Explicit multiobjective model predictive control for nonlinear systems with symmetries

摘要

Model predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real-time constraints, solving model-based optimal control problems in a very short amount of time can be challenging. For linear-quadratic problems, Bemporad et al have proposed an explicit formulation where the underlying optimization problems are solved a priori in an offline phase. In this article, we present an extension of this concept in two significant ways. We consider nonlinear problems and-more importantly-problems with multiple conflicting objective functions. In the offline phase, we build a library of Pareto optimal solutions from which we then obtain a valid compromise solution in the online phase according to a decision maker's preference. Since the standard multiparametric programming approach is no longer valid in the nonlinear situation, we instead use interpolation between different entries of the library. To reduce the number of problems that have to be solved in the offline phase, we exploit symmetries in the dynamical system and the corresponding multiobjective optimal control problem. The results are verified using two different examples from autonomous driving.