Adaptive fuzzy finite-time PID backstepping control for chaotic systems with full states constraints and unmodeled dynamics

Abstract

To solve the problem that the controlled object and system model cannot be fully mastered or the system parameters cannot be well obtained through conventional measurement methods, in this paper, a novel adaptive fuzzy finite-time PID backstepping control method is developed for a class of nonlinear chaotic systems with full state constraints and unmodeled dynamics. The unmodeled dynamics are handled by employing a dynamic signal. To avoid the violations of full state constraints (FSCs), a barrier Lyapunov function is used to implement a PID backstepping framework, whose merit consists in that three control gain constants KP, KI and KD with corresponding proportional relationships are designed to further improve control precision. Besides, the PID control method also embodies three dynamic gain components ΔKP, ΔKI and ΔKD, all of which are free functions that can be self-tuning online, and have a significant link with the adaptive law and modify accordingly. Finally, theoretical analysis confirms that all signals are ultimately uniformly bounded, the error signal converges to a nearby area near the origin in a finite-time, and the FSCs are not smashed. The practicality of the proposed method is confirmed by two simulation studies using the second-order Duffing chaotic system and third-order Chua's circuit.