In the present paper, an efficient pseudospectral method for solving the Hamiltonian boundary value problems arising from a class of switching optimal control problems is presented. For this purpose, based on the Pontryagin's minimum principle, the first-order necessary conditions of optimality are derived. Then, by partitioning the time interval related to the problem under study into some subintervals, the states (and costates) and control functions are approximated on each subintervals with piecewise interpolating polynomials based on Legendre–Gauss–Radau points and a piecewise constant function, respectively. As a result, solution of the problem is turned into solution of a number of algebraic equations, in which the values of the states (and costates) and control functions at Legendre–Gauss–Radau points as well as switching and terminal points are allowed to be unknown. Numerical examples are presented at the end to show the efficiency of the proposed method.

中文翻译：

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一种间接求解一类切换最优控制问题的改进伪谱方法

在本文中，提出了一种有效的伪谱方法来解决由一类切换最优控制问题引起的哈密顿边值问题。为此，基于庞特里亚金最小原理，推导出最优性的一阶必要条件。然后，通过将与正在研究的问题相关的时间间隔划分为一些子间隔，状态（和协变量）和控制函数在每个子间隔上分别用基于勒让德-高斯-拉道点的分段插值多项式和分段常数函数近似. 结果，问题的解变成了许多代数方程的解，其中允许在 Legendre-Gauss-Radau 点以及开关点和终端点的状态（和坐标）和控制函数的值是未知的。最后给出了数值例子来说明所提出方法的有效性。