Without necessarily assuming that switching sequences are fixed, a dynamic optimization method is proposed for optimal control of state-dependent switched systems. First, a parameterization method is developed to parameterize the switching instants and control vectors to facilitate the calculation of the gradient information, and then the original problem becomes a finite-dimensional mixed discrete–continuous nonlinear program as the switching sequence is discrete and the other variables are continuous. Secondly, the mixed discrete–continuous nonlinear program is transformed into an equivalent problem that contains only continuous variables by relaxing 0 and 1 discrete variables into continuous variables between 0 and 1 and adding proper linear and quadratic constraints. Thirdly, the formulas to compute the gradients of the objective function with respect to all the arguments are derived by solving the variational systems and a two-point boundary value differential algebraic equations (DAEs). Fourthly, an algorithm is proposed to locate a feasible point satisfying the Karush–Kuhn–Tucker (KKT) conditions to a specified tolerance of dynamic optimization of switched systems (DOSS) while guaranteeing feasibility of inequality path constraints, and the finite convergence of the algorithm is proved. Finally, the performance of the algorithm is analyzed via a numerical example.

不必假设开关序列是固定的，提出了一种动态优化方法，用于状态相关开关系统的最优控制。首先，开发了一种参数化方法，将开关时刻和控制向量参数化，以方便梯度信息的计算，由于开关序列是离散的，其他变量，原问题变成了一个有限维混合离散-连续非线性程序是连续的。其次，通过将 0 和 1 离散变量放宽为 0 和 1 之间的连续变量，并添加适当的线性和二次约束，将混合离散-连续非线性规划转化为仅包含连续变量的等效问题。第三，通过求解变分系统和两点边值微分代数方程 (DAE) 推导了计算目标函数相对于所有参数的梯度的公式。第四，提出了一种算法来定位满足 Karush–Kuhn–Tucker (KKT) 条件的可行点到指定的切换系统动态优化 (DOSS) 容差，同时保证不等式路径约束的可行性，以及算法的有限收敛性被证明。最后通过算例分析了算法的性能。提出了一种算法，在保证不等式路径约束可行性的同时，将满足Karush-Kuhn-Tucker（KKT）条件的可行点定位到指定的切换系统动态优化（DOSS）容差，并证明了该算法的有限收敛性. 最后通过算例分析了算法的性能。提出了一种算法，在保证不等式路径约束可行性的同时，将满足Karush-Kuhn-Tucker（KKT）条件的可行点定位到指定的切换系统动态优化（DOSS）容差，并证明了该算法的有限收敛性. 最后通过算例分析了算法的性能。