Identification of finite dimensional models of infinite dimensional dynamical systems

Coca, Daniel; Billings, S.A.

doi:10.1016/s0005-1098(02)00099-7

Cited by 84 publications

(47 citation statements)

References 15 publications

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“…[13,14] for the application of Galerkin approximation schemes, [15] for rational approximations, [16] for collocation methods and [17] for minimal finite element approximations. Our approach, as illustrated to an advection-reaction system, is to handle the parameter estimation problem via a linear regressive realization of the approximate discrete-time system in order to obtain unique estimates.…”

Section: Discussionmentioning

confidence: 99%

Linear regressive realizations of LTI state space models

Keesman¹,

Khairudin

2009

IFAC Proceedings Volumes

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In this paper, linear regressive model structures are deduced from single input -single output (SISO) deterministic LTI systems in state space form. The resulting linear regression and predictor are exact representations of a discrete-time LTI state space model Σ d belonging to a certain class S. As an illustrative example, a process with first-order reaction and advective transport is approximated by a discrete-time state space model Σ d , where the one-dimensional space is divided into n compartments and is reparametrized such that Σ d ⊆ S. The system output can then be explicitly predicted by y(t) = θ T φ(t−1)−γ(t−1) as a function of the number of compartments n, the sensor position j * , the parameter vector θ = ξ(ϑ) with ϑ a vector with original (physical) parameters, and input-output data. The method is attractive for experimental design, direct parameter estimation and prediction when prior (physical) parameter knowledge is to be preserved.

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Section: Discussionmentioning

confidence: 99%

Linear regressive realizations of LTI state space models

Keesman¹,

Khairudin

2009

IFAC Proceedings Volumes

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“…A similar approach was recently presented in (Coca and Billings, 2002) where the distributed parameter system is approximated with a linear combination of splines weighted with dynamically-varying coefficients.…”

Section: Lpv Approximation Of Distributed Parameter Systemsmentioning

confidence: 99%

LPV approximation of distributed parameter systems in environmental modelling

Belforte

Dabbene

2005

Environmental Modelling & Software

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Environmental systems often involve phenomena that are continuous functions not only of time, but also of other independent variables, such as space coordinates. Typical examples are transportation phenomena of mass or energy, such as heat transmission and/or exchange, humidity diffusion or concentration distributions. These systems are intrinsically distributed parameter systems whose description usually requires the introduction of partial differential equations (PDE). Therefore, their modelling can be quite complex, both for what concerns the model construction and its identification. Indeed, a typical approach for the simulation of such systems is the use of finite elements techniques. However, this kind of description usually involves a huge number of parameters and requires time-consuming computations while not being suited for identification. For this reason, such models are generally not suitable for control purposes. In many cases, however, the involved phenomena depend on the independent (space) variables in a smooth way, and for fixed values of the independent variables, input-output relations can be satisfactorily represented by linear time-invariant models. In such conditions, a possible alternative to PDE consists in representing the physical system with a Linear Parameter Varying (LPV) model whose parameters are functions of the independent variables. The advantage of this approach is the relatively simple model obtained, which is directly suitable for control purposes and can be easily identified from input-output data by means of classical techniques. Moreover, optimal identification schemes can be derived for such models, allowing the optimization of the number of measurements. This can be particularly useful in several environmental applications for which the cost of measurements represents a severe constraint.In this paper, the derivation of LPV models for the representation of distributed phenomena in environmental systems is discussed, and the issue of model uncertainty is addressed. In particular, it is shown that the derived models are linear in the parameters, and therefore classical methods for handling uncertainty are directly applicable. The proposed approach is illustrated by means of a simulated and a practical example concerning soil disinfestation by solarization.

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“…The modeling performance relies on the choice of the spatial basis functions. Local spatial basis function (e.g., finite element bases [7] ) will lead to a high-order ODE model, while global spatial basis functions (e.g., fourier series [8] ), eigen-functions of the system [1] , and basis functions derived from Karhunen-Love (K-L) decomposition [9] could derive an accurate low-order ODE model, which is suitable for real-time control. Among these global spatial basis functions, basis functions derived from K-L decomposition is optimal in the sense that the model dimension is the lowest given the desired model accuracy.…”

Section: Introductionmentioning

confidence: 99%

A time/space separation based 3D fuzzy modeling approach for nonlinear spatially distributed systems

Zhang

et al. 2017

Int. J. Autom. Comput.

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Spatially distributed systems (SDSs) are usually infinite-dimensional spatio-temporal systems with unknown nonlinearities. Therefore, to model such systems is difficult. In real applications, a low-dimensional model is required. In this paper, a time/space separation based 3D fuzzy modeling approach is proposed for unknown nonlinear SDSs using input-output data measurement. The main characteristics of this approach is that time/space separation and time/space reconstruction are fused into a novel 3D fuzzy system. The modeling methodology includes two stages. The first stage is 3D fuzzy structure modeling which is based on Mamdani fuzzy rules. The consequent sets of 3D fuzzy rules consist of spatial basis functions estimated by Karhunen-Love decomposition. The antecedent sets of 3D fuzzy rules are used to construct temporal coefficients. Going through 3D fuzzy rule inference, each rule realizes time/space synthesis. The second stage is parameter identification of 3D fuzzy system using particle swarm optimization algorithm. After an operation of defuzzification, the output of the 3D fuzzy system can reconstruct the spatio-temporal dynamics of the system. The model is suitable for the prediction and control design of the SDS since it is of low-dimension and simple nonlinear structure. The simulation and experiment are presented to show the effectiveness of the proposed modeling approach.

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Identification of finite dimensional models of infinite dimensional dynamical systems

Cited by 84 publications

References 15 publications

Linear regressive realizations of LTI state space models

Linear regressive realizations of LTI state space models

LPV approximation of distributed parameter systems in environmental modelling

A time/space separation based 3D fuzzy modeling approach for nonlinear spatially distributed systems

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