Mixed sliding mode fuzzy control for discrete-time non-linear stochastic systems subject to variance and passivity constraints

• Published in: IET control theory & applications Vol. 9; no. 16; pp. 2369 - 2376
• Main Authors: Chang, Wen-Jer, Chen, Po-Hsun, Ku, Cheung-Chieh
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 29.10.2015
• Subjects: closed loop systems; closed‐loop system; covariance analysis; covariance theory; discrete time systems; discrete‐time nonlinear stochastic systems; Fuzzy; Fuzzy control; iterative linear matrix inequality algorithm; iterative methods; linear matrix inequalities; LMI; Lyapunov methods; Lyapunov theory; Mathematical models; mixed sliding mode fuzzy control; multiobjective control technique; nonlinear control systems; Nonlinearity; parallel distributed compensation; Passivity; passivity constraints; ship steering system; Sliding mode; stability; state variance constraints; Stochastic systems; Takagi‐Sugeno models; T‐S models; variable structure systems; Variance; iterative methods; T-S models; state variance constraints; iterative linear matrix inequality algorithm; fuzzy control; passivity constraints; linear matrix inequalities; stochastic systems; parallel distributed compensation; multiobjective control technique; ship steering system; stability; discrete time systems; mixed sliding mode fuzzy control; LMI; Lyapunov theory; closed loop systems; Takagi-Sugeno models; covariance theory; discrete-time nonlinear stochastic systems; nonlinear control systems; covariance analysis; variable structure systems; closed-loop system; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2015.0221

In this study, a novel multi-objective sliding mode fuzzy control technique is presented for a class of discrete-time non-linear stochastic systems that are represented by Takagi–Sugeno (T–S) fuzzy models. Subject to variance and passivity constraints, parallel distributed compensation based sliding mode fuzzy control approach is investigated for the discrete-time T–S fuzzy models. Combining Lyapunov theory, passivity theory and covariance theory, sufficient conditions are derived to satisfy stability, passivity and variance constraints. The iterative linear matrix inequality algorithm is employed in this study to solve these sufficient conditions. The contribution of this study is to develop a novel sliding mode fuzzy control method such that the closed-loop discrete-time non-linear stochastic system achieves passivity constraint and individual state variance constraints, simultaneously. At last, the simulations of controlling a discrete-time non-linear ship steering system are given in a numerical example to demonstrate the effectiveness and usefulness of proposed sliding mode fuzzy control methodology.