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RLS Algorithms and Convergence Analysis Method for Online DLQR Control Design via Heuristic Dynamic Programming

In this paper, a method to design online optimal policies that encompasses Hamilton-Jacobi-Bellman (HJB) equation solution approximation and heuristic dynamic programming (HDP) approach is proposed. Recursive least squares (RLS) algorithms are developed to approximate the HJB equation solution that is supported by a sequence of greedy policies. The proposal investigates the convergence properties of a family of RLS algorithms and its numerical complexity in the context of reinforcement learning and optimal control. The algorithms are computationally evaluated in an electric circuit model that represents an MIMO dynamic system. The results presented herein emphasize the convergence behaviour of the RLS, projection and Kaczmarz algorithms that are developed for online applications.