论文标题
模型预测控制中的全局最优性通过隐藏的不变凸度
Global optimality in model predictive control via hidden invariant convexity
论文作者
论文摘要
在例如水或电力系统中出现的非凸线最佳控制问题通常涉及通过非线性平等约束相关的大量变量。理想的目标是找到全球最佳解决方案，数值体验表明，针对Karush-Kuhn-Tucker点的算法通常会发现（接近）最佳解决方案。在我们的论文中，我们为这种现象提供了理论的基础，表明在广泛的问题上，当使用隐式函数理论消除状态变量时，可以证明目标是控制决策变量的不变凸功能（INVEX函数）。通过这种方式，可以证明几乎全球最优性，其中全局最佳保证的确切性质取决于解决方案在可行集合中的位置。在一个数字示例中，我们显示了如何通过局部搜索室内控制问题获得高质量的解决方案。
Non-convex optimal control problems occurring in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush-Kuhn-Tucker points often find (near-)optimal solutions. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariantly convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, near-global optimality can be demonstrated, where the exact nature of the global optimality guarantee depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.
