Online Constraint Tightening in Stochastic Model Predictive Control: A Regression Approach

TL;DR

This paper introduces a data-driven, online method for learning constraint-tightening parameters in stochastic model predictive control, improving constraint satisfaction and reducing costs by using Gaussian process regression.

Contribution

It proposes a novel regression-based approach to adaptively learn constraint-tightening parameters during control, addressing the challenge of unknown noise distributions.

Findings

Constraints are satisfied with high probability.

Lower average costs compared to existing methods.

Tight constraint satisfaction in numerical experiments.

Abstract

Solving chance-constrained stochastic optimal control problems is a significant challenge in control. This is because no analytical solutions exist for up to a handful of special cases. A common and computationally efficient approach for tackling chance-constrained stochastic optimal control problems consists of reformulating the chance constraints as hard constraints with a constraint-tightening parameter. However, in such approaches, the choice of constraint-tightening parameter remains challenging, and guarantees can mostly be obtained assuming that the process noise distribution is known a priori. Moreover, the chance constraints are often not tightly satisfied, leading to unnecessarily high costs. This work proposes a data-driven approach for learning the constraint-tightening parameters online during control. To this end, we reformulate the choice of constraint-tightening parameter for the closed-loop as a binary regression problem. We then leverage a highly expressive \gls{gp} model for binary regression to approximate the smallest constraint-tightening parameters that satisfy the chance constraints. By tuning the algorithm parameters appropriately, we show that the resulting constraint-tightening parameters satisfy the chance constraints up to an arbitrarily small margin with high probability. Our approach yields constraint-tightening parameters that tightly satisfy the chance constraints in numerical experiments, resulting in a lower average cost than three other state-of-the-art approaches.