2020/08/25 by Emily Jensen, Jensen, Emily, Bassam Bamieh +1
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #Formal Methods in Verification #Petri Nets in System Modeling #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2008.11291
openalex publication_date 2020/08/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We consider the optimal distributed controller design problem subject to two\nstructural requirements: locality, i.e. available measurements and\nsub-controllers' interactions are governed by a graph structure, and relative\nfeedback, i.e. only differences of measurements are available to the\ncontroller. We formalize controller locality in terms of the controller's\ntransfer function, state-space realization, or resulting closed-loop mapping.\nWe demonstrate that the relative feedback requirement can be written as a\nconvex constraint on the controller and (in special cases) on the resulting\nclosed-loop, and we characterize the allowable structures of relative feedback\ncontrollers. We prove that sparse closed-loop design is a convex relaxation of\nstructured controller state-space design, even in the continuous time IIR\nsetting. This formalizes and extends results of the recently developed System\nLevel Synthesis framework. We take a first step toward quantifying the\nperformance gap associated with this convex relaxation by constructing a class\nof examples (based on relative feedback requirements) for which the difference\nin performance, measured by an H2 norm, is infinite. The results presented are\nused to contrast several issues of structural constraints in distributed\ncontrol design that remain as open problems.\n