Bayesian Optimisation for Robust Model Predictive Control under Model Parameter Uncertainty

TL;DR

This paper introduces a Bayesian optimisation method with heteroscedastic noise modeling for tuning stochastic MPC hyper-parameters and estimating model parameters, resulting in improved control performance and stability.

Contribution

It presents a novel Bayesian optimisation algorithm that accounts for varying noise levels in hyper-parameter tuning of stochastic MPC, enhancing robustness and performance.

Findings

Higher cumulative rewards achieved in simulations.

More stable controllers demonstrated in robotics tasks.

Effective joint estimation of control and dynamics parameters.

Abstract

We propose an adaptive optimisation approach for tuning stochastic model predictive control (MPC) hyper-parameters while jointly estimating probability distributions of the transition model parameters based on performance rewards. In particular, we develop a Bayesian optimisation (BO) algorithm with a heteroscedastic noise model to deal with varying noise across the MPC hyper-parameter and dynamics model parameter spaces. Typical homoscedastic noise models are unrealistic for tuning MPC since stochastic controllers are inherently noisy, and the level of noise is affected by their hyper-parameter settings. We evaluate the proposed optimisation algorithm in simulated control and robotics tasks where we jointly infer control and dynamics parameters. Experimental results demonstrate that our approach leads to higher cumulative rewards and more stable controllers.