Performance control for interconnection of identical systems: Application to PLL network design

Korniienko, Anton; Scorletti, Gérard; Colinet, Éric; Blanco, Eric

doi:10.1002/rnc.3285

Cited by 13 publications

(47 citation statements)

References 46 publications

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“…In the particular case where interconnected systems are identical, a new paradigm has emerged, known as large-scale (distributed/decentralised) systems or homogeneous multi-agent systems approach. In the last decade, this approach has been successful in diverse areas of application such as formation flying [1], micro-Electronics [2], [3], biological networks [4], etc.…”

Section: Introductionmentioning

confidence: 99%

Frequency Design of Interconnected Dissipative Systems: a Unified LMI Approach

Perodou¹,

Korniienko²,

Zarudniev³

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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This paper deals with the design of a system, defined as the interconnection of identical LTI subsystems, whose frequency-response is under modulus constraints. Based on the notions of LFT and dissipativity, we propose a method able to compute a solution by solving a linear minimisation problem under LMI constraints. This extends the usual approach by especially generalising the spectral factorisation technique from systems with state-space model to identical dissipative systems interconnection.

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Section: Introductionmentioning

confidence: 99%

Frequency Design of Interconnected Dissipative Systems: a Unified LMI Approach

Perodou¹,

Korniienko²,

Zarudniev³

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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“…In this technical report, the interconnection form used in formation control or multi-agent systems (see e.g. [17], [18]) is under consideration. Each subsystem S i (θ i ) is operated with a decentralized controller K i (s), see (2), and the signal r i is a locally available reference signal that will be computed via (3).…”

Section: Problem Statementmentioning

confidence: 99%

“…We also assume that there is a design procedure allowing to compute local controllers K i (s) such that the nominal global transfer function Tw →z (s, θ), with θ =θ an estimate of θ 0 , respects the frequency dependent bound (6). Such design procedures could be found in [18], [19].…”

Section: Problem Statementmentioning

confidence: 99%

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Hierarchical Robust Analysis for Identified Systems in Network

et al. 2018

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This technical report considers worst-case robustness analysis of a network of locally controlled uncertain systems with uncertain parameter vectors belonging to the ellipsoid sets found by identification procedures. In order to deal with computational complexity of large-scale systems, an hierarchical robustness analysis approach is adapted to these uncertain parameter vectors thus addressing the trade-off between the computation time and the conservatism of the obtained result. I. INTRODUCTIONIn this technical report, the problem of worst-case robustness analysis of a network of locally controlled uncertain Linear Time Invariant (LTI) subsystems is under consideration. The uncertainty of each subsystem is an uncertain real vector that belongs to an ellipsoid: an uncertainty set in the model parameter space typically obtained after identification.This work is motivated by recent technological advances in Microelectronics, Computer Sciences, Robotics, and related topics in the field of the Multi-Agent systems [1]. The control of these network systems is usually decentralized and in order to compute controllers achieving high performance level, the model of the subsystems needs to be known. An efficient method to build the appropriate models is system identification [2]. However, due to the presence of the noise and since the identification experiment is limited in time, the model parameters can only be identified within some prescribed uncertainty region which is typically an ellipsoid. For these reasons, in order to ensure that the computed controllers achieve the performance not only for the nominal identified model but for the true network system, it is important to take into account these uncertainties. The evaluation of the uncertainty effects on the system stability and performance is called robustness analysis.The large scale of today's systems raises additional challenges on identification, controller design as well as on the robustness analysis. In this technical report we focus on the robustness analysis in the context of large-scale network systems.In the 80's-90's, µ-analysis [3], [4] was developed to investigate the performance of LTI systems in the presence of structured uncertainties. The performance is evaluated in the frequency domain [5]. This approach is based on the computation of the structured singular value µ of the frequency dependent matrices, which was proved to be NP-hard [6]. Fortunately, lower and upper bounds on µ can be efficiently computed; the µ upper bounds in [7] guarantee a certain level of performance with some conservatism. By efficient, it is understood that the computation time is bounded by a polynomial function of the problem size [8]. An adaptation of these results to classes of the uncertainties obtained by identification can be found in [9]- [11].Nevertheless, even if the computation of the µ upper bound is efficient, its computation time can be important in the case of uncertain large-scale systems. The purpose of this technical report is to extend the results [9]-[11...

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“…With the technological development and the miniaturization of components, high complexity systems are designed in order to achieve a high level of performance, see e.g. Phase Locked Loop (PLL) networks in synchronous multi-core microprocessor systems [2], [3]. However, during the fabrication process, technological dispersions, system ageing, etc.…”

Section: Introductionmentioning

confidence: 99%

Phase IQC for the hierarchical performance analysis of uncertain large scale systems

Laib

Korniienko

Scorletti

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

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This paper investigates the performance analysis of uncertain large scale systems. Due to their complexity, the usual robustness analysis methods based on e.g; µ or Integral Quadratic Constraints cannot be practically applied. In order to address this problem, in [1], we propose to represent a large scale system as an interconnection of sub-systems and to perform a hierarchical analysis by propagating the IQC characterization of each uncertain sub system through the interconnection. For a given computational time, the conservatism of the analysis dramatically depends on the class of IQC under consideration. In this paper, we propose a new class of IQC which characterizes the phase of uncertain system. An application to the robustness analysis of a PLL network reveal that the use of this class of IQC improves the trade-off between conservatism and computation time.

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Performance control for interconnection of identical systems: Application to PLL network design

Cited by 13 publications

References 46 publications

Frequency Design of Interconnected Dissipative Systems: a Unified LMI Approach

Frequency Design of Interconnected Dissipative Systems: a Unified LMI Approach

Hierarchical Robust Analysis for Identified Systems in Network

Phase IQC for the hierarchical performance analysis of uncertain large scale systems

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