Motivated by various distributed control applications, we consider a linear system with Gaussian noise observed by multiple sensors which transmit measurements over a dynamic lossy network. We characterize the stationary optimal sensor scheduling policy for the finite horizon, discounted, and longterm average cost problems and show that the value iteration algorithm converges to a solution of the average cost problem. We further show that the suboptimal policies provided by the rolling horizon truncation of the value iteration also guarantee geometric ergodicity and provide nearoptimal average cost. Lastly, we provide qualitative characterizations of the multidimensional set of measurement loss rates for which the system is stabilizable for a static network, significantly extending earlier results on intermittent observations.
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A minplus fundamental solution semigroup for a class of approximate infinite dimensional optimal control problems
By exploiting minplus linearity, semiconcavity,
and semigroup properties of dynamic programming, a fundamental
solution semigroup for a class of approximate finite
horizon linear infinite dimensional optimal control problems is
constructed. Elements of this fundamental solution semigroup
are parameterized by the time horizon, and can be used to
approximate the solution of the corresponding finite horizon
optimal control problem for any terminal cost. They can also
be composed to compute approximations on longer horizons.
The value function approximation provided takes the form of
a minplus convolution of a kernel with the terminal cost. A
general construction for this kernel is provided, along with a
spectral representation for a restricted class of subproblems.
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 Award ID(s):
 1908918
 NSFPAR ID:
 10170566
 Date Published:
 Journal Name:
 Proceedings of the American Control Conference
 ISSN:
 07431619
 Page Range / eLocation ID:
 794799
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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