In this paper, we consider an optimal control problem in which the control is almost smooth and the state and control are subject to terminal state constraints and continuous state and control inequality constraints. By introducing an extra set of differential equations for this almost smooth control, we transform this constrained optimal control problem into an equivalent problem involving both control function and system parameter vector as decision variables. Then, by the control parametrization technique and a time scaling transformation, the equivalent problem is approximated by a sequence of constrained optimal parameter selection problems, each of which is a finite dimensional optimization problem. For each of these constrained optimal parameter selection problems, a novel exact penalty function method is constructed by appending penalized constraint violations to the cost function. This gives rise to a sequence of unconstrained optimal parameter selection problems; and each of which can be solved by existing optimization algorithms or software packages. Finally, a practical container crane operation problem is solved, showing the effectiveness and applicability of the proposed approach.

中文翻译：

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最小化非线性最优控制问题中几乎平滑的控制变化

在本文中，我们考虑了一个最优控制问题，其中控制几乎是平滑的，并且状态和控制受终端状态约束以及连续状态和控制不等式约束的约束。通过为这种几乎平滑的控制引入额外的微分方程组，我们将这个约束最优控制问题转换为等效问题，该问题涉及控制函数和系统参数向量作为决策变量。然后，通过控制参数化技术和时间缩放变换，通过一系列约束的最优参数选择问题来近似等效问题，每个问题都是有限维优化问题。对于这些受约束的最佳参数选择问题，通过将惩罚约束违规附加到成本函数上，构造了一种新颖的精确惩罚函数方法。这就产生了一系列不受约束的最优参数选择问题。并且可以通过现有的优化算法或软件包来解决。最后，解决了一个实际的集装箱起重机操作问题，表明了该方法的有效性和适用性。