论文部分内容阅读
In this paper we study optimal control problems with the control variable appearing linearly.A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented.This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem.The optimal control problem is partitioned as several stages,with each stage corresponding to a particular control arc.A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming (NLP) problem.The control profiles and stage lengths act as decision variables.Based on the Pontryagin maximal principle,a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers.Two examples are studied to demonstrate the effectiveness of this strategy.