Suboptimal guaranteed cost fuzzy control design for nonlinear ODE coupled with semi-linear parabolic PDE system

This paper proposes a suboptimal guaranteed cost fuzzy control design for a class of nonlinear coupled systems, which are described by an n-dimensional nonlinear ordinary differential equations (ODEs) and a semi-linear scalar parabolic partial differential equation (PDE) connected in feedback. Initially, the nonlinear coupled system is represented by a Takagi-Sugeno (T-S) fuzzy coupled ODE-PDE model. Then, on the basis of the obtained T-S fuzzy coupled model, the control design method is developed in terms of linear matrix inequalities (LMIs) to exponentially stabilize the fuzzy coupled system while providing an upper bound on the cost function. The proposed feedback controller consists of the ODE state feedback and the PDE static output feedback employing collocated pointwise actuators-sensors. By utilizing the existing LMI optimization techniques, a suboptimal fuzzy control problem is also devoted to minimize the upper bound of the cost function. Finally, the effectiveness of the proposed method is verified by a numerical simulation on the control of a hypersonic rocket car.