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首页> 外文期刊>Journal of Optimization Theory and Applications >An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem
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An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem

机译：连续不等式约束最优控制问题的精确罚函数法

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摘要

In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous state and control inequality constraints. By using the control parametrization technique and a time scaling transformation, the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality terminal state constraints and continuous state inequality constraints. Each of these constrained optimal parameter selection problems can be regarded as an optimization problem subject to equality constraints and continuous inequality constraints. On this basis, an exact penalty function method is used to devise a computational method to solve these optimization problems with equality constraints and continuous inequality constraints. The main idea is to augment the exact penalty function constructed from the equality constraints and continuous inequality constraints to the objective function, forming a new one. This gives rise to a sequence of unconstrained optimization problems. It is shown that, for sufficiently large penalty parameter value, any local minimizer of the unconstrained optimization problem is a local minimizer of the optimization problem with equality constraints and continuous inequality constraints. The convergent properties of the optimal parameter selection problems with equality constraints and continuous inequality constraints to the original optimal control problem are also discussed. For illustration, three examples are solved showing the effectiveness and applicability of the approach proposed.
机译：在本文中，我们考虑了一类受相等的终端状态约束以及连续状态和控制不等式约束的最优控制问题。通过使用控制参数化技术和时间缩放变换，可以通过一系列具有相等终端状态约束和连续状态不等式约束的最优参数选择问题来近似约束最优控制问题。这些受约束的最优参数选择问题中的每一个都可以视为受等式约束和连续不等式约束的优化问题。在此基础上，采用精确的罚函数法设计一种计算方法，以解决这些具有等式约束和连续不等式约束的优化问题。主要思想是将由等式约束和连续不等式约束构成的精确惩罚函数增加到目标函数，从而形成一个新的惩罚函数。这引起了一系列无约束的优化问题。结果表明，对于足够大的惩罚参数值，无约束优化问题的任何局部极小值都是具有相等约束和连续不等式约束的优化问题的局部极小值。还讨论了具有相等约束和连续不等式约束的最优参数选择问题与原始最优控制问题的收敛性质。为了说明，解决了三个示例，显示了所提出方法的有效性和适用性。

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