Learning-Based Robust Adaptive Rapid Exponential Stabilization for a Class of Nonlinear CPSs Under DoS Attacks

For a class of uncertain nonlinear sampled-data cyber-physical systems (CPSs) under denial-of-service (DoS) attacks with average frequency and duration constraints, a learning-based rapidly exponentially stabilizing robust adaptive controller (RESRAC) is proposed to improve the control performance in this article. In order to enhance the system robustness against DoS attacks, a rapid exponential stabilization (RES) method is leveraged in controller design to accelerate the convergence rate of the system state. Meanwhile, to take into account the performance boundary of the system state, the learning algorithms are designed to mitigate the peaking phenomenon due to the high-gain feedback in the RES method. In the adaptation law design, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula>-modification combined with G+D estimator is adopted to robustly shape the dynamics of closed-loop system and enhance the steady-state performance. Through Lyapunov stability analysis, it is proved that the CPSs under the proposed control scheme can accommodate the effect of DoS attacks of nearly arbitrary intensity, i.e., the communication is not completely blocked. Finally, a numerical simulation is carried out to illustrate the effectiveness and superiority of the proposed control scheme.