A Framework for the Competitive Analysis of Model Predictive Controllers

Stijn Bellis, Joachim Denil, Ramesh Krishnamurthy, Tim Leys, Guillermo A. Pérez, Ritam Raha

Abstract: This paper presents a framework for the competitive analysis of Model Predictive Controllers (MPC). Competitive analysis means evaluating the relative performance of the MPC as compared to other controllers. Concretely, we associate the MPC with a regret value which quantifies the maximal difference between its cost and the cost of any alternative controller from a given class. Then, the problem we tackle is that of determining whether the regret value is at most some given bound. Our contributions are both theoretical as well as practical: (1) We reduce the regret problem for controllers modeled as hybrid automata to the reachability problem for such automata. We propose a reachability-based framework to solve the regret problem. Concretely, (2) we propose a novel CEGAR-like algorithm to train a deep neural network (DNN) to clone the behavior of the MPC. Then, (3) we leverage existing reachability analysis tools capable of handling hybrid automata with DNNs to check bounds on the regret value of the controller.