Distributed LQR Design for Identical Dynamically Decoupled Systems

We consider a set of identical decoupled dynamical systems and a control problem where the performance index couples the behavior of the systems. The coupling is described through a communication graph where each system is a node and the control action at each node is only function of its state and...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2008-09, Vol.53 (8), p.1901-1912
Main Authors: Borrelli, F., Keviczky, T.
Format: Article
Language:English
Subjects:
Applied sciences
Communication system control
Communication systems
Computer science
control theory
systems
Computer systems and distributed systems. User interface
Control system synthesis
Control systems
Control theory. Systems
Controllers
Design engineering
Design methodology
Distributed computing
Distributed control
Dynamical systems
Dynamics
Exact sciences and technology
Graphs
linear quadratic regulator (LQR)
network control systems
Optimal control
Performance analysis
Process control. Computer integrated manufacturing
Regulators
Robust stability
Robustness
Software
Stability analysis
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Summary:We consider a set of identical decoupled dynamical systems and a control problem where the performance index couples the behavior of the systems. The coupling is described through a communication graph where each system is a node and the control action at each node is only function of its state and the states of its neighbors. A distributed control design method is presented which requires the solution of a single linear quadratic regulator (LQR) problem. The size of the LQR problem is equal to the maximum vertex degree of the communication graph plus one. The design procedure proposed in this paper illustrates how stability of the large-scale system is related to the robustness of local controllers and the spectrum of a matrix representing the desired sparsity pattern of the distributed controller design problem.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2008.925826