A Novel Interval Arithmetic Approach for Solving Differential-Algebraic Equations with ValEncIA-IVP

Rauh, Andreas; Brill, Michael; Günther, Christine

doi:10.2478/v10006-009-0032-4

Cited by 28 publications

(22 citation statements)

References 18 publications

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“…slowly varying in the experiment compared with the dominant time constants of the test rig), the structural analysis performed by the verified DAE solver VALENCIA-IVP [16][17][18][19], see also Section 3, provides the result displayed in Figure 2.…”

Section: Structural Analysis For Specification Of Flat Outputsmentioning

confidence: 99%

Parameter identification and observer-based control for distributed heating systems– the basis for temperature control of solid oxide fuel cell stacks

Rauh

Aschemann

2012

Mathematical and Computer Modelling of Dynamical Systems

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The control of high-temperature fuel cell stacks is the prerequisite to guarantee maximum efficiency and lifetime under both constant and varying electrical load conditions. Especially, for time-varying electrical load demands, it is necessary to develop novel observer-based control approaches that are robust against parameter uncertainties and disturbances that cannot be modelled a priori. Since we aim at real-time applicability of these control procedures, classical high-dimensional models -which result from a discretization of mathematical descriptions given by the partial differential equations for heat and mass transfer -cannot be applied. Furthermore, these models have to be linked to the electrochemical properties of the fuel cell. To reduce the order of these models to a degree that allows us to use them in real-time, information on both the temperature distribution in the fuel cell stack and the heat flow into its interior due to electrochemical reactions is required. However, a direct temperature measurement is not possible from a practical point of view. For that reason, it is essential to reliably estimate the temperature distribution and the heat flow on the basis of easily available measured data. These data have to be available not only during development stages but also in future series products. For such products, it is desirable to reduce the number of sensors to improve the system's reliability and to decrease the operating costs. The basic strategies that are applicable for model-based open-loop and closed-loop control of heating systems as well as for the identification of parameters, operating conditions and disturbances as well as for state monitoring are summarized in this article. They are demonstrated for exemplary set-ups in both simulation and experiment.

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Section: Structural Analysis For Specification Of Flat Outputsmentioning

confidence: 99%

Parameter identification and observer-based control for distributed heating systems– the basis for temperature control of solid oxide fuel cell stacks

Rauh

Aschemann

2012

Mathematical and Computer Modelling of Dynamical Systems

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“…Hoefkens et al (2003) developed a discrete-time approach for the propagation of Taylor models using differential algebras (Berz and Makino, 1998) through index-one semi-explicit DAEs. Likewise, Rauh et al (2009) built upon an existing validated discrete-time method for ODEs (Rauh et al, 2006) to address semi-explicit index-1 DAEs through the combination with an interval Krawczyk method for bounding the algebraic constraints. More recently, Scott and Barton (2013) have presented a continuous-time method which combines the theory of differential inequalities with a Newton-type method to handle the algebraic constraints.…”

Section: Introductionmentioning

confidence: 99%

Continuous-Time Enclosures for Uncertain Implicit Differential Equations

et al. 2015

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The computation of enclosures for the reachable set of uncertain dynamic systems is a crucial component in a wide variety of applications, from global and robust dynamic optimization to safety verification and fault detection. Even though many systems in engineering are best modeled as implicit differential equations (IDEs) and differential algebraic equations (DAEs), methods for the construction of enclosures for these are not as well developed as they are for ordinary differential equations (ODEs). In this paper, we propose a continuous-time approach for the guaranteed over approximations of the reachable set for quasilinear IDEs. This approach builds on novel high-order inclusion techniques for the solution set of algebraic equations and state-of-the-art techniques for bounding the solution of nonlinear ODEs. We show how this approach can be used to bound the reachable set of uncertain semi-explicit DAEs by bounding the underlying IDEs. We demonstrate this approach on two case studies, a double pendulum where it proves superior with delayed break-down times compared to other methods, and anaerobic digestion of microalgae which has nine differential and two algebraic states.

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“…IVPs for ODEs were covered rather extensively from the verified point of view (Nedialkov, 2002;Eble, 2007;Makino, 1998). There are also several works on interval IVPs for DAEs (Rauh et al, 2009). Certain complementarity problems can be solved by verified optimization methods (Hansen and Walster, 2004;Kearfott, 1996;Jaulin et al, 2001).…”

Section: 4mentioning

confidence: 99%

A verified method for solving piecewise smooth initial value problems

Auer

Kiel

Rauh

2013

International Journal of Applied Mathematics and Computer Science

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In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview of possibilities to formulate non-smooth problems and point out connections between the traditional non-smooth theory and interval analysis. Moreover, we summarize already existing verified methods for solving initial value problems with non-smooth (in fact, even not absolutely continuous) right-hand sides and propose a way of handling a certain practically relevant subclass of such systems. We implement the approach for the solver VALENCIA-IVP by introducing into it a specialized template for enclosing the first-order derivatives of non-smooth functions. We demonstrate the applicability of our technique using a mechanical system model with friction and hysteresis. We conclude the paper by giving a perspective on future research directions in this area.

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A Novel Interval Arithmetic Approach for Solving Differential-Algebraic Equations with ValEncIA-IVP

Cited by 28 publications

References 18 publications

Parameter identification and observer-based control for distributed heating systems– the basis for temperature control of solid oxide fuel cell stacks

Parameter identification and observer-based control for distributed heating systems– the basis for temperature control of solid oxide fuel cell stacks

Continuous-Time Enclosures for Uncertain Implicit Differential Equations

A verified method for solving piecewise smooth initial value problems

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