Semi-global stabilization by an output feedback law from a hybrid state controller

Marx, Swann; Andrieu, Vincent; Prieur, Christophe

doi:10.1016/j.automatica.2016.07.011

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…It is also important for nonlinear ones. See in particular Marx et al [2016] where dwell-time property has been employed to combine a high-gain observer with a hybrid controller for general nonlinear control systems.…”

Section: Perspectivesmentioning

confidence: 99%

Analysis and Synthesis of Reset Control Systems

Prieur

Queinnec²,

Tarbouriech³

et al. 2018

FNT in Systems and Control

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This survey paper overviews a large core of research results produced by the authors in the past decade about reset controllers for linear and nonlinear plants. The corresponding feedback laws generalize classical dynamic controllers because of the interplay of mixed continuous/discrete dynamics. The obtained closed-loop system falls then within the category of hybrid dynamical systems, with the specific feature that the hybrid nature arises from the nature of the controller, rather than the nature of the plant, which is purely continuous-time. Due to this fact, the presented results focus on performance and stability notions that prioritize continuous-time evolution as compared to the discrete-time one. Dwell-time logics are indeed enforced on solutions, to ensure that the continuous evolution of solutions is complete (no Zeno solutions occur). After presenting a historical motivation and an overview of the results on this topic in Part I, several results on stability and performance analysis and on control design for general linear continuous-time plants are developed in Part II. These results are developed by exploiting the well established formalism for nonlinear hybrid dynamical systems introduced by Andy Teel and co-authors around 2004. With this formalism, by ensuring sufficient regularity of the reset controller dynamics, we ensure robustness of stability with respect to small disturbances and uncertainties together with suitable continuity of solutions, generally regarded as well-posedness of the hybrid closed loop. Throughout Part II, we provide several simulation studies showing that reset control strategies may allow to attain better performance with respect to the optimal ones obtained by classical continuous-time controllers. Finally, In Part III we focus on planar systems, that is reset closed loops involving a one dimensional linear plant and a one dimensional reset controller. For this simple interconnection interesting stability conditions can be drawn and relevant extensions addressing the reference tracking problem are introduced, illustrating them on a few relevant 2 case studies emerging in the automotive field.

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Section: Perspectivesmentioning

confidence: 99%

Analysis and Synthesis of Reset Control Systems

Prieur

Queinnec²,

Tarbouriech³

et al. 2018

FNT in Systems and Control

Self Cite

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“…• Remark 2 Assumption 4 simply refers to the existence of a local tunable observer as introduced in [3] (similar definition of a local tunable asymptotic observer has been used in [1] and [9]). In other words, there must exist a local observer characterized by equation (9) such that the estimation error, x(t) − ζ obs (t) , is bounded and converges to zero for all trajectory x(·) does not leave the set Ω x .…”

Section: Problem Statementmentioning

confidence: 99%

“…In other words, there must exist a local observer characterized by equation (9) such that the estimation error, x(t) − ζ obs (t) , is bounded and converges to zero for all trajectory x(·) does not leave the set Ω x . The observer is called tunable in the sense that its convergence rate can be tuned.…”

Section: Problem Statementmentioning

confidence: 99%

Enlarging the basin of attraction by a uniting output feedback controller

et al. 2018

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We consider a system for which two predesigned stabilizing controllers with bounded domains of attraction are known. One renders the system asymptotically stable with some desired performance, and the other provides ultimate boundedness with larger domain of attraction. Assuming that two subsets of the domains of attraction are known, one larger than the other, this work states the problem of combining both controllers with the goal of guaranteeing asymptotic stability properties in the largest subset while the desired performance is locally achieved. We design a switching logic between the controllers that solves the problem, based on the existence of a local tunable observer. The resulting control law is defined by a hybrid output feedback controller. The effectiveness of the proposed solution is illustrated by a numerical example.

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Model predictive-based reset gain-scheduling dynamic control law for polytopic LPV systems

Vafamand

Khayatian

2018

ISA Transactions

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Semi-global stabilization by an output feedback law from a hybrid state controller

Cited by 5 publications

References 23 publications

Analysis and Synthesis of Reset Control Systems

Analysis and Synthesis of Reset Control Systems

Enlarging the basin of attraction by a uniting output feedback controller

Model predictive-based reset gain-scheduling dynamic control law for polytopic LPV systems

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