Abstract
SummaryModel 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 Since the standard multiparametric programming approach is no longer valid in the nonlinear situation, we instead use interpolation between different entries of the library.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.
Highlights
In many applications from industry and economy, several criteria are of equal interest
We present a detailed analysis of the algorithm developed in [12] and study under which conditions the multiobjective optimal control problem (MOCP) possesses symmetries that can be exploited to reduce the number of relevant parameters
Rather than using motion planning approaches, we exploit the motion primitive concept to design explicit model predictive control (MPC) algorithms for nonlinear MOCPs. This means that by identifying symmetries in the MOCP, Pareto sets are valid in multiple situations
Summary
In many applications from industry and economy, several criteria are of equal interest. Popular examples include production processes, where we want to maximize the quality while minimizing the production cost, or transportation, where the objectives are fast and energy efficient driving Since these objectives are in general contradictory, the solution consists of the set of optimal compromises – the so-called Pareto set – instead of a single optimum, and a compromise can be selected interactively according to a decision maker’s preference. A different approach is to stop the expensive computation prematurely and use non-converged solutions [7, 8] Another frequently applied way to incorporate multiple objectives is to use a classical feedback controller and optimize the controller parameters with respect to several criteria [9, 10].
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