Closed-loop analysis and feedback design in the presence of limited information

Li, Dapeng

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https://hdl.handle.net/2142/24370 Copy

Description

Title

Closed-loop analysis and feedback design in the presence of limited information

Author(s)

Li, Dapeng

Issue Date

2011-05-25T14:37:16Z

Director of Research (if dissertation) or Advisor (if thesis)

Hovakimyan, Naira

Doctoral Committee Chair(s)

Hovakimyan, Naira

Committee Member(s)

• Kumar, P.R.
• Dullerud, Geir E.
• Mehta, Prashant G.

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Date of Ingest

2011-05-25T14:37:16Z

Keyword(s)

• Control Theory
• Information Theory
• Robust Control
• Sensitivity Function
• Stochastic Control

Abstract

Recent progress in communication technologies and their use in feedback control systems motivate to look deeper into the interplay of control and communication in the closed-loop feedback architecture. Among several research directions on this topic, a great deal of attention has been given to the fundamental limitations in the presence communication constraints. Entropy rate inequalities corresponding to the information flux in a typical causal closed loop have been derived towards obtaining a Bode-like integral formula. This work extends the discrete-time result to continuous-time systems. The main challenge in this extension is that Kolmogorov's entropy rate equality, which is fundamental to the derivation of the result in discrete-time case, does not hold for continuous-time systems. Mutual information rate instead of entropy rate is used to represent the information flow in the closed-loop, and a limiting relationship due to Pinsker towards obtaining the mutual information rate between two continuous time processes from their discretized sequence is used to derive the Bode-like formula. The results are further extended to switched systems and a Bode integral formula is obtained under the assumption that the switching sequence is an ergodic Markov chain. To enable simplified calculation of the resulting lower bound, some Lie algebraic conditions are developed. Besides analysis results, this dissertation also includes joint control/communication design for closed-loop stability of performance. We consider the stabilization problem within Linear Quadratic Regulator framework, where a control gain is chosen to minimize a linear quadratic cost functional while subject to the input power constraint imposed by an additive Gaussian channel which closes the loop. Also focused on Gaussian channel, the channel noise attenuation problem is addressed, by using H-infinity/H2 methodology. Similar feedback optimal estimation problem is solved by using Kalman filtering theory.

Graduation Semester

2011-05

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http://hdl.handle.net/2142/24370

Copyright and License Information

Copyright 2011 Dapeng Li

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