Modern Nonlinear Optimization Techniques for an Optimal Control of System Dynamics Models

Please always quote using this URN: urn:nbn:de:0297-zib-48159
  • We study System Dynamics models with several free parameters that can be altered by the user. We assume that the user's goal is to achieve a certain dynamic behavior of the model by varying these parameters. In order to the find best possible combination of parameter settings, several automatic parameter tuning methods are described in the literature and readily available within existing System Dynamic software packages. We give a survey on the available techniques in the market and describe their theoretical background. Some of these methods are already six decades old, and meanwhile newer and more powerful optimization methods have emerged in the mathematical literature. One major obstacle for their direct use are tabled data in System Dynamics models, which are usually interpreted as piecewise linear functions. However, modern optimization methods usually require smooth functions which are twice continuously differentiable. We overcome this problem by a smooth spline interpolation of the tabled data. We use a test set of three complex System Dynamic models from the literature, describe their individual transition into optimization problems, and demonstrate the applicability of modern optimization algorithms to these System Dynamics Optimization problems.

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Author:Ingmar Vierhaus, Armin Fügenschuh, Robert Lion Gottwald, Stefan N. Grösser
Document Type:ZIB-Report
Tag:Nonlinear Optimization; Optimal Control; Spline Interpolation; System Dynamics
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES
Date of first Publication:2014/03/20
Series (Serial Number):ZIB-Report (14-08)
ISSN:1438-0064
Licence (German):License LogoCreative Commons - Namensnennung-Nicht kommerziell-Keine Bearbeitung

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