2018/06/09 by Xudong Chen, Chen, Xudong
Computer Science · Decision Sciences · Mathematics · #Actuator #Computer science #Constraint (computer-aided design) #Control (management) #Control theory (sociology) #Controller (irrigation) #Convex optimization #Distributed Sensor Networks and Detection Algorithms #FOS: Electrical engineering #Gaussian #Linear system #Linear-quadratic-Gaussian control #Markov Chains and Monte Carlo Methods #Mathematical optimization #Mathematics #Nonlinear system #Optimal control #Optimization problem #Point (geometry) #Regular polygon #Risk and Portfolio Optimization #Separation principle #Stochastic control #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1806.03396
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2018/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.