Finite-Time Admissibility and Controller Design for T-S Fuzzy Stochastic Singular Systems with Distinct Differential Term Matrices

The finite-time admissibility analysis and controller design issues for extended T-S fuzzy stochastic singular systems (FSSSs) with distinct differential term matrices and Brownian parameter perturbations are discussed. When differential term matrices are allowed to be distinct in fuzzy rules, such fuzzy models can describe a wide class of nonlinear stochastic systems. Using fuzzy Lyapunov function (FLF), a new and relaxed sufficient condition is proposed via strict linear matrix inequalities (LMIs). Different from the existing stability conditions by FLF, the derivative bounds of fuzzy membership functions are not required in this condition. Based on admissibility analysis results, a design method for parallel distribution compensation (PDC) controller of FSSSs is given to guarantee the finite-time admissibility of the closed-loop system. Finally, the feasibility and effectiveness of the proposed methods in this article are illustrated with three examples.

Robust H∞ Takagi–Sugeno fuzzy output-feedback control for differential speed steering vehicles

This paper studied the modelling and control of four-wheel independently driven electric vehicles using differential speed steering. The Takagi–Sugeno fuzzy modelling approach represents the nonlinearities of the four-wheel independently driven electric vehicle state variables in several system models. The proposed controller design is a robust Takagi–Sugeno fuzzy output-feedback control based on a fuzzy Lyapunov function approach. More precisely, the Lyapunov function is chosen to be dependent on the membership functions. Sufficient conditions for the existence of the robust Takagi–Sugeno fuzzy controller are given in terms of linear matrix inequality constraints. The designed parameters are tested by simulating the four-wheel independently driven electric vehicles under varying operating conditions. The simulation results underscore the robustness and disturbance rejection importance of the proposed controller, which is then contrasted to better highlight the improved performance of the proposed approach over a fixed robust controller design.

Velocity control of a two-wheeled inverted pendulum mobile robot: a fuzzy model-based approach

This paper presents the design of a fuzzy tracking controller for balancing and velocity control of a Two-Wheeled Inverted Pendulum (TWIP) mobile robot based on its Takagi-Sugino (T-S) fuzzy model, fuzzy Lyapunov function and non-parallel distributed compensation (non-PDC) control law. The T-S fuzzy model of the TWIP mobile robot was developed from its nonlinear dynamical equations of motion. Stabilization conditions in a form of linear matrix inequalities (LMIs) were derived based on the T-S fuzzy model of the TWIP mobile robot, a fuzzy Lyapunov function and a non-PDC control law. Based on the derived stabilization conditions and the T-S fuzzy model of the TWIP mobile robot, a state feedback velocity tracking controller was then proposed for the TWIP mobile robot. The balancing and velocity tracking performance of the proposed controller was investigated via simulations. The simulation result shows the effectiveness of the proposed control scheme.

H∞ static output feedback control for electrical power steering subject to actuator saturation via fuzzy Lyapunov functions

This paper presents an H∞ static output-feedback control of electrical power steering (EPS) subject to actuator saturation. It deals with different practical problems in designing control of EPS systems, such as unavailability for measurement of the sideslip angle, friction effect, disturbances and the assist motor input current optimization. In order to guarantee good and stable driving, the nonlinear model of the EPS combined with bicycle model of electrical vehicles is used. Firstly, a new Takagi-Sugeno model is established, then using a fuzzy Lyapunov function, an H∞ static output-feedback is designed in terms of linear matrix inequalities. Finally, the proposed control schemes are applied to an EPS system. Simulation results and comparison with previous works show the effectiveness of the proposed control methods.