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arXiv 1806.03396eess.SYcs.SY
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随机线性系统的联合执行器-传感器设计

Joint Actuator-sensor Design for Stochastic Linear Systems

University of Colorado, Boulder(科罗拉多大学博尔德分校)

Xudong Chen

AI总结:

本文研究随机线性控制系统中执行器-传感器联合设计问题,通过梯度下降算法最小化时间平均成本,证明在特定条件下算法能收敛到全局最优解。

摘要:

本文研究随机线性控制系统中执行器-传感器联合设计问题,具体针对识别一组传感器和执行器,以实现二次成本的最小期望值。众所周知,在线性二次高斯(LQG)控制问题中,最优反馈控制律可通过著名的分离原理获得。此外,如果系统是可稳定化和可检测的,那么无限时间平均成本存在。但此类成本依赖于传感器和执行器的布置。本文提出了在可接受的执行器-传感器对上最小化时间平均成本的优化问题,约束条件是它们的欧几里得范数固定。该问题是非凸的,通常难以解决。本文提出了一种梯度下降算法(在可接受的对集上)以最小化时间平均成本。此外,我们证明在某些特殊条件下,该算法可以导致唯一的局部(因此全局)最小点。

英文摘要:

We investigate the joint actuator-sensor design problem for stochastic linear control systems. Specifically, we address the problem of identifying a pair of sensor and actuator which gives rise to the minimum expected value of a quadratic cost. It is well known that for the linear-quadratic-Gaussian (LQG) control problem, the optimal feedback control law can be obtained via the celebrated separation principle. Moreover, if the system is stabilizable and detectable, then the infinite-horizon time-averaged cost exists. But such a cost depends on the placements of the sensor and the actuator. We formulate in the paper the optimization problem about minimizing the time-averaged cost over admissible pairs of actuator and sensor under the constraint that their Euclidean norms are fixed. The problem is non-convex and is in general difficult to solve. We obtain in the paper a gradient descent algorithm (over the set of admissible pairs) which minimizes the time-averaged cost. Moreover, we show that the algorithm can lead to a unique local (and hence global) minimum point under certain special conditions.

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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