Explicit multiobjective model predictive control for nonlinear systems with symmetries
Explicit multiobjective model predictive control for nonlinear systems with symmetries
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DOI：
10.1002/rnc.5281
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发表时间：
2018-09
影响因子：
3.9
通讯作者：
S. Ober-Blöbaum;Sebastian Peitz
中科院分区：
文献类型：
--
作者：
S. Ober-Blöbaum;Sebastian Peitz
模型预测控制是构造动态系统反馈控制回路的一种重要方法。由于实时的限制，在很短的时间内解决基于模型的最优控制问题可能是具有挑战性的。对于线性二次问题，Bemporad等人提出了一个显式的公式，其中潜在的优化问题是在离线阶段先验地解决的。在本文中，我们从两个重要方面介绍了这一概念的扩展。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，我们建立一个帕累托最优解的库，然后在在线阶段根据决策者的偏好得到一个有效的折衷解。由于标准的多参数规划方法在非线性情况下不再有效，我们转而使用库的不同条目之间的内插。为了减少离线阶段必须解决的问题的数量，我们利用了动力系统的对称性和相应的多目标最优控制问题。用两个不同的自动驾驶算例验证了结果。
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 Since the standard multiparametric programming approach is no longer valid in the nonlinear situation, we instead use interpolation between different entries of the library.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.