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

Abstract

This article focuses on the design of fuzzy secure control for a class of coupled systems, which are modeled by a nonlinear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -dimensional ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -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.