Supplementary Control for Quantized Discrete-Time Nonlinear Systems Under Goal Representation Heuristic Dynamic Programming

This article is concerned with supplementary control of discrete-time nonlinear systems with multiple controllers in the framework of goal representation heuristic dynamic programming (GrHDP), where a logarithmic quantizer is used to govern the network communication. For the addressed problem, a neural network (NN)-based observer is first proposed to estimate the unknown system state in the simultaneous presence of quantized influence. In light of the estimated states and the ideal control inputs via a zero-sum game, a GrHDP algorithm with a reinforced term is developed to implement the supplementary control task, where some novel weight updating rules are constructed by virtue of an additional tunable parameter to improve the system performance. Furthermore, a set of conditions about the stability of estimated error dynamics of both observer states and updated NNs' weights are derived by resorting to the Lyapunov stability theory. Finally, the effectiveness of the developed method is verified by a power system and a numerical experiment.