In this article, an algorithm is presented for solving the optimal control problem for the general form of a hybrid switching system. The cost function comprises terminal, running and switching costs. The controlled system is an autonomous hybrid switching system with jumps either at some switching times or some time varying switching manifolds. The proposed algorithm is an extension of the first‐order gradient method for the conventional optimal control problem. The algorithm requires a low computational effort. The system's dynamical equations together with a set of algebraic equations are solved at each iteration in order to find the descent direction. The convergence of algorithm is proved and examples are provided to demonstrate the efficiency of the algorithm for different types of hybrid switching system optimal control problems.

中文翻译：

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一种求解混合切换系统最优控制问题的梯度算法

在本文中，提出了一种用于解决混合开关系统一般形式的最优控制问题的算法。成本函数包括终端，运行和转换成本。受控系统是一种自主混合开关系统，在某些开关时间或某些时间变化的开关歧管处具有跳跃。该算法是对传统最优控制问题的一阶梯度法的扩展。该算法需要较少的计算量。在每次迭代中求解系统的动力学方程以及一组代数方程，以找到下降方向。证明了算法的收敛性，并举例说明了该算法对不同类型的混合切换系统最优控制问题的有效性。