Economical Input Design for Identification of Multivariate Systems

Kumar, Abhishankar; Nabil, M.; Narasimhan, Sridharakumar

doi:10.1016/j.ifacol.2015.12.313

Cited by 4 publications

(12 citation statements)

References 10 publications

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“…We will do that for the classical model structures used in prediction-error identification (ARX, FIR, BJ, OE model structures) and for both multisine input vector and for an input vector generated as u(t ) = N (z)v(t ) with v a vector of independent white noises of arbitrary dimension and N a matrix of transfer functions. These conditions can, e.g., be of importance for MIMO optimal experiment design (see, e.g., [1,11]) since it will allow to choose the input vector parametrization in such a way that data informativity is guaranteed.…”

Section: Introductionmentioning

confidence: 99%

Data informativity for the open-loop identification of MIMO systems in the prediction error framework

et al. 2020

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In Prediction Error identification, to obtain a consistent estimate of the true system, it is crucial that the input excitation yields informative data with respect to the chosen model structure. We consider in this paper the data informativity property for the identification of a Multiple-Input Multiple-Output system in open loop and we derive conditions to check whether a given input vector will yield informative data with respect to the chosen model structure. We do that for the classical model structures used in prediction-error identification and for the classical types of input vectors, i.e., input vectors whose elements are either multisines or filtered white noises.

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Section: Introductionmentioning

confidence: 99%

Data informativity for the open-loop identification of MIMO systems in the prediction error framework

et al. 2020

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“…Although not comprehensive, this paragraph would touch upon some of the seminal pieces of work in this area and discuss in brief, the methodologies used therein. In each of Barenthin et al [2008], Kumar et al [2015], the power spectrum is parameterized as…”

Section: Figurementioning

confidence: 99%

“…Ljung et al [2011] is an excellent article which discusses the applications of system identification in communication systems, sensor networks and machine learning algorithms. In addition, automotive systems and chemical engineering processes also find the need for system identification and optimal input design (Alberer et al [2011], Kumar et al [2015]).…”

Section: Figurementioning

confidence: 99%

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Optimal input design for system identification using spectral decomposition

Mohan

Mithun

Bhikkaji

2018

International Journal of Control

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The aim of this paper is to design a band-limited optimal input with power constraints for identifying a linear multi-input multi-output system. It is assumed that the nominal system parameters are specified. The key idea is to use the spectral decomposition theorem and write the power spectrum as φu(jω) = 1 2 H(jω)H * (jω). The matrix H(jω) is expressed in terms of a truncated basis for L 2 ([−ωcut-off, ωcut-off]). With this parameterization, the elements of the Fisher Information Matrix and the power constraints turn out to be homogeneous quadratics in the basis coefficients. The optimality criterion used are the well-known D−optimality, A−optimality, T −optimality and E−optimality. The resulting optimization problem is non-convex in general. A lower bound on the optimum is obtained through a bi-linear formulation of the problem, while an upper bound is obtained through a convex relaxation. These bounds can be computed efficiently as the associated problems are convex. The lower bound is used as a sub-optimal solution, the sub-optimality of which is determined by the difference in the bounds. Interestingly, the bounds match in many instances and thus, the global optimum is achieved. A discussion on the non-convexity of the optimization problem is also presented. Simulations are provided for corroboration.

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“…We address this problem by first describing the expected dynamic operating region (EDOR) of the plant described by linear time invariant (LTI) models. , The EDOR is the region in the input/output or state space where the system is likely to operate (modulo a probability level) . This is a function of the disturbances and additional perturbation introduced due to identification, and under fairly general conditions, it is an ellipsoid.…”

Section: Introductionmentioning

confidence: 99%

Economically Optimal Input Design Approach for Identification of Constrained Processes

Kumar

Jan

Narasimhan

2018

Ind. Eng. Chem. Res.

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Input design is the process of designing informative inputs which maximizes the information about system dynamics using minimal cost and resources in a system identification experiment. In this work, we focus on designing inputs based on the economic framework for identification of constrained processes. The process is nominally constrained and feasibility during identification is ensured by "backing off" (or moving away) from the active constraints. The economic cost or penalty due to the "back-off" is minimized while ensuring feasibility and satisfying constraints on the quality of the identified model. The proposed economic based formulation results in a nonconvex optimization problem. This problem can be solved using the bisection algorithm for single input−single output (SISO) systems. We present a two-stage iterative solution algorithm to solve for multi-input−multi-output (MIMO) systems where a convex optimization problem is solved at each stage. The optimal input is realized as a white noise passing through an M-tap filter. The filter coefficients are obtained by a noniterative spectral factorization technique. The efficacy of the proposed approach has been successfully demonstrated in a mass spring damper system as well as in a Van der Vusse reactor system.

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Economical Input Design for Identification of Multivariate Systems

Cited by 4 publications

References 10 publications

Data informativity for the open-loop identification of MIMO systems in the prediction error framework

Data informativity for the open-loop identification of MIMO systems in the prediction error framework

Optimal input design for system identification using spectral decomposition

Economically Optimal Input Design Approach for Identification of Constrained Processes

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