Semi‐Global Adaptive Dynamic Programming

This chapter explores the adaptive dynamic programming (ADP) methods to handle affine nonlinear systems via neural network‐based approximation. An online learning method with convergence analysis is provided and it achieves semi‐global stabilization for nonlinear systems in that the domain of attraction can be made arbitrarily large, but bounded, by tuning the controller parameters or design functions. Two most frequently used techniques in reinforcement learning are value iteration and policy iteration. When the system dynamics are uncertain, the approximation can be realized using online information via reinforcement learning and ADP methods. Neural network‐based ADP methods for nonlinear control systems are being actively developed by a good number of researchers. Some recent theoretical results include ADP for non‐affine nonlinear systems, ADP for saturated control design, ADP for nonlinear games, and ADP for nonlinear tracking problems.