Synchronized Optimization With Prescribed Performance for High-order Strict-feedback System

This paper investigates synchronized optimization with prescribed performance for the strict-feedback system with time-synchronized convergence property, which is the highly essential performance desired in various real-world high-precision control applications. The prescribed performance is considered to keep the state-variables within a predefined region during the control period to meet the required system performance. To consider optimization performance while also concurrently attaining the time-synchronized properties simultaneously of each backstepping subsystem, optimized backstepping is utilized to establish the learning framework; wherein the normnormalized sign function is appropriately incorporated in each backstepping subsystem, which generates the decomposition of the optimal system control and gradient term of the cost function with appropriate time-synchronized control items and unknown independently learning parts to be approximated with neural networks. With this decomposition design, the learning objective is transformed to adaptively explore the optimal control parameter in the admissible policy region. By additionally employing the adaptive dynamic programming technique, actor-critic method, and gradient-constrained method, the solution of the Hamilton-Jacobi-Bellman equation is iteratively approximated while the learnable parameter stays within the predefined region. The work here has the outcome of time-synchronized convergence which surpasses the usual typical developments in this class of problems considered. The proposed method is verified with the vehicle platoon problem to show its effectiveness in that the system preserves special properties of time-synchronized stability and control while optimizing the overall system control.