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Online ADP-based Optimal Control of Nonlinear Time-delay Systems

Drawing upon Lyapunov stability theories and Neural Networks (NNs) techniques, we propose an online adaptive dynamic programming (ADP) based optimal control of nonlinear system with time delays. Our contribution is three-fold. First, we investigate the asymptotical stability on nonlinear time delay systems and reveal how the delay parameter may influence the stability. Second, we utilize two approximate NNs to estimate the optimal control policy such that the weights for both NNs are online tuned simultaneously. Third, we prove the convergence of NN weights estimation errors. Numerical examples are presented to illustrate our results.