On the Hybrid Optimal Control Problem: Theory and Algorithms
On the Hybrid Optimal Control Problem: Theory and Algorithms
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DOI：
10.1109/tac.2007.904451
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发表时间：
2007-09
影响因子：
6.8
通讯作者：
M. S. Shaikh;P. Caines
中科院分区：
文献类型：
--
作者：
M. S. Shaikh;P. Caines
构造了一类具有可控位置转移和自主位置转移系统的混合最优控制问题，给出了混合系统轨迹最优性的一组必要条件，这些条件共同构成了标准极大值原理的推广；给出了开有界控制值集和紧控制值集的情况。本文的推导采用：(i)经典变分和针变分技术；（ii）一个局部可控性条件，用于建立自主切换情况下的伴随和哈密顿跳跃条件。利用混合最小原则（HMP）的必要条件，提出了一类基于混合最小原则的混合系统优化算法，并对自主切换情况和受控切换情况进行了分析。利用罚函数法理论和Ekeland变分原理的结果，在合理的假设下证明了这些算法的收敛性。通过算例说明了所提算法的有效性。
A class of hybrid optimal control problems (HOCP) for systems with controlled and autonomous location transitions is formulated and a set of necessary conditions for hybrid system trajectory optimality is presented which together constitute generalizations of the standard Maximum Principle; these are given for the cases of open bounded control value sets and compact control value sets. The derivations in the paper employ: (i) classical variational and needle variation techniques; and (ii) a local controllability condition which is used to establish the adjoint and Hamiltonian jump conditions in the autonomous switching case. Employing the hybrid minimum principle (HMP) necessary conditions, a class of general HMP based algorithms for hybrid systems optimization are presented and analyzed for the autonomous switchings case and the controlled switchings case. Using results from the theory of penalty function methods and Ekeland's variational principle the convergence of these algorithms is established under reasonable assumptions. The efficacy of the proposed algorithms is illustrated via computational examples.