Adaptive Interleaved Reinforcement Learning: Robust Stability of Affine Nonlinear Systems with Unknown Uncertainty

This article investigates adaptive robust controller design for discrete-time (DT) affine nonlinear systems using an adaptive dynamic programming. A novel adaptive interleaved reinforcement learning algorithm is developed for finding a robust controller of DT affine nonlinear systems subject to matched or unmatched uncertainties. To this end, the robust control problem is converted into the optimal control problem for nominal systems by selecting an appropriate utility function. The performance evaluation and control policy update combined with neural networks approximation are alternately implemented at each time step for solving a simplified Hamilton-Jacobi-Bellman (HJB) equation such that the uniformly ultimately bounded (UUB) stability of DT affine nonlinear systems can be guaranteed, allowing for all realization of unknown bounded uncertainties. The rigorously theoretical proofs of convergence of the proposed interleaved RL algorithm and UUB stability of uncertain systems are provided. Simulation results are given to verify the effectiveness of the proposed method