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An LMI Approach to ControlOriented Identification and Model (In)Validation of LPV Systems
, 2003
"... This note proposes a controloriented identification framework for a class of linear parameter varying systems that takes into account both the dependence of part of the model on timevarying parameters as well as the possible existence of a nonparametric component. The main results of the note show ..."
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Cited by 7 (3 self)
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This note proposes a controloriented identification framework for a class of linear parameter varying systems that takes into account both the dependence of part of the model on timevarying parameters as well as the possible existence of a nonparametric component. The main results of the note show that the problems of obtaining and validating a model for these systems can be recast as linear matrix inequality feasibility problems. Moreover, as the information is completed, the algorithm is shown to converge in theinduced topology to the actual plant. Additional results include deterministic bounds on the identification error. These results are illustrated with a practical example arising in the context of active vision.
Identification of MIMO LPV models based on interpolation
"... This paper presents SMILE (Statespace Model Interpolation of Local Estimates), a new technique to estimate linear parameter varying statespace models for multipleinput multipleoutput systems whose dynamics depends on a single varying parameter, called the scheduling parameter. The SMILE techniqu ..."
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This paper presents SMILE (Statespace Model Interpolation of Local Estimates), a new technique to estimate linear parameter varying statespace models for multipleinput multipleoutput systems whose dynamics depends on a single varying parameter, called the scheduling parameter. The SMILE technique is based on the interpolation of linear timeinvariant models that are valid for fixed operating conditions of the system, that is, for constant values of the scheduling parameters. The methodology yields affine LPV models that are numerically wellconditioned and therefore suitable for LPV control synthesis procedures. The underlying interpolation technique is formulated as a nonlinear leastsquares optimization problem that can be efficiently solved by standard solvers. Application of the proposed methodology to a vibroacoustic setup, whose dynamics are highly sensitive to the ambient temperature, clearly demonstrates the potential of the SMILE technique.
An LMI Approach to the Identification and (In)Validation of LPV systems
"... In this chapter we present a controloriented identification and (in)validation framework for a class of LPV systems. The identification step takes into account both the dependence of part of the model on timevarying parameters as well as the possible existence of a nonparametric component. The va ..."
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In this chapter we present a controloriented identification and (in)validation framework for a class of LPV systems. The identification step takes into account both the dependence of part of the model on timevarying parameters as well as the possible existence of a nonparametric component. The validation step (in)validates the obtained model subject to unstructured uncertainty. The main result of this chapter shows that the problems of checking consistency between the experimental data and the a priori assumptions and that of obtaining a nominal model, can be recast as Linear Matrix Inequality feasibility problems that can be efficiently solved. Moreover, the overall computational complexity is similar to that of obtaining and/or (in)validating LTI models of comparable size. These results are illustrated with a practical example arising in the context of active vision.
Contents lists available at SciVerse ScienceDirect Robotics and Autonomous Systems
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Identification of MIMO LPV models based on interpolation
"... This paper presents SMILE (Statespace Model Interpolation of Local Estimates), a new technique to estimate linear parameter varying statespace models for multipleinput multipleoutput systems whose dynamics depends on a single varying parameter, called the scheduling parameter. The SMILE techniqu ..."
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This paper presents SMILE (Statespace Model Interpolation of Local Estimates), a new technique to estimate linear parameter varying statespace models for multipleinput multipleoutput systems whose dynamics depends on a single varying parameter, called the scheduling parameter. The SMILE technique is based on the interpolation of linear timeinvariant models that are valid for fixed operating conditions of the system, that is, for constant values of the scheduling parameters. The methodology yields affine LPV models that are numerically wellconditioned and therefore suitable for LPV control synthesis procedures. The underlying interpolation technique is formulated as a nonlinear leastsquares optimization problem that can be efficiently solved by standard solvers. Application of the proposed methodology to a vibroacoustic setup, whose dynamics are highly sensitive to the ambient temperature, clearly demonstrates the potential of the SMILE technique.
LPV MODELS: IDENTIFICATION FOR GAIN SCHEDULING CONTROL
"... In this paper the use of discretetime Linear Parameter Varying (LPV) models for the gain scheduling control and identification methods for nonlinear or timevarying system is considered. We report an overview on the existing literature on LPV systems for gain scheduling control and identificatio ..."
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In this paper the use of discretetime Linear Parameter Varying (LPV) models for the gain scheduling control and identification methods for nonlinear or timevarying system is considered. We report an overview on the existing literature on LPV systems for gain scheduling control and identification. Moreover, assuming that inputs, outputs and the scheduling parameters are measured, and a form of the functional dependence of the coefficients on the parameters is known, we show how the identification problem can be reduced to a linear regression so that a Least Mean Square and Recursive Least Square identification algorithm can be reformulated. Our methodology is applied for the identification of the LPV model of the stall and surge control for compressors of jet engines. 1
Identifiability Issues for ParameterVarying and Multidimensional Linear Systems
, 1997
"... This paper considers the identifiability of state space models for a system that is expressed as a linear fractional transformation (LFT): a constant matrix (containing identified parameters) in feedback with a finitedimensional, blockdiagonal ("structured") linear operator. This model s ..."
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This paper considers the identifiability of state space models for a system that is expressed as a linear fractional transformation (LFT): a constant matrix (containing identified parameters) in feedback with a finitedimensional, blockdiagonal ("structured") linear operator. This model structure can represent linear timeinvariant, linear parametervarying, uncertain, and multidimensional systems. Families of inputoutput equivalent realizations are characterized as manifolds in the parameter space whose tangent spacesand orthogonal complementscan be obtained via singular value decomposition. As illustrated by a numerical example, restricting iterative parameter estimation algorithms (e.g., maximumlikelihood with nonlinear programming) to the orthogonal directions offers significant computational advantages. 1 INTRODUCTION Recent years have seen the increasingly widespread use of linear fractional transformations (LFTs) to model linear systems. Such models consist of constant...
On the identification of timevarying systems in Reproducing Kernel Hilbert Spaces
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Modeling and Control of Linear ParameterVarying Systems
"... This paper applies recent advances in both modeling and control of Linear ParameterVarying (LPV) systems to a vibroacoustic setup whose dynamics is highly sensitive to variations in the temperature. Based on experimental data, an LPV model is derived for this system using the Statespace Model Inte ..."
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This paper applies recent advances in both modeling and control of Linear ParameterVarying (LPV) systems to a vibroacoustic setup whose dynamics is highly sensitive to variations in the temperature. Based on experimental data, an LPV model is derived for this system using the Statespace Model Interpolation of Local Estimates (SMILE) technique. This modeling technique interpolates linear timeinvariant models estimated at distinct operating conditions of the system (in this case, different temperatures). Using the obtained LPV model, gainscheduled and robust multiobjective H2/H ∞ state feedback controllers are designed such that can consider a priori known bounds on the rate of parameter variation. Numerical simulations using the closedloop systems are performed to validate the controllers and to show the advantages and versatility of the proposed techniques.