Minimization of constraint violation probability in model predictive control. (15th June 2021)

• Record Type: Journal Article
• Authors: Brüdigam, Tim; Gaßmann, Victor; Wollherr, Dirk; Leibold, Marion
• Is Part Of: International journal of robust and nonlinear control. Volume 31:Number 14(2021)
• Page Start: 6740
• Page End: 6772
• Publication Date: 2021-06-15
• Subjects: chance constraint -- recursive feasibility -- robust model predictive control -- safety‐critical system -- stochastic model predictive control; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5636
• Languages: English
• ISSNs: 1049-8923

Abstract

Abstract: For Model Predictive Control in safety‐critical systems it is not only important to bound the probability of constraint violation but to reduce this constraint violation 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 even under changing uncertainty. We propose a novel two‐step 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. Recursive feasibility and convergence of the method are proved. A simulation demonstrates the effectiveness of the proposed method for a collision avoidance example.