Optimal Control of Nonlinear Systems with Time Delays: An Online ADP Perspective

Abstract

Drawing upon Lyapunov stability theories and online adaptive dynamic programming (ADP) technique, we propose a novel optimal control scheme for the nonlinear time delay system. Our contribution is twofold. First, we investigate the asymptotical stability problem and obtain a generalized stability condition in terms of linear matrix inequalities (LMIs). An explicit, easy-computing delay bound is presented by virtue of Gronwall's inequality. Second, we propose the neural network (NN)-based optimal control strategy by utilizing two approximate NNs. The NN-based optimal control law converges to the real optimal control law since that the estimation errors of NNs weights converge to zero. Numerical examples are presented to illustrate our results.