On Approximate Dynamic Programming with Multivariate Splines for Adaptive Control

We define a SDP framework based on the RLS TD algorithm and multivariate simplex B-splines. We introduce a local forget factor capable of preserving the continuity of the simplex splines. This local forget factor is integrated with the RLS TD algorithm, resulting in a modified RLS TD algorithm that is capable of tracking time-varying systems. We present the results of two numerical experiments, one validating SDP and comparing it with NDP and another to show the advantages of the modified RLS TD algorithm over the original. While SDP requires more computations per time-step, the experiment shows that for the same amount of function approximator parameters, there is an increase in performance in terms of stability and learning rate compared to NDP. The second experiment shows that SDP in combination with the modified RLS TD algorithm allows for faster recovery compared to the original RLS TD algorithm when system parameters are altered, paving the way for an adaptive highperformance non-linear control method.