Offline and Online Adaptive Critic Control Designs With Stability Guarantee Through Value Iteration

This article is concerned with the stability of the closed-loop system using various control policies generated by value iteration. Some stability properties involving admissibility criteria, the attraction domain, and so forth, are investigated. An offline integrated value iteration (VI) scheme with a stability guarantee is developed by combining the advantages of VI and policy iteration, which is convenient to obtain admissible control policies. Also, based on the concept of attraction domain, an online adaptive dynamic programming algorithm using immature control policies is developed. Remarkably, it is ensured that the state trajectory under the online algorithm converges to the origin. Particularly, for linear systems, the online ADP algorithm with a general scheme possesses more enhanced stability property. The theoretical results reveal that the stability of the linear system can be guaranteed even if the control policy sequence includes finite unstable elements. The numerical results verify the effectiveness of the present algorithms.