Decomposition algorithms for on-line estimation with nonlinear DAE models

Albuquerque, J. Sodré; Biegler, Lorenz T.

doi:10.1016/s0098-1354(96)90029-0

Cited by 42 publications

(12 citation statements)

References 12 publications

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“…There are many challenges to the application of DAEs directly in nonlinear control and optimization (Biegler et al, 2012). Recent advances include simultaneous methods (Binder et al, 2001), decomposition methods (Albuquerque and Biegler, 1997;Diehl et al, 2002), efficient nonlinear programming solvers (Wächter Table 1 Estimation: two forms for dynamic data reconciliation.…”

Section: Nonlinear Control and Optimizationmentioning

confidence: 99%

Nonlinear modeling, estimation and predictive control in APMonitor

Hedengren

Shishavan

Powell

et al. 2014

Computers & Chemical Engineering

184

117

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This paper describes nonlinear methods in model building, dynamic data reconciliation, and dynamic optimization that are inspired by researchers and motivated by industrial applications. A new formulation of the 1-norm objective with a dead-band for estimation and control is presented. The dead-band in the objective is desirable for noise rejection, minimizing unnecessary parameter adjustments and movement of manipulated variables. As a motivating example, a small and well-known nonlinear multivariable level control problem is detailed that has a number of common characteristics to larger controllers seen in practice. The methods are also demonstrated on larger problems to reveal algorithmic scaling with sparse methods. The implementation details reveal capabilities of employing nonlinear methods in dynamic applications with example code in both Matlab and Python programming languages.

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Section: Nonlinear Control and Optimizationmentioning

confidence: 99%

Nonlinear modeling, estimation and predictive control in APMonitor

Hedengren

Shishavan

Powell

et al. 2014

Computers & Chemical Engineering

184

117

View full text Add to dashboard Cite

show abstract

“…Discretization-based estimation approaches have been widely studied in diverse fields such as chemical engineering [24][25][26] and aerospace engineering [27][28][29] (see [30] for a comprehensive review) but less so in computational biology. A major factor that has hindered wider adoption is the lack of easy-to-use computational frameworks that facilitate access to non-expert users.…”

Section: Interior-point Methodsmentioning

confidence: 99%

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Shin

Venturelli

Zavala

2018

Preprint

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We present a nonlinear programming (NLP) framework for the scalable solution of parameter estimation problems that arise in dynamic modeling of biological systems. Such problems are computationally challenging because they often involve highly nonlinear and stiff differential equations as well as many experimental data sets and parameters. The proposed framework uses cutting-edge modeling and solution tools which are computationally efficient, robust, and easy-to-use. Specifically, our framework uses a time discretization approach that: i) avoids repetitive simulations of the dynamic model, ii) enables fully algebraic model implementations and computation of derivatives, and iii) enables the use of computationally efficient nonlinear interior point solvers that exploit sparse and structured linear algebra techniques. We demonstrate these capabilities by solving estimation problems for synthetic human gut microbiome community models. We show that an instance with 156 parameters, 144 differential equations, and 1,704 experimental data points can be solved in less than 3 minutes using our proposed framework (while an off-the-shelf simulation-based solution framework requires over 7 hours). We also create large instances to show that the proposed framework is scalable and can solve problems with up to 2,352 parameters, 2,304 differential equations, and 20,352 data points in less than 15 minutes. Competing methods reported in the computational biology literature cannot address problems of this level of complexity. The proposed framework is flexible, can be broadly applied to dynamic models of biological systems, and enables the implementation of sophisticated estimation techniques to quantify parameter uncertainty, to diagnose observability/uniqueness issues, to perform model selection, and to handle outliers. Author summaryConstructing and validating dynamic models of biological systems spanning biomolecular networks to ecological systems is a challenging problem. Here we present a scalable computational framework to rapidly infer parameters in complex dynamic models of biological systems from large-scale experimental data. The framework was applied to infer parameters of a synthetic microbial community model from large-scale time series data. We also demonstrate that this framework can be used to analyze parameter uncertainty, to diagnose whether the experimental data are sufficient to PLOS 1/28 uniquely determine the parameters, to determine the model that best describes the data, and to infer parameters in the face of data outliers. PLOS

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“…Edgar and coworkers [14], [15] investigated moving horizon strategies for nonlinear data reconciliation. Biegler et al [16]- [18] investigated statistical and numerical issues related to optimization-based nonlinear data reconciliation. Marquardt et al [19], [20] discussed multi-scale strategies for MHE and the benefits of incorporating constraints in estimation.…”

Section: Introductionmentioning

confidence: 99%

Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations

Rao

Rawlings

Mayne

2003

IEEE Trans. Automat. Contr.

761

515

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Abstract-State estimator design for a nonlinear discrete-time system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ online optimization using a moving horizon approximation. In this article we propose a general theory for constrained moving horizon estimation. Sufficient conditions for asymptotic and bounded stability are established. We apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation. Examples are used to illustrate the benefits of constrained state estimation. Our framework is deterministic.

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Decomposition algorithms for on-line estimation with nonlinear DAE models

Cited by 42 publications

References 12 publications

Nonlinear modeling, estimation and predictive control in APMonitor

Nonlinear modeling, estimation and predictive control in APMonitor

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations

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