Method of passification in adaptive control, estimation, and synchronization

Andrievskii, B. R.; Fradkov, Alexander L.

doi:10.1134/s0005117906110014

Cited by 89 publications

(67 citation statements)

References 35 publications

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“…Then by Schur complement theorem (Gu, Kharitonov, & Chen, 2003, p. 318) it can be shown that H i < 0 for R = I, S = hI, G j = 0 (j = 1, 2, 3). When h → 0 allowable M * and M 1 tend to infinity, therefore, our results recover the global results from Andrievskii and Fradkov (2006) for delay-free case. Relations (14) give acceptable bounds h 1 and h 2 such that (7) holds for the closed-loop time-delay system (3), (6).…”

Section: Proof See Appendix Asupporting

confidence: 84%

“…For r 1 (t) = r 2 (t) ≡ 0 under Assumption 2 it has been shown in Andrievskii and Fradkov (2006) that solutions of the closed-loop system (3), (6) satisfy the following property: for all…”

Section: Problem Formulationmentioning

confidence: 96%

“…As it has been shown in Fradkov (1974), any hyperminimum-phase linear time-invariant system can be stabilized by a static output feedback u(t) = −ky(t) if k is large enough (for more established description see Andrievskii and Fradkov (2006)). For the case of uncertain systems an adaptive version of this controller has been derived via the speed gradient method (Fradkov, 1980).…”

Section: Introductionmentioning

confidence: 93%

“…It is clear that t * ≤ h. Assumption 1 is always satisfied for slowly-varying delays withṙ(t) ≤ 1 (since t − r(t) is increasing) and for networked control systems as considered in Section 4. Similar to Andrievskii and Fradkov (2006); Fradkov (1976) we assume…”

Section: Problem Formulationmentioning

confidence: 99%

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Passification-based adaptive control: Uncertain input and output delays

2015

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a b s t r a c tFor a class of uncertain systems we analyze passification-based adaptive controller in the presence of small, unavoidable input and output time-varying delays as may be present in controller implementation. We derive upper bounds for time delays such that in some domain of initial conditions the states of the closed-loop system tend to zero, whereas an adaptive controller gain tends to a constant value. The results are semi-global, that is the domain of initial conditions is bounded but can be made arbitrary large by tuning an appropriate controller parameter. For the first time, we apply an adaptive controller to linear uncertain networked control systems, where sensors, controllers, and actuators exchange their information through communication networks. The efficiency of the results is demonstrated by the example of adaptive network-based control of an aircraft.

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Section: Proof See Appendix Asupporting

confidence: 84%

Section: Problem Formulationmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 93%

Section: Problem Formulationmentioning

confidence: 99%

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Passification-based adaptive control: Uncertain input and output delays

2015

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“…Therefore, passivity enforcement [2] and passivation (passification) [3] have become important issues in recent years [4][5][6][7][8], especially as more and more software tools render transfer functions which need passivity enforcement as a postprocessing step in order to generate reliable physical models. However, most of the techniques [2][3][4][5][6][7] are local perturbative and/or feedback approaches with fixed poles, while [8] is based on Fourier approximation, yielding passivated systems with a large number of poles. In this paper we present a new global approach, in the sense that we obtain a passive real-rational transfer function G(s) that is an arbitrarily close approximation of the passive transfer function nearest to the nonpassive transfer function H(s).…”

Section: Introductionmentioning

confidence: 99%

Matrix nearness-based guaranteed passive system approximation

Knockaert

2013

Systems & Control Letters

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In this paper we present a new approach towards global passive approximation in order to find a passive real-rational transfer function G(s) that is an arbitrarily close approximation of the passive transfer function nearest to a non-passive square transfer function H(s). It is based on existing solutions to pertinent matrix nearness problems. It is shown that the key point in constructing the passive real-rational transfer function G(s), is to find a good rational approximation of the well-known ramp function over an interval defined by the minimum and maximum dissipation of H(s). The proposed algorithms rely on the stable anti-stable decomposition of a given transfer function. Pertinent examples are given to show the scope and accuracy of the proposed algorithms.

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Simple and robust adaptive control

Barkana¹,

Fradkov

2014

Adaptive Control & Signal

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SUMMARYMost papers of this special issue are extended and revised versions of the papers from the invited sessions dedicated to 'simple and robust adaptive control' from the 17th IFAC World Congress (IFAC 2011) and 11th IFAC Workshop on Adaptation and Learning in Control and Signal Processing (ALCOSP 2013). They provide sufficient coverage both for the rigorous mathematical explanation and treatment of the theoretical problems related to stability and performance and the detailed presentation of the specific realistically large application.

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Method of passification in adaptive control, estimation, and synchronization

Cited by 89 publications

References 35 publications

Passification-based adaptive control: Uncertain input and output delays

Passification-based adaptive control: Uncertain input and output delays

Matrix nearness-based guaranteed passive system approximation

Simple and robust adaptive control

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