Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution

Cao, Yang; Li, Shengtai; Petzold, Linda R.; Serban, Radu

doi:10.1137/s1064827501380630

Cited by 354 publications

(282 citation statements)

References 23 publications

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“…The dynamic optimization is carried out using Dyos HoneyBee 1.9 with single shooting and SNOPT as optimizer [43]. The sensitivity information is obtained from SLIMEX via the integration of the sensitivity equations [11,12,44]. The lower-level program is solved by integration over a fine grid.…”

Section: Numerical Case Studiesmentioning

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: Numerical Case Studiesmentioning

confidence: 99%

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Faust

Chachuat

et al. 2015

Automatica

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“…In the sequel, we now consider an approach based on (backward) adjoint integration [7]. We differentiate (4) w.r.t.…”

Section: Transient Sensitivity Analysismentioning

confidence: 99%

“…The method has been popularized in [8,12] for linear problems. For more general DAEs the method has been studied in [7] in a more mathematical way.…”

Section: Introductionmentioning

confidence: 99%

Adjoint Transient Sensitivity Analysis in Circuit Simulation

Ilievski

Xu²,

Verhoeven

et al. 2007

Scientific Computing in Electrical Engineering

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Summary. Sensitivity analysis is an important tool that can be used to assess and improve the design and accuracy of a model describing an electronic circuit. Given a model description in the form of a set of differential-algebraic equations it is possible to observe how a circuit's output reacts to varying input parameters, which are introduced at the requirements stage of design. In this paper we consider the adjoint method more closely. This method is efficient when the number of parameters is large. We extend the transient sensitivity work of Petzold et al., in particular we take into account the parameter dependency of the dynamic term. We also compare the complexity of the direct and adjoint sensitivity and derive some error estimates. Finally we sketch out how Model Order Reduction techniques could be used to improve the efficiency of adjoint sensitivity analysis.

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“…Because only one row K † i * (t, T ) of the adjoint solution is required, we solve a vector, rather than matrix equation. This solution can be computed using a standard solver, but effort will be reduced if a package such as the DASPKAdjoint is used [34], [35]. Figure 4 shows the results of a numerical experiment in which a small perturbation is made to the state representing Per/Cry mRNA (PCm) in the clock model.…”

Section: Phase Sensitivity To State Perturbationsmentioning

confidence: 99%

Sensitivity Measures for Oscillating Systems: Application to Mammalian Circadian Gene Network

Taylor

Petzold

Doyle³

2007

IEEE Trans. Circuits Syst. I

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Vital physiological behaviors exhibited daily by bacteria, plants, and animals are governed by endogenous oscillators called circadian clocks. The most salient feature of the circadian clock is its ability to change its internal time (phase) to match that of the external environment. The circadian clock, like many oscillators in nature, is regulated at the cellular level by a complex network of interacting components. As a complementary approach to traditional biological investigation, we utilize mathematical models and systems theoretic tools to elucidate these mechanisms. The models are systems of ordinary differential equations exhibiting stable limit cycle behavior. To study the robustness of circadian phase behavior, we use sensitivity analysis. As the standard set of sensitivity tools are not suitable for the study of phase behavior, we introduce a novel tool, the parametric impulse phase response curve (pIPRC).

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Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution

Cited by 354 publications

References 23 publications

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Local optimization of dynamic programs with guaranteed satisfaction of path constraints

Adjoint Transient Sensitivity Analysis in Circuit Simulation

Sensitivity Measures for Oscillating Systems: Application to Mammalian Circadian Gene Network

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