Variance and Passivity Constrained Fuzzy Control for Nonlinear Ship Steering Systems with State Multiplicative Noises

Abstract

The variance and passivity constrained fuzzy control problem for the nonlinear ship steering systems with state multiplicative noises is investigated. The continuous-time Takagi-Sugeno fuzzy model is used to represent the nonlinear ship steering systems with state multiplicative noises. In order to simultaneously achieve variance, passivity, and stability performances, some sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. By solving the corresponding linear matrix inequality conditions, a parallel distributed compensation based fuzzy controller can be obtained to guarantee the stability of the closed-loop nonlinear ship steering systems subject to variance and passivity performance constraints. Finally, a numerical simulation example is provided to illustrate the usefulness and applicability of the proposed multiple performance constrained fuzzy control method.

Robust fuzzy controller design for dynamic positioning system of ships

“…Additionally, it can be observed that the proposed controller is more effective since the response time is as small as below 0.2 seconds for position and heading, and 0.5 seconds for velocities. Based on the simulation results, the proposed controller performs better compared to that given in [25,27] and [35], by having small response time of less than 0.5 seconds. Fig.…”

“…The purpose of the study given in [29] was to achieve the H ∞ performance constraints and cope with the nastiest case effects of the disturbances. More works related to robust fuzzy have been given in [27][28][29][30][31][32][33][34][35][37][38]. Some of these literatures have no direct comparison to the proposed work but show the richness of fuzzy control designs.…”

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

“…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.…”

H∞Enhanced Control Design of Discrete-Time Takagi-Sugeno State-Multiplicative Noisy Systems

“…An important fact is that the design problem is a standard feasibility problem with several LMIs. According to the T-S fuzzy model with multiplicative noise, there exist only few approaches investigated to solve the abovementioned problems of control design and stability analysis for continuous-time [23,24], as well as for discrete-time TS models [25][26][27] and these papers only present some results on stability analysis, mean-square stabilization, and control for TS fuzzy stochastic systems with multiplicative noises.…”