Numerical Algebraic Geometry for Optimal Control Applications
Numerical Algebraic Geometry for Optimal Control Applications
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DOI：
10.1137/090768308
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
P. Rostalski;I. Fotiou;Daniel J. Bates;A. Beccuti;M. Morari
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文献类型：
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作者：
P. Rostalski;I. Fotiou;Daniel J. Bates;A. Beccuti;M. Morari
提出了一种求解多项式非线性约束最优控制问题的新方法。该问题被重新表述为参数优化问题，进而通过两步过程来求解。首先，在预计算步骤中，对于参数的通用值，求解对应的一阶最优性条件的方程部分。这第一个解依赖于基本的代数几何，使得在每个后续时间步长的测量参数值上有效地和实时地求解相应的最优控制问题成为可能。这种方法在每一步都有找到全局最优解的概率保证。针对电力电子领域中DC-AC转换器和DC-DC转换器的两种应用，讨论了控制器综合问题。
A new technique for solving polynomial nonlinear constrained optimal control problems is presented. The problem is reformulated into a parametric optimization problem, which in turn is solved in a two-step procedure. First, in a precomputation step, the equation part of the corresponding first order optimality conditions is solved for a generic value of the parameter. Relying on the underlying algebraic geometry, this first solution makes it possible to solve efficiently and in real time the corresponding optimal control problem at the measured parameter value for each subsequent time step. This approach has a probability one guarantee of finding the global optimal solution at each step. Controller synthesis for two applications from the area of power electronics featuring a dc-ac converter and a dc-dc converter are discussed to motivate the proposed approach.