Broad Learning System Approximation-Based Adaptive Optimal Control for Unknown Discrete-Time Nonlinear Systems

This article investigates optimal control problem for a class of discrete-time (DT) nonlinear systems with unknown dynamics. With the help of a broad learning system (BLS), a novel online adaptive dynamic programming (ADP) controller is presented. First, to approximate the unknown system dynamics, an approximator based on BLS is presented. The connection weights are calculated by the data of the system by using the ridge regression algorithm. Then, two BLSs are adopted to approximate the optimal cost function and optimal control law, respectively. The connection weights of these two BLSs are updated using the given weights tuning law at each sampling instant. The proposed optimal controller is proved to ensure that all the system states and estimation errors are uniform ultimate bounded. Finally, simulation examples are carried out to further demonstrate the effectiveness of the proposed BLS-based approximator and optimal controller.