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  • 1
    Electronic Resource
    Electronic Resource
    Fully discrete approximation methods for the estimation of parabolic systems and boundary parameters (1986)
    Springer
    Acta applicandae mathematicae 7 (1986), S. 1-34 
    Details
    ISSN: 1572-9036
    Keywords: 41A15 ; 65N30 ; Parabolic systems ; parameter estimation ; approximation methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A spatially and temporally discrete numerical approximation scheme is developed for the identification of a class of semilinear parabolic systems with unknown boundary parameters. The identification problem is formulated as a least squares fit to data subject to an equivalent representation for the dynamics in the form of an abstract evolution equation. Finite-dimensional difference equation state approximations are constructed using a cubic spline-based, Galerkin method and the Padé rational function approximations to the exponential. A sequence of approximating identification problems result, the solutions of which are shown to exist and, in a certain sense, approximate solutions to the original identification problem. Numerical results for two examples, one involving the modeling of biological mixing in deep sea sediment cores, and the other, the estimation of transport parameters for indoor mixing, are discussed. In both examples, the identification is based upon actual experimental data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046975
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  • 2
    Electronic Resource
    Electronic Resource
    Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems (1991)
    Springer
    Applied mathematics & optimization 24 (1991), S. 233-256 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We develop an abstract framework and convergence theory for Galerkin approximation for inverse problems involving the identification of nonautonomous, in general nonlinear, distributed parameter systems. We provide a set of relatively easily verified conditions which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite-dimensional identification problems. Our approach is based upon the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasi-linear elliptic operators along with some applications and numerical results are presented and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01447744
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  • 3
    Electronic Resource
    Electronic Resource
    Parameter estimation techniques for interaction and redistribution models: a predator-prey example (1987)
    Springer
    Oecologia 74 (1987), S. 356-362 
    Details
    ISSN: 1432-1939
    Keywords: Parameter estimation ; Species interaction ; redistribution ; Heterogeneous environments
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The use of parameter estimation techniques for partial differential equations is illustrated using a predatorprey model. Whereas ecologists have often estimated parameters in models, they have not previously been able to do so for models that describe interactions in heterogeneous environments. The techniques we describe for partial differential equations will be generally useful for models of interacting species in spatially complex environments and for models that include the movement of organisms. We demonstrate our methods using field data from a ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interaction. Our parameter estimation algorithms can be employed to identify models that explain better than 80% of the observed variance in aphid and ladybird densities. Such parameter estimation techniques can bridge the gap between detail-rich experimental studies and abstract mathematical models. By relating the particular bestfit models identified from our experimental data to other information on Coccinella behavior, we conclude that a term describing local taxis of ladybirds towards prey (aphids in this case) is needed in the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00378930
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  • 4
    Electronic Resource
    Electronic Resource
    Modeling insect dispersal and estimating parameters when mark-release techniques may cause initial disturbances (1985)
    Springer
    Journal of mathematical biology 22 (1985), S. 259-277 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider the problem of quantitatively modeling movements of marked flea beetles in cultivated arrays of the cole crop, collards (Brassica oleraceae). Methods for the estimation of temporally and spatially dependent parameters in general dispersal models are outlined and a summary of our findings using these methods with flea beetle data is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276485
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  • 5
    Electronic Resource
    Electronic Resource
    Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow models (1983)
    Springer
    Journal of mathematical biology 17 (1983), S. 253-273 
    Details
    ISSN: 1432-1416
    Keywords: Parameter estimation ; Transport in tissue ; Insect dispersal ; Spline approximations ; Parabolic equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We develop techniques for estimating the coefficients, boundary data, and initial data associated with transport equations (or more generally, parabolic distributed models). Our estimation schemes are based on cubic spline approximations, for which convergence results are given. We discuss the performance of these techniques in two investigations of biological interest: (1) transport of labeled sucrose in brain tissue white matter, (2) insect dispersal that cannot be modeled by a random diffusion mechanism alone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276516
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  • 6
    Electronic Resource
    Electronic Resource
    Statistical methods for model comparison in parameter estimation problems for distributed systems (1990)
    Springer
    Journal of mathematical biology 28 (1990), S. 501-527 
    Details
    ISSN: 1432-1416
    Keywords: Hypothesis testing ; Parameter estimation ; Partial differential equations ; Approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00164161
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  • 7
    Electronic Resource
    Electronic Resource
    Estimation of growth and survival in size-structured cohort data: an application to larval striped bass (Morone saxatilis) (1991)
    Springer
    Journal of mathematical biology 30 (1991), S. 125-150 
    Details
    ISSN: 1432-1416
    Keywords: Size-structural population models ; Parameter estimation ; Growth and mortality rates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a method for estimating growth and mortality rates in size-structured population models. The methods are based on least-square fits to data using approximate models (using spline approximations) for the underlying partial differential equation population model. In a series of numerical tests, we compare our approach to an existing method (due to Hackney and Webb). As an example, we apply our techniques to experimental data from larval striped bass field studies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160331
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  • 8
    Electronic Resource
    Electronic Resource
    Approximation of nonlinear functional differential equation control systems (1979)
    Springer
    Journal of optimization theory and applications 29 (1979), S. 383-408 
    Details
    ISSN: 1573-2878
    Keywords: Functional differential equations ; nonlinear control problems ; semigroups ; approximation techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We develop a general approximation framework for use in optimal control problems governed by nonlinear functional differential equations. Our approach entails only the use of linear semigroup approximation results, while the nonlinearities are treated as perturbations of a linear system. Numerical results are presented for several simple nonlinear optimal control problem examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933142
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  • 9
    Electronic Resource
    Electronic Resource
    Feedback Control Methodologies for Nonlinear Systems (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 1-33 
    Details
    ISSN: 1573-2878
    Keywords: nonlinear optimal feedback control ; Hamilton–Jacobi–Bellman equation ; state-dependent Riccati equation ; interpolation of open-loop controls
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A number of computational methods have been proposed in the literature to design and synthesize feedback controls when the plant is modeled by nonlinear dynamics. However, it is not immediately clear which is the best method for a given problem; this may depend on the nature of the nonlinearities, size of the system, whether the amount of control used or time needed for the method is a concern, and other factors. In this paper, a comprehensive comparison study of five methods for the synthesis of nonlinear control systems is carried out. The performance of the methods on several test problems are studied, and some recommendations are made as to which feedback control method is best to use under various conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004607114958
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  • 10
    Electronic Resource
    Electronic Resource
    The synthesis of optimal controls for linear, time-optimal problems with retarded controls (1971)
    Springer
    Journal of optimization theory and applications 8 (1971), S. 319-366 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optimization problems involving linear systems with retardations in the controls are studied in a systematic way. Some physical motivation for the problems is discussed. The topics covered are: controllability, existence and uniqueness of the optimal control, sufficient conditions, techniques of synthesis, and dynamic programming. A number of solved examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00929286
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