Stochastic MPC with robustness to bounded parametric uncertainty

TL;DR

This paper introduces a stochastic model predictive control method that effectively manages bounded parametric uncertainty and stochastic noise using homothetic tubes and probabilistic reachable sets, providing less conservative guarantees.

Contribution

It presents a novel stochastic MPC scheme combining homothetic tubes for parametric uncertainty and probabilistic reachable sets for noise, with a strategy to generate robustified PRS based on moments.

Findings

Demonstrated effectiveness on an illustrative example.

Applied to building temperature control with promising results.

Provided an average asymptotic performance bound for the closed-loop system.

Abstract

The performance of model-based control techniques strongly depends on the quality of the employed dynamics model. If strong guarantees are desired, it is therefore common to robustly treat all possible sources of uncertainty, such as model inaccuracies or external disturbances. This, however, can result in overly conservative control strategies. In this paper, we present a stochastic model predictive control approach for discrete-time LTI systems subject to bounded parametric uncertainty and potentially unbounded stochastic additive noise. The proposed scheme makes use of homothetic tubes along the prediction horizon for a robust treatment of parametric uncertainty. Stochastic noise is handled by non-conservatively tightening constraints using the concept of probabilistic reachable sets (PRS). In order to accommodate all possible parametric uncertainties, we provide a strategy for generating "robustified" PRS based only on first and second moments of the noise sequence. In the case of quadratic cost functions, and under a further i.i.d. assumption on the noise distribution, we also provide an average asymptotic performance bound for the l2-norm of the closed-loop state. Finally, we demonstrate our scheme on both an illustrative example, and in a building temperature control problem.