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Differential Inclusion (differential + inclusion)

Distribution by Scientific Domains
Engineering50%

Selected Abstracts

Models of non-smooth switches in electrical systems

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2005
Christoph Glocker
Abstract Idealized modelling of diodes, relays and switches in the framework of linear complementarity is introduced. Within the charge approach, the classical electromechanical analogy is extended to passively and actively switching components in electrical circuits. The associated branch relations are expressed in terms of set-valued functions, which allow to formulate the circuit's dynamic behaviour as a differential inclusion. This approach is demonstrated by the example of the DC,DC buck converter. A difference scheme, known in mechanics as time stepping, is applied for numerical approximation of the evolution problem. The discretized inclusions are formulated as a linear complementarity problem in standard form, which implicitly takes care of all switching events by its solution. State reduction, which requires manipulation of the set-valued branch relations in order to obtain a minimal model, is performed on the example of the buck converter. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Cadenced runs of impulse and hybrid control systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2001
Jean-Pierre Aubin
Abstract Impulse differential inclusions, and in particular, hybrid control systems, are defined by a differential inclusion (or a control system) and a reset map. A run of an impulse differential inclusion is defined by a sequence of cadences, of reinitialized states and of motives describing the evolution along a given cadence between two distinct consecutive impulse times, the value of a motive at the end of a cadence being reset as the next reinitialized state of the next cadence. A cadenced run is then defined by constant cadence, initial state and motive, where the value at the end of the cadence is reset at the same reinitialized state. It plays the role of a ,discontinuous' periodic solution of a differential inclusion. We prove that if the sequence of reinitialized states of a run converges to some state, then the run converges to a cadenced run starting from this state, and that, under convexity assumptions, that a cadenced run does exist. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Extremal solutions for nonlinear second order differential inclusions

MATHEMATISCHE NACHRICHTEN, Issue 1-2 2005
P. Douka
Abstract We consider a nonlinear second order differential inclusion driven by the scalar p -Laplacian and with nonlinear multivalued boundary conditions. Assuming the existence of an ordered pair of upper-lower solutions and using truncation and penalization techniques together with Zorn's lemma, we show that the problem has extremal solutions in the order interval formed by the upper und lower solutions. We present some special cases of interest and show that our method applies also to the periodic problem. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Cadenced runs of impulse and hybrid control systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2001
Jean-Pierre Aubin
Abstract Impulse differential inclusions, and in particular, hybrid control systems, are defined by a differential inclusion (or a control system) and a reset map. A run of an impulse differential inclusion is defined by a sequence of cadences, of reinitialized states and of motives describing the evolution along a given cadence between two distinct consecutive impulse times, the value of a motive at the end of a cadence being reset as the next reinitialized state of the next cadence. A cadenced run is then defined by constant cadence, initial state and motive, where the value at the end of the cadence is reset at the same reinitialized state. It plays the role of a ,discontinuous' periodic solution of a differential inclusion. We prove that if the sequence of reinitialized states of a run converges to some state, then the run converges to a cadenced run starting from this state, and that, under convexity assumptions, that a cadenced run does exist. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Extremal solutions for nonlinear second order differential inclusions

MATHEMATISCHE NACHRICHTEN, Issue 1-2 2005
P. Douka
Abstract We consider a nonlinear second order differential inclusion driven by the scalar p -Laplacian and with nonlinear multivalued boundary conditions. Assuming the existence of an ordered pair of upper-lower solutions and using truncation and penalization techniques together with Zorn's lemma, we show that the problem has extremal solutions in the order interval formed by the upper und lower solutions. We present some special cases of interest and show that our method applies also to the periodic problem. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Chemical networks with inflows and outflows: A positive linear differential inclusions approach

BIOTECHNOLOGY PROGRESS, Issue 3 2009
David Angeli
Abstract Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009 [source]