Optimal control: linear quadratic methods
Optimal control: linear quadratic methods
An introduction to infinite-dimensional linear systems theory
An introduction to infinite-dimensional linear systems theory
State-Space and Frequency Domain Methods in the Control of Distributed Parameter Systems
State-Space and Frequency Domain Methods in the Control of Distributed Parameter Systems
Convex synthesis of localized controllers for spatially invariant systems
Automatica (Journal of IFAC)
Design of optimal controllers for spatially invariant systems with finite communication speed
Automatica (Journal of IFAC)
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Design of optimal distributed controllers with a priori assigned localisation constraints is a difficult problem. Alternatively, one can ask the following question: given a localised distributed exponentially stabilising controller, is it inversely optimal with respect to some cost functional? We study this problem for linear spatially invariant systems and establish a frequency domain criterion for inverse optimality (in the LQR sense). We utilise this criterion to separate localised controllers that are never optimal from localised controllers that are optimal. For the latter, we provide examples to demonstrate optimality with respect to physically appealing cost functionals. These are characterised by state penalties that are not fully decentralised and they provide insight about spatial extent of the LQR weights that lead to localised controllers.