Resilient Safe Optimized Backstepping Control for High-Order Strict-Feedback System

Resilient performance is a critical safety aspect required for the learning-enabled control of safety-critical mechanical systems, which is an additional consideration for standalone static safety sets and currently is not yet well investigated. To address this limitation, this work proposed an adaptive safe optimized backstepping control for the high-order strict-feedback system that realizes resilient performance by flexibly adjusting the safe performance boundary with consideration of the system saturation limitation. Therefore, the concept of safety in the proposed method codifies the inherent safe adaptive learning mechanism and this resilient performance. More specifically, firstly, the adaptive optimized safe control of the overall system is designed with safe optimized backstepping and constraint adaptation mechanism to ensure the ultimate policy within the safe region during the whole learning phase. The constructed adaptive safe learning framework embodies the decomposition design with Barrier Lyapunov Functions-based optimized backstepping control that considers the performance-based state-variables constraints. Secondly, considering the resilient performance, the auxiliary system is designed to adaptively generate flexible performance boundaries based on the input saturation error while conflicts of saturation limitation occur, enabling the overall learning system to attain additional resilient performance during the whole control period. Comparison simulations consider the typical vehicle's longitudinal control problem to verify the effectiveness of the proposed method in showing the resilient performance of learning-enabled control of safety-critical systems.