State event location in differential-algebraic models

Park, Taeshin; Barton, Paul I.

doi:10.1145/232807.232809

Cited by 122 publications

(103 citation statements)

References 21 publications

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“…This hybrid system can be solved accurately using adaptive step-size solvers with rigorous state-event location [38], thereby providing the maximum constraint violation as g max (ū) = γ(t f ,ū). Likewise, the global maximizer t max (ū) is obtained at the time point at which the last event is triggered during the integration.…”

Section: If Feasiblementioning

confidence: 99%

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Faust

Chachuat

et al. 2015

Automatica

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An algorithm is proposed for locating a feasible point satisfying the KKT conditions to a specified tolerance of feasible inequalitypath-constrained dynamic programs (PCDP) within a finite number of iterations. The algorithm is based on iteratively approximating the PCDP by restricting the right-hand side of the path constraints and enforcing the path constraints at finitely many time points. The main contribution of this article is an adaptation of the semi-infinite program (SIP) algorithm proposed in [Mitsos, Optimization, 2011, 60(10-11):1291-1308] to PCDP. It is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first-order KKT conditions of the PCDP to a specified tolerance. The main assumptions are: i) availability of a nonlinear program (NLP) local solver that generates a KKT point of the constructed approximation to PCDP at each iteration if this problem is indeed feasible; ii) existence of a Slater point of the PCDP that also satisfies the first-order KKT conditions of the PCDP to a specified tolerance; iii) all KKT multipliers are nonnegative and uniformly bounded with respect to all iterations. The performance of the algorithm is analyzed through two numerical case studies.

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Section: If Feasiblementioning

confidence: 99%

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Faust

Chachuat

et al. 2015

Automatica

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“…A similar idea has been used by Park and Barton [14] for handling transitions in hybrid systems of differential algebraic equations.…”

Section: Techniques For the Efficient Simulation Of Discontinuous Ivpsmentioning

confidence: 99%

An efficient unified approach for the numerical solution of delay differential equations

ZivariPiran

Enright

2009

Numer Algor

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In this paper we propose a new framework for designing a delay differential equation (DDE) solver which works with any supplied initial value problem (IVP) solver that is based on a standard step-by-step approach, such as Runge-Kutta or linear multi-step methods, and can provide dense output. This is done by treating a general DDE as a special example of a discontinuous IVP. Using this interpretation we develop an efficient technique to solve the resulting discontinuous IVP. We also give a more clear process for the numerical techniques used when solving the implicit equations that arise on a time step, such as when the underlying IVP solver is implicit or the delay vanishes.The new modular design for the resulting simulator we introduce, helps to accelerate the utilization of advances in the different components of an effective numerical method. Such components include the underlying discrete formula, the interpolant for dense output, the strategy for handling discontinuities and the iteration scheme for solving any implicit equations that arise.

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“…These techniques are able to detect multiple transition however they tend to be expensive. Most recently, Park and Barton [17] combine some of these ideas and uses methods from interval arithmetic to create efficient tests to determine intervals where it is possible an event had occured. This event detection method seems to be the most reliable technique in the literature, it is streamlined and well suited to stiff problems.…”

Section: Motivation and Previous Workmentioning

confidence: 99%

Accurate Event Detection for Simulating Hybrid Systems

Esposito

Kumar

Pappas

2001

Lecture Notes in Computer Science

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Abstract. It has been observed that there are a variety of situations in which the most popular hybrid simulation methods can fail to properly detect the occurrence of discrete events. In this paper, we present a method for detecting discrete which, using techniques borrowed from control theory, selects integration step sizes in such a way that the simulation slows down as the state approaches a set which triggers an event (a guard set). Our method guarantees that the state will approach the boundary of this set exponentially; and in the case of linear or polynomial guard descriptions, terminating on it, without entering it. Given that any system with a nonlinear guard description can be transformed to an equivalent system with a linear guard description, this technique is applicable to a broad class of systems. Even in situations where nonlinear guards have not been transformed to the canonical form, the method is still increases the chances of detecting and event in practice. We show how to extend the method to guard sets which are constructed from many simple sets using boolean operators (e.g. polyhedral or semi-algebraic sets) . The technique is easily used in combination with existing numerical integration methods and does not adversely affect the underlying accuracy or stability of the algorithms.

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State event location in differential-algebraic models

Cited by 122 publications

References 21 publications

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

An efficient unified approach for the numerical solution of delay differential equations

Accurate Event Detection for Simulating Hybrid Systems

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