Policy-Iteration-Based Active Disturbance Rejection Control for Uncertain Nonlinear Systems With Unknown Relative Degree

In this article, a policy-iteration-based active disturbance rejection control (ADRC) is proposed for uncertain nonlinear systems to achieve real-time output tracking performance, regardless of the specific relative degree of the system. The approach integrates a partial control input generator with a policy-iteration-based reinforcement learning (RL) agent for degree weight adjustment. The partial control input generator includes each ith order partial control input, which is constructed following the ADRC design framework for an ith order system. The RL agent adjusts the degree weights (its actions) to enhance the dominance of the partial control input corresponding to the unknown relative degree through iterative policy refinement. The RL agent is designed to minimize the quadratic reward as the performance index function while enhancing the influence of the partial control input associated with the correct relative degree via the policy iteration procedure. All signals in the closed-loop system (including the time-varying degree weights) ensure semi-global uniformly ultimately boundness using the Lyapunov stability theorem and the affinely quadratically stable property. Consequently, the degree weight adjustments by the RL agent do not affect the closed-loop stability. The proposed method does not require system dynamics, specific relative degree, external disturbances, and other state variable sensing beyond output sensing. The performance of the proposed method was validated via simulations for two different-order uncertain nonlinear systems and experiments using a permanent magnet synchronous motor testbed.