A comparison of least squares algorithms for estimating Markov parameters

Fledderjohn, Matthew; Holzel, Matthew S.; Palanthandalam-Madapusi, Harish J.; Fuentes, Robert J.; Bernstein, Dennis S.

doi:10.1109/acc.2010.5530673

Cited by 20 publications

(11 citation statements)

References 10 publications

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“…In the SISO case, this approach relies on knowledge of the first nonzero Markov parameter and knowledge of the nonminimum-phase (NMP) zeros, if any; in the MIMO case, the number of Markov parameters that must be known depends on whether the plant is square, tall, or wide, as well as on the rank of the Markov parameters. Markov parameters provide a convenient foundation for plant modeling since they are independent of the state space basis, and they can be identified by various system identification methods [11]. When a sufficient number of Markov parameters are used within RCAC, the locations of the NMP zeros are approximately captured, which avoids the need to determine a state space realization and compute the NMP zeros.…”

Section: Introductionmentioning

confidence: 99%

Robustness of retrospective cost adaptive control to Markov-parameter uncertainty

Sumer

D’Amato

Морозов

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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In this paper we investigate the robustness of an extended version of retrospective cost adaptive control (RCAC), in which less modeling information is required than in prior versions of this method. RCAC is applicable to MIMO possibly nonminimum-phase (NMP) plants without the need to know the locations of the NMP zeros. The only required modeling information is an FIR approximation of the plant, which may be based on a limited number of Markov parameters. In this paper we investigate the effect of phase mismatch between the true plant and the FIR approximation. Numerical examples demonstrate the relationship between phase mismatch at the command and disturbance frequencies as well as the required level of regularization in the controller update.

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Section: Introductionmentioning

confidence: 99%

Robustness of retrospective cost adaptive control to Markov-parameter uncertainty

Sumer

D’Amato

Морозов

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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“…. , H µ is possible in the presence of arbitrary output noise using standard least squares [22], [23] when the input u is white. The µ-Markov model (30) can be expressed as…”

Section: Nmp Zero Identificationmentioning

confidence: 99%

Adaptive control of aircraft lateral motion with an unknown transition to nonmimimum-phase dynamics

Rahman

Aljanaideh

Sumer

et al. 2014

2014 American Control Conference

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We apply retrospective cost adaptive control (RCAC) to a linearized aircraft dynamics with an unknown transition to nonminimum-phase (NMP) dynamics. In prior work, RCAC was used for command-following with unknown NMP zeros. In this work we extend those results to command following for cases where the dynamics transition from minimum-phase to NMP. We use system identification techniques to identify the NMP zero, and use this information in RCAC. We consider both full-state feedback and output feedback, and in both cases we follow step commands with transitioning dynamics. We first consider the case where RCAC is unaware of the change and NMP zero identification is unavailable to RCAC. We then assume that NMP zero information is available to RCAC from system identification.

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“…For the case of a white input signal and arbitrary, unknown output noise, standard least squares yields consistent estimates of the Markov parameters [17,18]. The estimated Markov parameters can subsequently be used for approximation and order reduction.…”

Section: Introductionmentioning

confidence: 99%

Closed-loop identification of unstable systems using noncausal FIR models

Aljanaideh

Coffer

Bernstein

2013

2013 American Control Conference

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Motivated by the potential advantages of FIR model structures, the present paper considers the applicability of FIR models to closed-loop identification of open-loopunstable plants. We show that FIR models can be used effectively for closed-loop identification of open-loop-unstable plants.The key insight in this regard is to realize that a noncausal FIR model can serve as a truncated Laurent expansion inside the annulus between the asymptotically stable pole of largest modulus and the unstable pole of smallest modulus. The key to identifying the noncausal plant model is to delay the measured output relative to the measured input. With this techniques, the identified FIR model is precisely a noncausal approximation of the unstable plant, that is, an approximation of the Laurent expansion of the plant inside the annulus of analyticity lying between the disk of stable poles and the punctured plane of unstable poles.

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A comparison of least squares algorithms for estimating Markov parameters

Cited by 20 publications

References 10 publications

Robustness of retrospective cost adaptive control to Markov-parameter uncertainty

Robustness of retrospective cost adaptive control to Markov-parameter uncertainty

Adaptive control of aircraft lateral motion with an unknown transition to nonmimimum-phase dynamics

Closed-loop identification of unstable systems using noncausal FIR models

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