Model-Free Optimal Control for Affine Nonlinear Systems With Convergence Analysis


In this paper, a self-learning management scheme is proposed for the infinite horizon optimal management of affine nonlinear systems based on the action dependent heuristic dynamic programming algorithm. The policy iteration technique is introduced to derive the optimal control policy with feasibility and convergence analysis. It shows that the “greedy” management action for every state is uniquely existent, the learned management policy when each policy iteration is admissible, and also the optimal management policy is ready to be obtained. 2 3-layer perceptron neural networks are employed to implement the scheme. The critic network is trained by a completely unique rule to evolve to the Bellman equation, and the action network is trained to yield a higher management policy. Each coaching processes alternate until the optimal management policy is achieved. Two simulation examples are provided to validate the effectiveness of the approach. Note to Practitioners - The objective of planning optimal controllers without mathematical models is sought by control practitioners, whereas existing approaches usually derive optimal controllers by accessing the mathematical models or identified models. This paper proposes a brand new approach which derives optimal controllers by numerical iteration method without accessing any information of the mathematical models. It offers evaluation for each state-action try in the full state-action house through the collected knowledge of the underlying system, and then selects the action with the most effective evaluation for each state. What is needed initial admissible control policy. Theorems show that optimal controllers will be acquired and simulation studies verify effectiveness. Further research will extend this approach to on-line self-learning optimal control approach, so it will adapt the variation of underlying systems.

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