Fuzzy output tracking control of semi-linear first-order hyperbolic PDE systems with matched perturbations

This paper considers the design problem of a fuzzy output tracking controller via a finite number of actuators for a class of nonlinear distributed parameter systems with unknown matched perturbations described by semi-linear first-order hyperbolic partial differential equations (PDEs). Firstly, a T–S fuzzy hyperbolic PDE model is assumed to be used to accurately represent the semi-linear first-order hyperbolic PDE system. Subsequently, based on the T–S fuzzy PDE model, the classic variable structure control technique is adopted to develop a fuzzy output tracking controller such that the output of the semi-linear PDE system exponentially tracks a desired reference and the state of the system is uniformly bounded in the Filippov sense. By constructing a strict Lyapunov function, the sufficient condition on the existence of the fuzzy output tracking controller is derived and presented in terms of algebraic linear matrix inequalities (LMIs) in space with an equality constraint. It has been shown that when these algebraic LMIs with an equality constraint are feasible, fuzzy tracking control design can be obtained via the existing convex optimization techniques. Finally, the developed design methodology is successfully applied to the control of a semi-linear Lotka–Volterra PDE system and the achieved results illustrate its effectiveness.