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Optimal \(\mathcal H_2\) filtering for periodic linear stochastic systems with multiplicative white noise perturbations and sampled measurements. (English) Zbl 1395.93532

Summary: This paper addresses the problem of optimal \(\mathcal H_2\) filtering for a class of continuous-time periodic stochastic systems with periodic sampled measurements. The class of admissible filters consist of deterministic continuous-time periodic systems with finite jumps. The optimal solution of the considered optimization problem is obtained by integrating a suitable generalized continuous-time Riccati equation with finite jumps. To illustrate the proposed filtering strategy, we consider a problem of field monitoring where sensors are distributed on a rectangular region in order to estimate the state of a diffusion process. We consider that the sensors and the filter communicate over a communication channel and we assume that the communication channel induces some communication constraints. More specifically, we consider a medium access constraint under which the shared network can only accommodate a limited number of simultaneous communications between components.

MSC:

93E11 Filtering in stochastic control theory
93C05 Linear systems in control theory
93E03 Stochastic systems in control theory (general)
93C55 Discrete-time control/observation systems
93C73 Perturbations in control/observation systems
93C57 Sampled-data control/observation systems
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References:

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