In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples.
Bibliographical noteFunding Information:
This research has been supported partially supported by NSF ECS-0901846 and NSF CCF-1320643 . The material in this paper was partially presented at the 50th IEEE Conference on Decision and Control, December 12–15, 2011, Orlando, FL, USA. This paper was recommended for publication in revised form by Associate Editor Giancarlo Ferrari-Trecate under the direction of Editor Ian R. Petersen. Partial version of this paper has appeared in Li and Elia (2011) .
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- Kalman filter
- Networked control systems
- Sensor scheduling
- Sensor selection
- Stochastic scheduling