Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory

Pence, Benjamin L.; Fathy, Hosam K.; Stein, Jeffrey L.

doi:10.1016/j.automatica.2011.08.014

Cited by 28 publications

(12 citation statements)

References 8 publications

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“…State space models can describe the dynamics of systems and play an important part in the signal filtering [1,2], control theory [3,4], and system analysis [5][6][7]. It is easy to estimate the parameters of linear time-invariant state space systems by resorting to the subspace identification methods [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle

Wang

Ding

2015

Signal Processing

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Section: Introductionmentioning

confidence: 99%

Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle

Wang

Ding

2015

Signal Processing

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“…For instance, the gPC is combined with maximum likelihood method to estimate parameters. Point estimates of the process parameters are developed by substituting the gPC expressions into a likelihood function to solve the resulting maximum likelihood problem, and the estimates of parameters are transformed into a best‐fit problem of random variables . However, the accuracy of these methods is highly related to the number of data points used in the likelihood function, which maximizes the likelihood by fitting predictions obtained from gPC models and data.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation for an Inverse Nonlinear Stochastic Problem: Reactivity Ratio Studies in Copolymerization

Budman

Duever

2017

Macro Theory & Simulations

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A generalized polynomial chaos (gPC)‐based methodology is developed to estimate the reactivity ratio in copolymerization, where the reactivity ratio is assumed to be stochastic unknown and determined by comparing model predictions with limited experimental data. The estimation step is formulated as a stochastic inverse problem of finding the distributional stochastic reactivity ratio parameters with a maximum likelihood function. The results show that the gPC‐based reactivity ratio estimation is efficient and powerful, since it simultaneously provides the best estimates and their corresponding variances. Beyond achieving accurate estimation results, it is shown that the computational cost of the gPC‐based methodology is significantly lower than Markov chain Monte Carlo simulations, thus demonstrating the potential of the gPC method for dealing with other more complicated nonlinear problems.

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“…Subspace model identification has been investigated for use in MPC and can be carried out through a variety of techniques such as the canonical variate algorithm (CVA), the multivariable output error state‐space algorithm (MOESP), and numerical algorithms for subspace state‐space system identification (N4SID) . Grey box nonlinear state‐space system identification methods include maximum likelihood parameter estimation methods and optimization‐based methods …”

Section: Introductionmentioning

confidence: 99%

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

2015

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The focus of this work is on economic model predictive control (EMPC) that utilizes well-conditioned polynomial nonlinear state-space (PNLSS) models for processes with nonlinear dynamics. Specifically, the article initially addresses the development of a nonlinear system identification technique for a broad class of nonlinear processes which leads to the construction of PNLSS dynamic models which are well-conditioned over a broad region of process operation in the sense that they can be correctly integrated in real-time using explicit numerical integration methods via time steps that are significantly larger than the ones required by nonlinear state-space models identified via existing techniques. Working within the framework of PNLSS models, additional constraints are imposed in the identification procedure to ensure well-conditioning of the identified nonlinear dynamic models. This development is key because it enables the design of Lyapunov-based EMPC (LEMPC) systems for nonlinear processes using the well-conditioned nonlinear models that can be readily implemented in real-time as the computational burden required to compute the control actions within the process sampling period is reduced. A stability analysis for this LEMPC design is provided that guarantees closed-loop stability of a process under certain conditions when an LEMPC based on a nonlinear empirical model is used. Finally, a classical chemical reactor example demonstrates both the system identification and LEMPC design techniques, and the significant advantages in terms of computation time reduction in LEMPC calculations when using the nonlinear empirical model.

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Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory

Cited by 28 publications

References 8 publications

Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle

Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle

Parameter Estimation for an Inverse Nonlinear Stochastic Problem: Reactivity Ratio Studies in Copolymerization

On identification of well‐conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes

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