Static output-feedback $$H_\infty$$ control for T–S fuzzy vehicle lateral dynamics

Abstract

This paper deals with static output-feedback H ∞ control for a system of the vehicle lateral dynamics, represented by Takagi-Sugeno (T-S) fuzzy models. Sufficient conditions of the existence of H ∞ control based on the static output-feedback are presented. The bilinear matrix inequalities are converted to a set of linear matrix inequalities, with the aid of some special derivations. Simulation results demonstrate the effectiveness of the proposed method.

T-S Fuzzy Observers to Design Actuator Fault-Tolerant Control for Automotive Vehicle Lateral Dynamics

“…The challenge in modeling vehicle dynamics accurately is that contact forces are complex to measure and to model. By using the T-S models' method proposed in [15,17], it is a highly useful mathematical representation of nonlinear systems, as they can represent any nonlinear system, regardless of its complexity, by a simple structure based on linear models interpolated by nonlinear positive functions. They have a simple structure with some interesting properties.…”

Unknown input observer design for vehicle lateral dynamics described by Takagi–Sugeno fuzzy systems

“…A nonlinear sector transformation is an interesting approach that allows correct T‐S representation to be achieved without loss of information on a compact state space set. By using identification and linearization of the cornering forces on the vehicle which can be approximated as in Reference 35. They are given by the following expressions and where , , and are the front, the rear tire cornering stiffness, and absolute value of slip angle , respectively.…”

Relaxed State and Fault Estimation for Vehicle Lateral Dynamics Represented by T–S Fuzzy Systems

“…e vehicle motions are defined by a set of translations and rotational movements illustrated to the top left of Figure 1 [28]. e model used in this paper describes the vehicle lateral dynamics (see Figure 1), which is obtained by considering the bicycle model; the lateral velocity v y and the yaw rate _ ψ of the vehicle are taken to be differential variables.…”

“…e best-known model used to describe the lateral movements of the vehicle is the bicycle model, developed in [23], which will be represented by the Takagi-Sugeno (T-S) multiple-model approach, widely used in the literature to solve nonlinearity problems in nonlinear systems [24][25][26], which consists in developing the global model by interpolation of local linear models. is technique accurately describes the behavior of nonlinear systems, including the vehicle's lateral dynamics system [27,28]. e stability of the estimation error toward zero is mainly studied by using the Lyapunov quadratic function, and sufficient asymptotic stability conditions are given in the form of linear matrix inequalities (LMIs), which can be solved very effectively using optimization techniques of LMI [29].…”

“…Figure 3: Profile of the steering angle given by driver δ f (t) [rad]. Parameters of membership functions and stiffness coefficients are given in Table2[28].…”