Neuro-accelerated model predictive control via a low-fidelity to high-fidelity warmstart : a methodological exploration of how to speed up MPC through cascaded multifidelity schemes that combine interpolation and learning-based warmstarting

Abstract

This work investigates how an interior-point algorithm used to solve an optimal control problem (OCP) may be warmstarted by interpolating the solution of a related OCP, differing only in discretization time, thereby accelerating the solve. Transferring the solutions between the OCPs requires a mapping function, for this a zero-order-hold-based approximation is derived, and, separately, feedforward neural-networks are trained. Both mappings are evaluated against raw data, and, once embedded in a selection of proposed cascaded multifidelity solver topologies, by the net solve-time advantage they provide. In-distribution, the proposed topologies reduced the mean time to solve the high-fidelity OCP by approximately 40% compared to a direct high-fidelity solve. More importantly, the warmstart roughly halved the worst-case fresh-solve time. While the neural networks achieved better mapping accuracy, their in-deployment benefit was at most comparable to that of the zero-order-hold approach, and they proved susceptible to out-of-distribution inputs. The approach delivers a meaningful benefit that scales with applications in which good solver initializations are otherwise hard to obtain, and it does so without compromising any optimality guarantees.