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Optimal Distributed Control of Spatially Invariant Time Varying Linear Systems

by Seddik M Djouadi, Bhagyashri Telsang, Fatima Taousser, Mohammed M Olama
Publication Type
Conference Paper
Journal Name
IEEE Conference on Decision and Control (CDC)
Publication Date
Page Numbers
1 to 6
Conference Name
The 57th IEEE Conference on Decision and Control (CDC 2018)
Conference Location
Miami, Florida, United States of America
Conference Sponsor
Conference Date

In this paper, the optimal distributed linear time vaying H2 control problem for cone causal spatially invariant linear time varying (SILTV) systems is considered. This class of systems was initially defined in the work of Voulgaris et al. for cone causal spatially invariant (SI) linear time invariant (LTI) systems. First, the optimal time varying H2 problem is posed using a version of the Youla parameterization. This allows to transform the problem into an affine form which results in a convex but infinite dimensional distributed optimization. Next, the problem is solved by computing an operator projection on a class of time varying Youla parameters with a cone causal distributed structure. The cone causal spatially invariant systems are viewed as input-output multiplicative operators with a mixed causal time varying structure with respect to time, and spatially invariant with respect to the space dimension.