Design of optimal controllers for spatially invariant systems with finite communication speed

Makan Fardad; Mihailo R. Jovanović

doi:10.1016/j.automatica.2011.01.032

Design of optimal controllers for spatially invariant systems with finite communication speed

Makan Fardad, Mihailo R. Jovanović

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed. We introduce a state-space framework in which all spatially invariant systems with this property can be characterized. After establishing the closure of such systems under linear fractional transformations, we formulate the ^H2 optimal control problem using the model-matching framework. We demonstrate that, even though the optimal control problem is non-convex with respect to some state-space design parameters, a variety of numerical optimization algorithms can be employed to relax the original problem, thereby rendering suboptimal controllers. In particular, for the case in which every subsystem has scalar input disturbance, scalar measurement, and scalar actuation signal, we investigate the application of the SteiglitzMcBride, GaussNewton, and Newton iterative schemes to the optimal distributed controller design problem. We apply this framework to examples previously considered in the literature to demonstrate that, by designing structured controllers with infinite impulse response, superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree.

Original language	English (US)
Pages (from-to)	880-889
Number of pages	10
Journal	Automatica
Volume	47
Issue number	5
DOIs	https://doi.org/10.1016/j.automatica.2011.01.032
State	Published - May 2011

Bibliographical note

Funding Information:
Dr. Jovanović’s research focuses on modeling, dynamics, and control of large-scale and distributed systems. He is a member of IEEE, SIAM, and APS and an Associate Editor of the IEEE Control Systems Society Conference Editorial Board. He received a CAREER Award from the National Science Foundation in 2007, and an Early Career Award from the University of Minnesota Initiative for Renewable Energy and the Environment in 2010.

Funding Information:
Financial support from the National Science Foundation under awards CMMI-09-27509, CMMI-09-27720, and CAREER Award CMMI-06-44793 is gratefully acknowledged. The material in this paper was partially presented at the 47th IEEE Conference on Decision and Control, December 9–11, 2008, Cancun, Mexico. This paper was recommended for publication in revised form by Associate Editor Xiaobo Tan under the direction of Editor Miroslav Krstic.

Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

Keywords

Cone causality
Finite propagation speed
Funnel causality
Optimal distributed control
Quadratic invariance
Spatially invariant systems

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title = "Design of optimal controllers for spatially invariant systems with finite communication speed",

abstract = "We consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed. We introduce a state-space framework in which all spatially invariant systems with this property can be characterized. After establishing the closure of such systems under linear fractional transformations, we formulate the H2 optimal control problem using the model-matching framework. We demonstrate that, even though the optimal control problem is non-convex with respect to some state-space design parameters, a variety of numerical optimization algorithms can be employed to relax the original problem, thereby rendering suboptimal controllers. In particular, for the case in which every subsystem has scalar input disturbance, scalar measurement, and scalar actuation signal, we investigate the application of the SteiglitzMcBride, GaussNewton, and Newton iterative schemes to the optimal distributed controller design problem. We apply this framework to examples previously considered in the literature to demonstrate that, by designing structured controllers with infinite impulse response, superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree.",

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N2 - We consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed. We introduce a state-space framework in which all spatially invariant systems with this property can be characterized. After establishing the closure of such systems under linear fractional transformations, we formulate the H2 optimal control problem using the model-matching framework. We demonstrate that, even though the optimal control problem is non-convex with respect to some state-space design parameters, a variety of numerical optimization algorithms can be employed to relax the original problem, thereby rendering suboptimal controllers. In particular, for the case in which every subsystem has scalar input disturbance, scalar measurement, and scalar actuation signal, we investigate the application of the SteiglitzMcBride, GaussNewton, and Newton iterative schemes to the optimal distributed controller design problem. We apply this framework to examples previously considered in the literature to demonstrate that, by designing structured controllers with infinite impulse response, superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree.

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Design of optimal controllers for spatially invariant systems with finite communication speed

Abstract

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Keywords

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