Joint Actuator-sensor Design for Stochastic Linear Systems
This work provides a method for optimizing sensor and actuator placement in LQG control systems, which is important for control engineers but is incremental as it extends existing gradient-based optimization to a specific non-convex problem.
The paper addresses the joint actuator-sensor design problem for stochastic linear systems to minimize the expected quadratic cost, proposing a gradient descent algorithm that converges to a unique global minimum under certain conditions.
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.