Conference Paper

Checking if controllers are stabilizing using closed-loop data

Res. Sch. of Inf. Sci. & Eng., Australian Nat. Univ., Canberra, ACT
DOI: 10.1109/CDC.2006.377549 Conference: Decision and Control, 2006 45th IEEE Conference on
Source: IEEE Xplore

ABSTRACT Suppose an unknown plant is stabilized by a known controller. Suppose also that some knowledge of the closed-loop system is available and on the basis of that knowledge, the use of a new controller appears attractive, as may arise in iterative control and identification algorithms, and multiple-model adaptive control. The paper presents tests using a limited amount of experimental data obtained with the existing known controller for verifying that introduction of the new controller will stabilize the plant

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    • "In Section III, we will present a framework for implementing controllers in a specialized way, which enables presentation of the proposed experimental setting. This builds on our earlier results [28], [29] and leads to the development of the proposed novel validation tests of Section IV for SISO/MIMO systems. Simulation examples of Section V show the versatility and applicability of the proposed tests. "
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    ABSTRACT: We introduce novel tests utilizing a limited amount of experimental and possibly noisy data obtained with an existing known stabilizing controller connected to an unknown plant for verifying that the introduction of a proposed new controller will stabilize the plant. The tests depend on the assumption that the unknown plant is stabilized by a known controller and that some knowledge of the closed-loop system, such as noisy frequency response data, is available and on the basis of that knowledge, the use of a new controller appears attractive. The desirability of doing this arises in iterative identification and control algorithms, multiple-model adaptive control, and multi-controller adaptive switching. The proposed tests can be used for SISO and/or MIMO linear time-invariant systems.
    IEEE Transactions on Automatic Control 12/2009; DOI:10.1109/TAC.2009.2031587 · 3.17 Impact Factor
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    • "Then the following are equivalent: a) [P, C 1 ] is internally stable; b) T −1 ∈ RH ∞ ; c) det T (jω) = 0 ∀ω and wno det T = 0; d) det T (jω) = 0 ∀ω and arg det T (j∞) = arg det T (j0). Proof: See [25]. "
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    ABSTRACT: This article introduces novel tests which utilize a limited amount of experimental and possibly noisy data obtained from a stable closed-loop system, i.e. an interconnection of an existing known stabilizing controller and an unknown plant, to infer if the introduction of a prospective controller will stabilize the unknown plant. This extends our earlier results to include the MIMO systems.
    Decision and Control, 2007 46th IEEE Conference on; 01/2008
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    • "Section II collects the required and necessary definitions and notations, and elucidates the problem of concern by citing the internal stability results from the relevant literature. Section III is built on our earlier results [13], [14] and discusses the experimental setting which leads to the development of the novel validation tests of Section IV for SISO/MIMO systems. Two simulation examples are presented in Section V, and Section VI contains concluding remarks and future research directions. "
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    ABSTRACT: In this paper, we further illustrate the versatility and effectiveness of our novel tests for ensuring safe adaptive control in practice. The tests utilize a limited amount of experimental and possibly noisy data obtained from a closed-loop-consisting of an existing known stabilizing controller connected to an unknown plant-to infer if the introduction of a prospective controller will stabilize the unknown plant. The need and importance of this arise in iterative identification and control algorithms, multiple-model adaptive control (MMAC), and multi-controller adaptive switching.
    Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008, December 9-11, 2008, Cancún, México; 01/2008
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