Fuzzy Control With Guaranteed Cost for Nonlinear Coupled Parabolic PDE-ODE Systems via PDE Static Output Feedback and ODE State Feedback

This paper investigates the guaranteed cost fuzzy control (GCFC) problem for a class of nonlinear systems modeled by an $n$-dimension ordinary differential equation (ODE) coupled with a semilinear scalar parabolic partial differential equation (PDE). A Takagi–Sugeno (T–S) fuzzy coupled parabolic PDE-ODE model is initially proposed to accurately represent the nonlinear coupled system. Then, on the basis of the T–S fuzzy coupled model, a GCFC design is developed in terms of linear matrix inequalities to exponentially stabilize the coupled system while providing an upper bound for a prescribed quadratic cost function. The proposed fuzzy control scheme consists of the ODE state feedback and the PDE static output feedback employing locally collocated piecewise uniform actuators and sensors. Moreover, a suboptimal GCFC problem is also addressed to minimize the cost bound. Finally, the developed method is applied to the cruise control and surface temperature cooling of a hypersonic rocket car.