Optimal control of switched systems based on parameterization of the switching instants
Optimal control of switched systems based on parameterization of the switching instants
复制标题
DOI：
10.1109/tac.2003.821417
复制
发表时间：
2004-01
影响因子：
6.8
通讯作者：
Xuping Xu;P. Antsaklis
中科院分区：
文献类型：
--
作者：
Xuping Xu;P. Antsaklis
本文提出了一种解决切换系统最优控制问题的新方法。我们专注于给定了活动子系统的预先指定序列的问题。对于此类问题，我们需要寻找最优切换时刻以及最优连续输入。为了搜索最优切换时刻，需要知道最优成本关于切换时刻的导数。本文最重要的贡献是一种方法，该方法首先将一个最优控制问题转化为一个由切换时刻参数化的等价问题，然后基于由状态方程、协态方程、驻点方程、边界条件和连续性条件以及它们的导数所构成的两点边值微分代数方程的解来获得导数的值。这种方法被应用于一般的切换线性二次型问题，并且开发了一种基于初值常微分方程解的高效方法。该方法的一个扩展也被应用于具有内部强制切换的问题。文中给出了示例以说明结果。
This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a prespecified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. In order to search for the optimal switching instants, the derivatives of the optimal cost with respect to the switching instants need to be known. The most important contribution of the paper is a method which first transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and then obtains the values of the derivatives based on the solution of a two point boundary value differential algebraic equation formed by the state, costate, stationarity equations, the boundary and continuity conditions, along with their differentiations. This method is applied to general switched linear quadratic problems and an efficient method based on the solution of an initial value ordinary differential equation is developed. An extension of the method is also applied to problems with internally forced switching. Examples are shown to illustrate the results in the paper.