State and parameter estimation in nonlinear systems as an optimal tracking problem

Creveling, Daniel R.; Gill, Philip E.; Abarbanel, Henry D. I.

doi:10.1016/j.physleta.2007.12.051

Cited by 44 publications

(47 citation statements)

References 18 publications

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“…The DSPE method (Creveling et al, 2008) is an optimization technique that uses principles from observer theory (Nijmeijer, 2001) and synchronization (Pecora & Carroll, 1990) of non-linear systems to determine parameters and unmeasured state variables in an experimental system. DSPE allows one to derive the properties of a non-linear dynamical system using only experimental measurements coupled with a mathematical model of the studied system.…”

Section: The Dynamic State and Parameter Estimation Methodsmentioning

confidence: 99%

Dynamic State and Parameter Estimation Applied to Neuromorphic Systems

2012

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Neuroscientists often propose detailed computational models to probe the properties of their studied neural systems. With the advent of neuromorphic engineering, there * emre@ini.phys.ethz.ch † btoth@physics.ucsd.edu 1 is an increasing number of hardware electronic analogs of biological neural systems being proposed as well. However, for both biological and hardware systems, it is often difficult to estimate the parameters of the model such that they are meaningful to the studied experimental system, especially when these models involve a large number of states and parameters which cannot be simultaneously measured. We have developed a procedure to solve this problem in the context of interacting neural populations using a recently developed Dynamic State and Parameter Estimation (DSPE) technique.This technique uses synchronization as a tool for dynamically coupling experimentally measured data to its corresponding model to determine its parameters and internal state variables. While in its conventional use, the experimental data is obtained from the biological neural system, and the model is simulated in software, here we show that this technique is also efficient in validating proposed network models for neuromorphic spike-based Very Large Scale Integration (VLSI) chips, and that it is able to systematically extract network parameters such as synaptic weights, time constants and other variables which are not accessible by direct observation. Our results suggest that this method can become a very useful tool for model-based identification and configuration of neuromorphic multi-chip VLSI systems.

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Section: The Dynamic State and Parameter Estimation Methodsmentioning

confidence: 99%

Dynamic State and Parameter Estimation Applied to Neuromorphic Systems

2012

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“…In general, J (p) will contain many local minima; the mathematical model (3) that is most representative of the experimental system (2) is obtained when the parameters p correspond to the global minimum of the above objective function (4).…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…In this work, we focus specifically on problems where the functional form of the system of differential equations is known, as studied in [3][4][5][6][7]. In the context of deterministic global optimization [8], the present work focuses on the development of a new theory using homotopy optimization to obtain globally optimal parameters in systems governed by nonlinear ordinary differential equations (ODEs).…”

Section: Introductionmentioning

confidence: 99%

“…In such cases, an optimization approach [13,14] is required, of which there are two varieties: single-shooting and multiple-shooting, the latter of which can be implemented with [3,4] or without [14] penalty terms. Provided the conditions of parameter identifiability [15] are met, it is possible to recover the system parameters using only partial state measurements; however, it might not be possible to recover the unknown initial conditions of unmeasured states.…”

Section: Introductionmentioning

confidence: 99%

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Single-shooting homotopy method for parameter identification in dynamical systems

Vyasarayani

McPhee

2012

Phys. Rev. E

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An algorithm for identifying parameters in dynamical systems is developed in this work using homotopy transformations and the single-shooting method. The equations governing the dynamics of the mathematical model are augmented with observer-like homotopy terms that smooth the objective function. As a result, premature convergence to a local minimum is avoided and the obtained parameter estimates are globally optimal. Numerical examples are presented to demonstrate the application of the proposed approach to chaotic systems.

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“…Among the more difficult cases are chaotic dynamical systems given by nonlinear ordinary differential equations (ODE's) in which a sensitive dependence on variables and parameters may lead to a nontrivial estimation problem. To cope with this identification task, several methods have been proposed in the past, including synchronization-based methods [1][2][3][4][5][6][7][8][9], adaptive observers and control system [10][11][12][13][14][15], optimization-based methods [16][17][18][19][20], probabilistic and geometric approaches [21,22], path-integral methods [23,24], and a reformulation of the problem as a boundary-value problem [25,26].…”

Section: Introductionmentioning

confidence: 99%

State and parameter estimation using unconstrained optimization

Schumann-Bischoff

Parlitz

2011

Phys. Rev. E

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We present an efficient method for estimating variables and parameters of a given system of ordinary differential equations by adapting the model output to an observed time series from the (physical) process described by the model. The proposed method is based on (unconstrained) nonlinear optimization exploiting the particular structure of the relevant cost function. To illustrate the features and performance of the method, simulations are presented using chaotic time series generated by the Colpitts oscillator, the three-dimensional Hindmarsh-Rose neuron model, and a nine-dimensional extended Rössler system.

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State and parameter estimation in nonlinear systems as an optimal tracking problem

Cited by 44 publications

References 18 publications

Dynamic State and Parameter Estimation Applied to Neuromorphic Systems

Dynamic State and Parameter Estimation Applied to Neuromorphic Systems

Single-shooting homotopy method for parameter identification in dynamical systems

State and parameter estimation using unconstrained optimization

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