Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

Abstract

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

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

“…For studying the multi‐objective control design problem, the passivity constraint is also included in the proposed fuzzy controller design process in addition to individual state variance constraint. In recent years, the passivity constraint has been considered in the fuzzy controller design for non‐linear systems [20, 24, 34–36]. The notion of passivity has been found to be of considerable utility in capturing features of physical problems where natural notions of energy storage and dissipation exist.…”

“…The above attractive features make passivity an important tool to analyse and synthesise stable control systems. According to individual state variance constraint and passivity constraint, a multi‐objective fuzzy control approach has been investigated in [35, 36]. However, the advantage of the sliding mode control was not adopted in [35, 36].…”

“…According to individual state variance constraint and passivity constraint, a multi‐objective fuzzy control approach has been investigated in [35, 36]. However, the advantage of the sliding mode control was not adopted in [35, 36]. Extending the results of [35, 36], the motivation of this paper is to combine sliding mode control, covariance control, passivity‐based control and fuzzy control to develop a novel multi‐objective control scheme for the discrete‐time non‐linear stochastic systems.…”

“…However, the advantage of the sliding mode control was not adopted in [35, 36]. Extending the results of [35, 36], the motivation of this paper is to combine sliding mode control, covariance control, passivity‐based control and fuzzy control to develop a novel multi‐objective control scheme for the discrete‐time non‐linear stochastic systems. To the best of the authors’ knowledge, so far the problem of the above combined multi‐objective control approach for discrete‐time non‐linear stochastic systems has not been discussed in the literature.…”

Robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with multiplicative noises

“…Extending covariance control theory, the individual state variance constrained control problem for the nonlinear stochastic systems has been successfully investigated via Takagi-Sugeno (T-S) fuzzy models [8][9][10]. T-S fuzzy model consists of several linear subsystems, and it approximates a nonlinear model by using IF-THEN fuzzy rules.…”