Extreme Theory of Functional Connections with Receding Horizon Control for Aerospace Applications

This paper introduces a novel closed-loop optimal controller that integrates the Extreme Theory of Functional Connections (X-TFC) with receding horizon control (RHC), referred to as X-TFC-RHC. The controller reformulates a sequence of linearized or quasi-linearized optimal control problems into two-point boundary value problems (TPBVPs) using the indirect method of optimal control. X-TFC then solves each TPBVP by approximating the solution with constrained expressions. These expressions consist of radial basis function neural networks (RBFNNs) and terms that satisfy the TPBVP constraints analytically. The RBFNNs are initialized offline using a particle swarm optimizer, which enables X-TFC to solve the TPBVPs efficiently online during each RHC iteration. The effectiveness of X-TFC-RHC is demonstrated through several aerospace guidance applications, which highlight its accuracy and computational efficiency in executing the RHC process. The proposed approach is also compared with state-of-the-art indirect pseudospectral methods and the traditional backward sweep method.