Abstract

In this chapter, optimal control problems of discrete-time nonlinear systems, including optimal regulation, optimal tracking control, and constrained optimal control, are studied by using a series of value iteration (VI) adaptive dynamic programming (ADP) approaches. First, an ADP scheme based on general value iteration (GVI) is developed to obtain near optimal control for discrete-time affine nonlinear systems. Then, the GVI-based ADP algorithm is employed to solve the infinite-horizon optimal tracking control problem for a class of discrete-time nonlinear systems. Moreover, using the globalized dual heuristic programming technique, the VI-based optimal control strategy of unknown discrete-time nonlinear systems with input constraints is established as a special case. Finally, an iterative \(\theta \)-ADP algorithm is developed to solve the optimal control problem of infinite-horizon discrete-time nonlinear systems, which shows that each of the iterative controls can stabilize the nonlinear system and the condition of initial admissible control is avoided effectively. Simulation examples are included to verify the effectiveness of the present control strategies.

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