Toward Near-Globally Optimal Nonlinear Model Predictive Control via Diffusion Models

TL;DR

This paper introduces a diffusion model-based method for nonlinear model predictive control that achieves near-globally optimal solutions efficiently, overcoming local optimization limitations and reducing computation time.

Contribution

The paper presents a novel diffusion model approach for NMPC that enables near-global optimality without initial guesses, combining offline data generation with online control optimization.

Findings

High performance in numerical simulations

Lower computation times than global optimizers

Effective approximation of multi-modal optima distribution

Abstract

Achieving global optimality in nonlinear model predictive control (NMPC) is challenging due to the non-convex nature of the underlying optimization problem. Since commonly employed local optimization techniques depend on carefully chosen initial guesses, this non-convexity often leads to suboptimal performance resulting from local optima. To overcome this limitation, we propose a novel diffusion model-based approach for near-globally optimal NMPC consisting of an offline and an online phase. The offline phase employs a local optimizer to sample from the distribution of optimal NMPC control sequences along generated system trajectories through random initial guesses. Subsequently, the generated diverse dataset is used to train a diffusion model to reflect the multi-modal distribution of optima. In the online phase, the trained model is leveraged to efficiently perform a variant of random shooting optimization to obtain near-globally optimal control sequences without relying on any initial guesses or online NMPC solving. The effectiveness of our approach is illustrated in a numerical simulation indicating high performance benefits compared to direct neural network approximations of NMPC and significantly lower computation times than online solving NMPC using global optimizers.