This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. A sliding mode is coped with differential-algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion surface. In the second part of the paper we demonstrate the correspondence between the discrete adjoint equations and the discretized version of the continuous adjoint equations in the case of system equations described by DAEs. We show that the discrete adjoint state trajectories converge to their continuous counterparts. Next, we describe the application of the proposed procedure to three optimal control problems. The first problem concerns optimal control of a simple mechanical system with dry friction. The second problem is related to the planning of a haemodialysis process. The third problem concerns the optimal steering of a racing car.
翻译:本文涉及用滑动模式解决混合最佳控制问题的数字程序。 滑动模式与差异- 位数方程( DAEs) 打交道, 保证精确跟踪滑动运动表面。 在文件第二部分, 我们展示了离散的双联方程与连续联合方程的离散版本( DAEs描述的系统方程)之间的对应关系。 我们显示离散的双联状态轨迹与连续的对等轨迹汇合在一起。 其次, 我们描述对三个最佳控制问题应用拟议程序的情况。 第一个问题涉及对一个简单的机械系统进行最佳控制, 与干摩擦有关。 第二个问题与热解过程的规划有关。 第三个问题涉及赛车的最佳方向。