Numerical solution of hybrid systems of differential-algebraic equations

Hamann, Peter; Mehrmann, Volker

doi:10.1016/j.cma.2007.09.002

Cited by 27 publications

(24 citation statements)

References 40 publications

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confidence: 99%

“…Particular challenges in the analysis as well as numerical solution of switched DAE systems arise from over-or underdeterminedness of the system after mode switching, the correct initialization of the model after a switch, as well as the treatment of special phenomena in the numerical solution as chattering, see e.g. [4].Definition 0.1 Let I = [t 0 , t f ] be an integration interval that is decomposed into subintervalsThen, a hybrid differential-algebraic system H is defined as a set of nonlinear DAEs …”

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Modeling and Numerical Simulation of General Nonlinear Switched Differential‐Algebraic Systems

Wunderlich

2008

Proc Appl Math and Mech

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We consider the modeling and numerical simulation of complex dynamical systems that switch between different modes of operation. In particular, we consider switched systems that are composed of several nonlinear differential-algebraic equations (DAEs) describing the behavior in the different operation modes and transition conditions that cause switching between these modes. Particular challenges in the analysis as well as numerical solution of switched DAE systems arise from over-or underdeterminedness of the system after mode switching, the correct initialization of the model after a switch, as well as the treatment of special phenomena in the numerical solution as chattering, see e.g. [4].Definition 0.1 Let I = [t 0 , t f ] be an integration interval that is decomposed into subintervalsThen, a hybrid differential-algebraic system H is defined as a set of nonlinear DAEs

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confidence: 99%

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confidence: 99%

Modeling and Numerical Simulation of General Nonlinear Switched Differential‐Algebraic Systems

Wunderlich

2008

Proc Appl Math and Mech

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“…17.2 can be applied for hybrid DAEs as shown in [22,34,57]. We assume that the discrete and continuous dynamics only interact via instantaneous discrete transitions at distinct points in time called events.…”

Section: Hybrid System Formulationmentioning

confidence: 99%

DAEs in Applications

Scholz

Steinbrecher

2015

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

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Differential-algebraic equations (DAEs) arise naturally in many technical and industrial applications. By incorporating the special structure of the DAE systems arising in certain physical domains, the general approach for the regularization of DAEs can be efficiently adapted to the system structure. We will present the analysis and regularization approaches for DAEs arising in mechanical multibody systems, electrical circuit equations, and flow problems. In each of these cases the DAEs exhibit a certain structure that can be used for an efficient analysis and regularization. Moreover, we discuss the numerical treatment of hybrid DAE systems, that also occur frequently in industrial applications. For such systems, the framework of DAEs provides essential information for a robust numerical treatment. IntroductionIn the simulation and control of constrained dynamical systems differential-algebraic equations (DAEs) are widely used, since they naturally arise in the modeling process. In particular, the automatic modeling using coupling of modularized subcomponents is frequently used in industrial applications yielding large-scale (but often sparse) DAE systems. An important aspect in the simulation of these systems is that conservation laws (e.g. conservation of mass or momentum, mass or population balances, etc.) included in the model equations should be preserved during the numerical integration. These algebraic relations pose constraints on the solution and may lead to so-called hidden constraints (for higher index DAEs). Also path-following constraints can be considered as additional algebraic constraints. The occurrence of hidden constraints leads to difficulties in the numerical solution as

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“…When partial or total subsystems are singular systems, the switched system becomes a class of switched singular systems. Besides, practical examples of switched singular systems arise in many areas, such as economic systems , complex networks , robot manipulators and biological systems , and references therein. Therefore, switched singular systems have received much attention in the past few decades.…”

Section: Introductionmentioning

confidence: 99%

RobustH_∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

Zhai

et al. 2015

Optim. Control Appl. Meth.

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Summary This paper addresses the robust H∞ control problem for continuous‐time switched singular systems with uncertainties in the state, input, and derivative matrices. A two‐phase method is proposed in this paper to optimize H∞ performance and to minimize the upper bound of the average dwell time. First, sufficient conditions for finding a state feedback controller guaranteeing the minimum H∞ disturbance attenuation are proposed. Besides, the average dwell time is obtained by solving linear matrices inequalities introduced in this paper. Second, to minimize the upper bound of the average dwell time, an improve average dwell time approach is put forward by introducing a new technique. And based on the result in the first phase, a new feedback controller, which optimizes H∞ performance and minimizes the upper bound of the average dwell time is obtained by using the improved average dwell time approach. The point is that when the upper bound of the average dwell time is decreasing, H∞ disturbance attenuation will increase and vice versa. Therefore, a trade‐off should be built between H∞ disturbance attenuation and average dwell time in practice. Finally, several numerical examples are presented to illustrate the effectiveness of the methods proposed. Copyright © 2015 John Wiley & Sons, Ltd.

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Numerical solution of hybrid systems of differential-algebraic equations

Cited by 27 publications

References 40 publications

Modeling and Numerical Simulation of General Nonlinear Switched Differential‐Algebraic Systems

Modeling and Numerical Simulation of General Nonlinear Switched Differential‐Algebraic Systems

DAEs in Applications

RobustH_∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

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Numerical solution of hybrid systems of differential-algebraic equations

Cited by 27 publications

References 40 publications

Modeling and Numerical Simulation of General Nonlinear Switched Differential‐Algebraic Systems

Modeling and Numerical Simulation of General Nonlinear Switched Differential‐Algebraic Systems

DAEs in Applications

RobustH∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

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Product

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RobustH_∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach