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arXiv 1107.3099eess.SYcs.SYmath.OC
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切换系统中最优模式调度算法

Algorithm for Optimal Mode Scheduling in Switched Systems

Georgia Institute of Technology(佐治亚理工学院)

Yorai Wardi, Magnus Egerstedt

AI总结:

针对切换系统模式调度问题,提出一种直接操作调度空间、避免时间优化的算法,基于Armijo步长沿Gateaux导数方向迭代,证明收敛到局部极小值且具有快速收敛性。

摘要:

本文考虑计算切换动力系统中模式调度的问题,该调度最小化定义在系统连续状态变量轨迹上的成本泛函。最近解决此类最优控制问题的方法包括交替计算给定序列中模式间最优切换时间,以及通过向序列插入有限数量的新模式来更新模式序列的算法。这些算法由于模式序列的稀疏更新而存在固有的低效性,同时大部分计算时间用于优化给定模式序列的切换时间。本文提出一种直接操作调度空间而不诉诸时间优化问题的算法。它基于沿性能泛函的某些Gateaux导数的Armijo步长,从而避免了与离散调度参数相关的一些计算困难。证明了其收敛到局部极小值以及收敛速率,并在一个非线性系统上的仿真示例显示出相当快的收敛速度。

英文摘要:

This paper considers the problem of computing the schedule of modes in a switched dynamical system, that minimizes a cost functional defined on the trajectory of the system's continuous state variable. A recent approach to such optimal control problems consists of algorithms that alternate between computing the optimal switching times between modes in a given sequence, and updating the mode-sequence by inserting to it a finite number of new modes. These algorithms have an inherent inefficiency due to their sparse update of the mode-sequences, while spending most of the computing times on optimizing with respect to the switching times for a given mode-sequence. This paper proposes an algorithm that operates directly in the schedule space without resorting to the timing optimization problem. It is based on the Armijo step size along certain Gateaux derivatives of the performance functional, thereby avoiding some of the computational difficulties associated with discrete scheduling parameters. Its convergence to local minima as well as its rate of convergence are proved, and a simulation example on a nonlinear system exhibits quite a fast convergence.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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