In this paper, we propose a novel method for addressing Optimal Control Problems (OCPs) with input-affine dynamics and cost functions. This approach adopts a Model Predictive Control (MPC) strategy, wherein a controller is synthesized to handle an approximated OCP within a finite time horizon. Upon reaching this horizon, the controller is re-calibrated to tackle another approximation of the OCP, with the approximation updated based on the final state and time information. To tackle each OCP instance, all non-polynomial terms are Taylor-expanded about the current time and state and the resulting Hamilton-Jacobi-Bellman (HJB) PDE is solved via Sum-of-Squares (SOS) programming, providing us with an approximate polynomial value function that can be used to synthesize a bang-bang controller.
@article{arxiv.2402.08148,
title = {Model Predictive Bang-Bang Controller Synthesis via Approximate Value Functions},
author = {Morgan Jones and Yuanbo Nie and Matthew M. Peet},
journal= {arXiv preprint arXiv:2402.08148},
year = {2024}
}