Minimization of Constraint Violation Probability in Model Predictive Control

TL;DR

This paper introduces a new stochastic model predictive control method that minimizes the probability of constraint violations in uncertain environments, ensuring safety and feasibility while optimizing control objectives.

Contribution

It proposes a novel MPC scheme that minimizes constraint violation probability under uncertainty, with guarantees of recursive feasibility and convergence.

Findings

Method effectively reduces constraint violation probability.

Ensures recursive feasibility and convergence.

Demonstrated success in simulation example.

Abstract

While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability depending on a predefined risk parameter. However, for safety-critical systems it is not only important to bound the constraint violation probability but to reduce this probability as much as possible. Therefore, an approach is necessary that minimizes the constraint violation probability while ensuring that the Model Predictive Control optimization problem remains feasible. We propose a novel Model Predictive Control scheme that yields a solution with minimal constraint violation probability for a norm constraint in an environment with uncertainty. After minimal constraint violation is guaranteed the solution is then also optimized with respect to other control objectives. Further, it is possible to account for changes over time of the support of the uncertainty. We first present a general method and then provide an approach for uncertainties with symmetric, unimodal probability density function. Recursive feasibility and convergence of the method are proved. A simulation example demonstrates the effectiveness of the proposed method.