positive definite diagonally dominant matrix and the Lyapunov function technique, a sufficient condition is presented for the solvability of the addressed problem, and the desired observer-based controller can be constructed via a convex optimization problem. In the end, a simulation example is employed to show the validity and practicability of the proposed design method.

scholarly journals Finite-Time Control of Singular Linear Semi-Markov Jump Systems

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 8
Author(s):  
Xiaofu Ji ◽  
Xuehua Liu
Keyword(s):  
Finite Time ◽  
Controller Design ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
One Dimensional ◽  
Time Control ◽  
Jump Systems

The problem of finite-time control for singular linear semi-Markov jump systems (SMJSs) with unknown transition rates is considered in this paper. By designing a new semi-positive definite Lyapunov-like function, state feedback controller design methods are given that allow closed-loop singular linear SMJSs to be regular, impulse-free and stochastically finite-time-stable without external disturbance, and stochastically finite-time bounded with external disturbance. The obtained conditions are expressed by a set of strict matrix inequalities, which can be simplified to a set of linear matrix inequalities by a one dimensional search for a scalar. Two numerical examples are given to illustrate the effectiveness of proposed method.

scholarly journals Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Lifan Kang ◽  
Yue Wang ◽  
Ting Hou
Keyword(s):  
Robust Control ◽  
Transition Probabilities ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Numerical Examples ◽  
Bounded Real Lemma ◽  
Jump Systems ◽  
Jacobi Equations

This note focuses on the finite horizon H2/H∞ control for stochastic nonlinear jump systems with partially unknown transition probabilities. We derive the nonlinear stochastic bounded real lemma and the nonlinear optimal regular result for the considered system at first. A sufficient condition and a necessary condition for the solution of H2/H∞ control are, respectively, offered by four cross-coupled Hamilton–Jacobi equations (HJEs). Besides, numerical examples show the effectiveness of the obtained results.

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

2021 ◽  
pp. 014233122199096
Author(s):  
Yunling Shi ◽  
Xiuyan Peng
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
Design Method ◽  
Transition Rates ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Reduced Order ◽  
Jump Systems ◽  
Stochastic Admissibility ◽  
Fault Detection Filters

This work is concerned with the problem of full-order and reduced-order fault detection filters (FDFs) design in a convex optimization frame for continuous-time singular Markov jump systems (CTSMJSs) with complexity transition rates (TRs). A novel Lyapunov function construct approach is utilized to cope with the stochastic admissibility problem for CTSMJSs with complexity TRs. In order to obtain effective full-order and reduced-order FDFs, we decoupled the inequality using the presupposed Lyapunov matrix. Owing to the use of Lyapunov stochastic admissibility theory and a novel decoupling method based on convex polyhedron technique, some sufficient conditions are obtained to guarantee that the resulting full-order and reduced-order FDFs are suitable for CTSMJSs with complexity TRs. In particular, the reduced-order FDF has the advantages of small storage space and fast detection speed compared with the full order FDF. Four illustrative examples are given to explain the effectiveness of the proposed full-order and reduced-order FDFs design method.

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