Adaptive Fixed-Time Prescribed Performance Control of Non-Smooth Systems Subject to Injection/Deception Attacks

Abstract

This paper studies a fixed-time output tracking control problem of non-smooth cyber-physical systems (CPSs) subject to injection/deception attacks and performance constraints. Cellina approximate selection theorem is employed to convert the non-smooth system into an equivalent smooth one, based on which we introduce a mapping transformation of the output tracking error to solve the performance constraints. Then an adaptive prescribed performance controller that involves a fuzzy logic system (FLS) to restrain the effect of unknown attacks is derived in the context of fixed-time control theory. By Lyapunov stability analysis, we prove that the proposed method is able to assure, in addition to the fixed-time stabilization of the closed-loop system, the evolvement of output tracking error along within the preset boundary regardless of injection/deception attacks. The effectiveness of the result, together with the superiority over the existing methods, is demonstrated by two simulation examples. Note to Practitioners—Numerous plants like connected vehicle and manipulator system actually belong to a class of CPSs with non-smooth dynamics, and thus are vulnerable to cyber attacks due to the use of network communication. Under the circumstance, the existing methods cannot enforce the control performance as required. Therefore, by introducing the mapping transformation based on measured error, we propose a practical prescribed performance control method, and this method is then improved by involving FLS to address the nonlinearity arising from attacks such that it is capable of achieving the pre-designated transient and steady-state performances despite the presence of either injection or deception attacks. Such merits make the proposed scheme widely suitable for the output tracking tasks that desire both control safety and performance guarantees, e.g., positioning-grabbing of the linked manipulator, collision-free-path tracking of the connected vehicle.