Optimal State Feedback Control for Discrete-Time Systems
In this chapter, the optimal state feedback control problem is studied based on ADP for both infinite horizon and finite horizon. Three different structures of ADP are utilized to solve the optimal state feedback control strategies, respectively. First, considering a class of affine constrained systems, a new DHP method is developed to stabilize the system with convergence proof. Then, due to the special advantages of GDHP structure, a new optimal control scheme is developed with discounted cost functional. Moreover, based on a least-square successive approximation method, a series of GHJB equations are solved to obtain the optimal control solutions. Finally, a novel finite-horizon optimal control scheme is developed to obtain the suboptimal control solutions within a fixed finite number of control steps. Compared with the existing results in the infinite-horizon case, the present finite-horizon optimal controller is preferred in real-world applications.
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