切换系统优化控制方法研究

Study on optimal control of switching systems and characteristic disparity

针对一类特殊的混杂系统——切换系统的优化控制问题 ,提出了分段梯度下降优化方法 ,它是连续系统优化控制梯度下降法的推广 .对分段线性切换系统 ,通过一定变换 ,可以把切换系统转化成关于特定变量的连续系统 ,证明了切换系统整体优化控制目标等价于各子模态连续系统的优化目标之和 ,从而得到切换系统最优控制的梯度下降优化算法 ,该方法能够有效地得出切换系统优化控制的局部最优解 .给出了具体示例 。

Piecewise gradient descendent optimization algorithm is proposed to solve optimal control prob- lems in switching systems,a special type of hybrid systems. This method is extension to the traditional gradientdescendentoptimization algorithm for continuousdynamic systems. Forlinearpiecewise switching systems,they can be transferred to continuous systems involving some special variables via a certain kind of transformation.It has been proved in this paper that the overall performance objective of the original switching system is equivalent to the sum of the performance objectives of respective continuous systems according to each discrete modal.On this basis,for optimal control problems of switching systems,the proposed gradient descendent optimization algorithm can be achieved. This method can give out the local optimal control solution effectively. An example of an optimal control problem happening in a switching system is illustrated to verify the effectiveness of the proposed algorithm.