The optimal control of nonlinear systems is an important topic both in control theory research and control engineering practice. Though dynamic programming has been a useful technique in solving optimal control problems for many years, it is often computationally untenable to run it to obtain the optimal solutions. Therefore, the adaptive dynamic programming (ADP) approach, which combines dynamic programming with reinforcement learning, has become one of the key foci of control science, especially the intelligent control field. As a main method to be able to design truly brain-like general-purpose intelligent systems, the ADP approach has wide application prospects. However, the architecture of ADP approach is far from perfect. Many theoretical and technical issues of optimal control of nonlinear systems based on ADP have yet to be addressed. Under the support of the National Natural Science Foundation of China (61034002), the optimal control of nonlinear discrete-time systems using ADP is further studied in this thesis, the iterative ADP algorithms for different cases are developed, and the application scope of ADP is broadened significantly. The main contributions of the thesis include the following four parts. 1. The advanced implementation structures of ADP are investigated and then employed to handle the optimal control problems of unknown nonlinear discrete-time systems. It is well-known that the mathematical models of many real-world systems are difficult to build. Besides, existing structures cannot reach the objectives of getting small computational error and outputting directly the cost function simultaneously. Thus, for the first time, the iterative ADP algorithm using globalized dual heuristic programming (GDHP) technique is developed with convergence proof, in order to solve the optimal control problems of nonlinear systems with unknown dynamics. In addition, the iterative ADP algorithm which only consists of model network and critic network is investigated for the purpose of simplifying the implementation structure. The simulation results show that the proposed control schemes can not only solve the unknown nonlinear optimal control problems successfully, but also obtain satisfactory control performances. 2. The finite-horizon iterative ADP algorithm is developed and employed to devise finite-horizon optimal tracking controller for nonlinear discrete-time systems. First, the optimal tracking problem is converted into designing a finite-...
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