Extensions of <scp>ValEncIA‐IVP</scp> for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization

Rauh, Andreas; Auer, Ekaterina; Minisini, Johanna; Hofer, Eberhard P.

doi:10.1002/pamm.200700022

Cited by 8 publications

(6 citation statements)

References 3 publications

(8 reference statements)

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“…One tool available to us is an extension of VALENCIA-IVP which is still under development. However, the first results as reported in (Rauh et al, 2007b) are promising. Since this solver requires an approximation of the DAE solution in its first stage, a reliable solver for this purpose should be integrated into SMARTMOBILE.…”

Section: Options For the Simulation Of Closed Loop Systems In Smartmomentioning

confidence: 95%

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Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems

Auer¹,

Luther²

2009

International Journal of Applied Mathematics and Computer Science

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Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SMARTMOBILE enhances the existing MSS MOBILE with verified techniques to provide a guarantee that the obtained results are correct and measure the influence of data uncertainty. In this paper, we outline the main features and functionalities of SMARTMOBILE. In particular, we focus on its use of newly developed methods for sensitivity analysis and DAE solving for several practically relevant mechanical systems.

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Section: Options For the Simulation Of Closed Loop Systems In Smartmomentioning

confidence: 95%

“…Such simulations are especially difficult since they have differential-algebraic equations (DAEs) as their basis. Finally, we overview our current work toward the integration of a verified DAE solver (Rauh et al, 2007b) and summarize the verifying and validating options SMART-MOBILE currently offers.…”

Section: Introductionmentioning

confidence: 99%

Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems

Auer¹,

Luther²

2009

International Journal of Applied Mathematics and Computer Science

Self Cite

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“…, N when x is only known to belong to some box [x]. Guaranteed numerical integration techniques could be employed, such as AWA [15], VNODE [20], COSY IV [6], VSPODE [13], or ValEncIA-IVP [25,26]. The main difficulty comes from the fact that obtaining accurate enclosures for the solutions when there are uncertain parameters, as here, and uncertain initial conditions is quite difficult.…”

Section: Guaranteed Numerical Integrationmentioning

confidence: 99%

Verified Global Optimization for Estimating the Parameters of Nonlinear Models

Kieffer

Markót

Schichl

et al. 2011

Modeling, Design, and Simulation of Systems With Uncertainties

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Nonlinear parameter estimation is usually achieved via the minimization of some possibly non-convex cost function. Interval analysis allows to derive algorithms for the guaranteed characterization of the set of all global minimizers of such a cost function when an explicit expression for the output of the model is available or when this output is obtained via the numerical solution of a set of ordinary differential equations. However, cost functions involved in parameter estimation are usually challenging for interval techniques, if only because of multi-occurrences of the parameters in the formal expression of the cost. This paper addresses parameter estimation via the verified global optimization of quadratic cost functions. It introduces tools instrumental for the minimization of generic cost functions. When an explicit expression of the output of the parametric model is available, significant improvements may be obtained by a new box exclusion test and by careful manipulations of the quadratic cost function. When the model is described by ODEs, some of the techniques available in the previous case may still be employed, provided that sensitivity functions of the model output with respect to the parameters are available.

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“…VALENCIA-IVP has been developed originally as an initial value problem solver for sets of ODEs with uncertainties in the initial states and parameters (Rauh et al, 2007a;Rauh et al, 2007b). The solution provided by VALENCIA-IVP is an interval enclosure which contains all reachable states of the dynamical system.…”

Section: Valencia-ivp For the Calculation Of Guaranteed State Enclosumentioning

confidence: 99%

“…In further extensions of VALENCIA-IVP, consistency tests based on backward integration of subintervals of the state enclosure [x encl (t)] have been implemented. These consistency tests aim at the reduction of overestimation by the detection and elimination of subintervals of [x encl (t)] which certainly result from overestimation (Rauh et al, 2007a;Rauh et al, 2007b). Finally, physical conservation properties can be exploited as further constraints to detect and reduce overestimation .…”

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confidence: 99%

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

Rauh

Brill

Günther

2009

International Journal of Applied Mathematics and Computer Science

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The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differentialalgebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial value problems for ordinary differential equations. For the application to DAEs, VALENCIA-IVP has been extended by an interval Newton technique to solve nonlinear algebraic equations in a guaranteed way. In addition to verified simulation of initial value problems for DAE systems, the developed approach is applicable to the verified solution of the so-called inverse control problems. In this case, guaranteed enclosures for valid input signals of dynamical systems are determined such that their corresponding outputs are consistent with prescribed time-dependent functions. Simulation results demonstrating the potential of VALENCIA-IVP for solving DAEs in technical applications conclude this paper. The selected application scenarios point out relations to other existing verified simulation techniques for dynamical systems as well as directions for future research.

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Extensions of ValEncIA‐IVP for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization

Cited by 8 publications

References 3 publications

Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems

Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems

Verified Global Optimization for Estimating the Parameters of Nonlinear Models

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

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