Convex relaxations for nonconvex optimal control problems
Convex relaxations for nonconvex optimal control problems
复制标题
非凸最优控制问题的凸松弛
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. I. Barton
中科院分区：
文献类型：
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作者：
Joseph K. Scott;P. I. Barton
研究了嵌入非线性控制系统的最优控制问题。利用控制系统的端点映射，这类问题可以写成关于允许控制集的非线性规划。虽然这类问题存在必要的最优性条件，但它们通常是非凸的，并且这样的条件是不充分的。给出了一个松弛过程，它产生一个凸规划，它的解值是原问题解值的一个有保证的下界。这一结果是使用分支定界框架开发用于最优控制问题的确定性全局优化技术的关键一步。主要的贡献在于，不同于沿着这些路线的其他发展，这里导出的凸低估程序在原始函数空间上是有效的；即不需要离散控制。
An optimal control problem with a nonlinear control system embedded is considered. Using the endpoint map of the control system, such problems can be written as nonlinear programs on the set of admissible controls. Though necessary optimality conditions exist for such problems, they are often nonconvex and such conditions are not sufficient. A relaxation procedure is outlined which generates a convex program whose solution value is a guaranteed lower bound on the solution value of the original problem. This result is a crucial step towards developing deterministic global optimization techniques for optimal control problems using a branch-and-bound framework. The major contribution is that, unlike other developments along these lines, the convex underestimating program derived here is valid on the original function space; i.e. there is no need to discretize the control.