Reduction Principles and the Stabilization of Closed Sets for Passive Systems

El-Hawwary, Mohamed I.; Maggiore, Manfredi

doi:10.1109/tac.2010.2041684

Cited by 31 publications

(26 citation statements)

References 18 publications

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“…Our recent work, El-Hawwary and Maggiore (2010), overcomes this problem by allowing the goal set to be a subset of the zero level set of the storage function, without imposing that it be compact. The end result in El-Hawwary and Maggiore (2010), reviewed in Section 2.1 of this article, is a set of necessary and sufficient conditions for a passivity-based feedback to stabilise a given goal set, expressed in terms of a new notion of À-detectability (where À denotes the goal set) that generalises the zero-state detectability property of Byrnes-Isidori-Willems. In the setting of El-Hawwary and Maggiore (2010), the property of À-detectability corresponds to asymptotic stability of À when the system dynamics are restricted to a special invariant subset of the state space.…”

Section: Introductionmentioning

confidence: 99%

Case studies on passivity-based stabilisation of closed sets

El-Hawwary¹,

Maggiore²

2011

International Journal of Control

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We present a novel control design procedure for the passivity-based stabilisation of closed sets which leverages recent theoretical advances. The procedure involves using part of the control freedom in order to enforce a detectability property, while the remaining part is used for passivity-based stabilisation. The procedure is illustrated in four case studies of path following coordination for one or two kinematic unicycles, and variations of these problems. Among other things, we present a smooth global path following controller making the unicycle converge to an arbitrary closed and strictly convex curve, and a coordinated path following controller for two unicycles.

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Section: Introductionmentioning

confidence: 99%

Case studies on passivity-based stabilisation of closed sets

El-Hawwary¹,

Maggiore²

2011

International Journal of Control

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“…The state space of the system is X = (R 2 × S 1 ) n , and we let χ = col(x 1 , · · · , x n ), and x 3 = col(x 1 3 , · · · , x n 3 ). This system can be written in the control affine formχ = g(χ)u.…”

Section: Introductionmentioning

confidence: 99%

“…Consider the n-unicycles in (1). For a given information flow digraph G with a globally reachable node, and a desired formation specification expressed by a vector of angles α ∈ S n , design a distributed control law which asymptotically stabilizes the set…”

Section: Introductionmentioning

confidence: 99%

“…The simplest PBF,ũ(χ) = −h(χ), has the property thatũ i is affected by rows 2i − 1 and 2i of (L (2) + L ⊤ (2) ). These rows are different from the corresponding rows of L (2) , unless L is symmetric, and thereforeũ(χ) violates the information flow constraint embodied in L.…”

Section: Introductionmentioning

confidence: 99%

“…The answer to this question is contained in the next result, taken from [1] (see [2] for the full version of the paper). Seibert and Florio in [3] proved an analogous result for the case when Γ is compact.…”

Section: Introductionmentioning

confidence: 99%

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Distributed circular formation stabilization of unicycles part II: Arbitrary information flow graph

El-Hawwary

Maggiore

2011

IEEE Conference on Decision and Control and European Control Conference

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In part I of this paper we presented a solution to the circular formation stabilization problem of kinematic unicycles when the information flow graph is undirected. This paper extends the results of part I in two directions. First, we present a control law that solves the circular formation stabilization problem when the information flow is described by an arbitrary directed graph with a globally reachable node. Second, we generalize our results to the case when the unicycles are dynamic.

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Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

Pang

Zhao

2017

Adaptive Control & Signal

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This paper investigates the adaptive quasi-passification-based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasipassification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi-passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods. KEYWORDSadaptive quasi-passification, recursive feedback quasi-passification, global practical stability, switched nonlinear systems, average dwell timeAs a special kind of hybrid dynamical systems, a switched system is composed of a family of continuous-time subsystems and a rule that governs the switching among them. Switched systems have attracted a great amount of attention because of their importance from both theoretical and practical points of view. 1-4 Many practical systems, such as aircraft control systems, mechanical systems and electrical systems, can be modeled as switched systems. 2,4-6 Stability analysis and stabilization problems for switched systems have been extensively studied. Since uncertainties which may cause instability and undesirable performance exist widely in real world systems, one should consider these effects on plant. H ∞ control, robust control and adaptive control are often used to deal with uncertainties. 7-13 For parametric uncertainties, adaptive control has been one of the most effective methods. The asymptotic stability is often the desired performance. 3,5,10,11,14 However, in many practical applications, asymptotic stability may be difficult to obtain due to large uncertainties. From an engineering point of view, the global practical stability can be often satisfactory. 12,13 On the other hand, passivity, introduced by Willems, 15 provides an effective tool for solving the problems of stability analysis and stabilization. 15-17 When a system involves unknown parameters, the adaptive passification and adaptive passivity-based stabilization problems were solved in. 6,18-21 However, the exact feedback passification and asymptotical stabilization problems were intractable because of the large system uncertainties. Therefore, the development of passivity-based methodology for this case would be desirable. The convention passivity property was extended to quasipassivity, 22,23 which were used to investigate the ultimate boundedness of state trajectories of nonlinear uncertain systems. Similar to the concept of strict quasi-passivity, the concepts of passivity with respect to a set and semipassivity were proposed to derive a stability property of the set....

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Reduction Principles and the Stabilization of Closed Sets for Passive Systems

Cited by 31 publications

References 18 publications

Case studies on passivity-based stabilisation of closed sets

Case studies on passivity-based stabilisation of closed sets

Distributed circular formation stabilization of unicycles part II: Arbitrary information flow graph

Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

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