Nonlinear system identification employing automatic differentiation |
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| Authors: | Jan Schumann-Bischoff Stefan Luther Ulrich Parlitz |
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| Institution: | Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany;Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen, Germany;DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, and Heart Research Center Göttingen, D-37077 Göttingen, Germany |
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| Abstract: | An optimization based state and parameter estimation method is presented where the required Jacobian matrix of the cost function is computed via automatic differentiation. Automatic differentiation evaluates the programming code of the cost function and provides exact values of the derivatives. In contrast to numerical differentiation it is not suffering from approximation errors and compared to symbolic differentiation it is more convenient to use, because no closed analytic expressions are required. Furthermore, we demonstrate how to generalize the parameter estimation scheme to delay differential equations, where estimating the delay time requires attention. |
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| Keywords: | Nonlinear modelling Parameter estimation Delay differential equations Data assimilation |
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