Fuzzy Secure Control for Nonlinear N-D Parabolic PDE-ODE Coupled Systems Under Stochastic Deception Attacks

This paper focuses on the design of fuzzy secure control for a class of coupled systems, which are modeled by a nonlinear $N$ -dimensional (N-D) parabolic partial differential equation (PDE) subsystem and an ordinary differential equation (ODE) subsystem. Under stochastic deception attacks, a fuzzy secure control scheme is designed, which is effective to tolerate the attacks and ensure the desired performance for the considered systems. A new fuzzy-dependent Poincare-Wirtinger's inequality (PWI) is proposed. Compared with the traditional Poincare's inequality, the fuzzy-dependent PWI is more flexible and less conservative. Meanwhile, an augmented Lyapunov-Krasovskii functional (LKF) is newly constructed, which strengthens the correlations of the PDE subsystem and ODE subsystem. Then, on the ground of the fuzzy-dependent PWI and the augmented LKF, new exponential stabilization criteria are set up for the PDE-ODE coupled systems. Finally, a hypersonic rocket car is presented to verify the effectiveness and less conservatism of the obtained results.