Zi-Peng Wang

On Fuzzy Sampled-Data Control of Chaotic Systems Via a Time-Dependent Lyapunov Functional Approach

In this paper, a novel approach to fuzzy sampled-data control of chaotic systems is presented by using a time-dependent Lyapunov functional. The advantage of the new method is that the Lyapunov functional is continuous at sampling times but not necessarily positive definite inside the sampling intervals. Compared with the existing works, the constructed Lyapunov functional makes full use of the information on the piecewise constant input and the actual sampling pattern. In terms of a new parameterized linear matrix inequality (LMI) technique, a less conservative stabilization condition is derived to guarantee the exponential stability for the closed-loop fuzzy sampled-data system. By solving a set of LMIs, the fuzzy sampled-data controller can be easily obtained. Finally, the chaotic Lorenz system and Rösslers system are employed to illustrate the feasibility and effectiveness of the proposed method.

Finite dimensional guaranteed cost sampled-data fuzzy control for a class of nonlinear distributed parameter systems

In this paper, a finite dimensional guaranteed cost sampled-data fuzzy control (GCSDFC) problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems. Initially, applying the Galerkins method to the PDE system, a nonlinear ordinary differential equation (ODE) system is derived. The resulting nonlinear ODE system can accurately describe the dominant dynamics of the PDE system, which is subsequently expressed by the Takagi-Sugeno (T-S) fuzzy model. Then, a guaranteed cost sampled-data fuzzy controller is developed to stabilize exponentially the closed-loop slow fuzzy system while providing an upper bound for the quadratic cost function. A novel time-dependent functional is constructed to derive the condition for the existence of the proposed controller which is presented by bilinear matrix inequalities (BMIs). Moreover, a suboptimal GCSDFC problem to minimize the cost bound can be formulated as a BMI optimization problem. A local optimization algorithm that views the BMI as a double linear matrix inequality (LMI) is given to solve this BMI optimization problem, in which a Latin hypercube sampling (LHS) method is proposed to find an initially feasible solution for starting the algorithm. Furthermore, it is shown that the proposed controller can ensure the exponential stability of the closed-loop PDE system. Finally, simulation results on the Fisher equation and the temperature profile of a catalytic rod show that the proposed design strategy is effective.

Fuzzy impulsive control for uncertain nonlinear systems with guaranteed cost

In this paper, a guaranteed cost fuzzy impulsive control (GCFIC) problem is addressed for uncertain continuous-time nonlinear systems which can be represented by the Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties. Based on the T-S fuzzy model, a novel time-varying Lyapunov function is initially constructed to derive the existence condition of guaranteed cost fuzzy impulsive controllers, which cannot only exponentially stabilize the uncertain fuzzy system, but also provide an upper bound on the quadratic cost function. Then, two procedures for designing suboptimal guaranteed cost fuzzy impulsive controllers are given in the sense of minimizing an upper bound of the cost function: one casts the controller design into a parameter-dependent linear matrix inequality (LMI) optimization problem and the other casts the controller design into a sequential minimization problem subject to LMI constraints by using the cone complementary linearization (CCL) algorithm. Finally, an example is presented to illustrate the effectiveness of the proposed method.

Attitude tracking of mars entry vehicles via fuzzy sampled-data control approach

In this paper, a fuzzy sampled-data attitude tracking controller is designed for Mars entry vehicles. Initially, to reduce the complexity of fuzzy modeling, the original nonlinear attitude system is divided into two subsystems by using two time-scale decomposition method. Subsequently, the dynamic inversion control technique is applied to the slow subsystem to generate the angular velocity command. Then, based on the Takagi-Sugeno (T-S) fuzzy model of the fast subsystem and the angular velocity command, the fuzzy sampled-data controller is designed for the fuzzy tracking error system to derive the desired control torques by using a time-dependent Lyapunov functional. Finally, the simulation results on the Mars entry vehicles are given to illustrate the feasibility and effectiveness of the proposed method.

Robust Guaranteed Cost Sampled-Data Fuzzy Control for Uncertain Nonlinear Time-Delay Systems

This paper presents a robust guaranteed cost sampled-data fuzzy control (GCSDFC) design for Takagi–Sugeno fuzzy systems with parametric uncertainties and time-delay. Initially, a robust guaranteed cost sampled-data fuzzy controller is developed to stabilize exponentially the closed-loop fuzzy system while providing an upper bound for the quadratic cost function. In order to make full information of the actual sampling pattern, a novel time-dependent Lyapunov functional is subsequently constructed to derive the condition for the existence of the proposed controller which is given in terms of linear matrix inequalities (LMIs). Then, to minimize the upper bound of the cost function, a suboptimal robust GCSDFC problem can be formed as an LMI optimization problem. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Sampled-Data Fuzzy Control for Nonlinear Coupled Parabolic PDE-ODE Systems

In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.