Optimal actuator placement for linear systems with limited number of actuators
Optimal actuator placement for linear systems with limited number of actuators
复制标题
执行器数量有限的线性系统的最佳执行器放置
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Azarm
中科院分区：
文献类型：
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作者：
Prasad Vilas Chanekar;N. Chopra;S. Azarm
一个完全可控的线性动力系统可以在输入控制能量的作用下从任意给定的初始状态转向任意指定的最终状态。输入控制能量是通过执行器的组合提供的。希望有有限数量的执行器，这也提出了多个执行器组合的可能性，使系统完全可控。因此，作动器的最优放置问题在系统设计中非常重要。以往的研究主要集中在利用贪心启发式方法求解执行器的最优放置问题，该方法可以提供次优解。本文将执行器的最优布局问题描述为一个0/1混合整数半定规划问题，并采用分支定界法求解。问题表述既适用于稳定系统，也适用于不稳定系统，求解过程不需要初始可控致动器组合（起点）。虽然在这项工作中没有提供关于计算解的最优性的理论保证，但对两个示例进行的数值模拟产生了最优执行器放置问题的全局最优解。
A completely controllable linear dynamical system can be steered from any given initial state to any specified final state with an application of input control energy. The input control energy is provided through a combination of actuators. It is desirable to have a limited number of actuators, which also presents the possibility of multiple actuator combinations that render the system completely controllable. Hence, the optimal actuator placement problem very important in system design. Previous studies have been mainly focused on solving the optimal actuator placement problem using greedy heuristic methods which can provide a sub-optimal solution. In this work, the optimal actuator placement problem is presented as a 0/1-mixed integer semidefinite programming problem, and is solved using the branch-and-bound procedure. The problem formulation can be applied to both stable and unstable systems, and the solution procedure does not require an initial controllable actuator combination (starting point). Although no theoretical guarantees regarding optimality of the computed solution is provided in this work, numerical simulations performed on two examples yield the global optimal solution for the optimal actuator placement problem.