Scheduling Kalman Filters in Continuous Time - Mathematics > Optimization and ControlReport as inadecuate

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Abstract: A set of N independent Gaussian linear time invariant systems is observed byM sensors whose task is to provide the best possible steady-state causalminimum mean square estimate of the state of the systems, in addition tominimizing a steady-state measurement cost. The sensors can switch betweensystems instantaneously, and there are additional resource constraints, forexample on the number of sensors which can observe a given systemsimultaneously. We first derive a tractable relaxation of the problem, whichprovides a bound on the achievable performance. This bound can be computed bysolving a convex program involving linear matrix inequalities. Exploiting theadditional structure of the sites evolving independently, we can decompose thisprogram into coupled smaller dimensional problems. In the scalar case withidentical sensors, we give an analytical expression of an index policy proposedin a more general context by Whittle. In the general case, we develop open-loopperiodic switching policies whose performance matches the bound arbitrarilyclosely.

Author: Jerome Le Ny, Eric Feron, Munther A. Dahleh


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