Model predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real-time constraints, the major challenge in MPC is to solve model-based optimal control problems in a very short amount of time. 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 Since the standard multi-parametric programming approach is no longer valid in this situation, we instead use interpolation between different entries of the library.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.

中文翻译：

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具有对称性的非线性系统的显式多目标模型预测控制

模型预测控制是构建动态系统反馈控制回路的重要方法。由于实时性的限制，MPC 的主要挑战是在很短的时间内解决基于模型的最优控制问题。对于线性二次问题，Bemporad 等人提出了一个明确的公式，其中潜在的优化问题在离线阶段先验地解决。在本文中，我们以两种重要的方式展示了这一概念的扩展。我们考虑非线性问题——更重要的是——具有多个相互冲突的目标函数的问题。在离线阶段，我们构建了一个帕累托最优解库，然后我们在在线阶段根据决策者的偏好从中获得有效的折衷解。由于标准的多参数编程方法在这种情况下不再有效，我们改为在库的不同条目之间使用插值。为了减少离线阶段必须解决的问题数量，我们利用动态系统中的对称性和相应的多目标最优控制问题。使用来自自动驾驶的两个不同示例验证了结果。