Nonlinear System Identification — A Continuous-Time Bilinear State Space Approach

Lee, Cheh-Han; Juang, Jer‐Nan

doi:10.1007/s40295-013-0025-2

Cited by 11 publications

(9 citation statements)

References 22 publications

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“…If n > 2, the above derivation can be continued replacing x(k +2) with Eq. (56) and taking care of the resulting terms as done above, getting an equation for x(k) with the only state-dependent term multiplied byĀ 3 a , again guaranteed to be zero if (A −1 , C) is an observable pair. The resulting IOSR is denoted as…”

Section: Mixed-anticausal Representationsmentioning

confidence: 99%

“…More importantly, by increasing the state dimension a bilinear model can be used to approximate a more general nonlinear system (Refs. [1,2,3]). Interest in bilinear systems has recently grown after a technique formally known as Carleman linearization was found to achieve such an approximation (Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Carleman bilinearization will convert the satellite attitude dynamics bilinear problem into this form of bilinear equations (Refs. [3,7]), so that one can think of system identification of bilinear systems, developing state estimators for bilinear systems, and control methods for bilinear systems as an approach to handle the satellite attitude control problem. Recently a bilinear model identification method was presented (Ref.…”

Section: Introductionmentioning

confidence: 99%

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Linear state representations for identification of bilinear discrete-time models by interaction matrices

et al. 2014

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Bilinear systems can be viewed as a bridge between linear and nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems. This paper provides a formal justification for the extension of interaction matrices to bilinear systems and uses them to express the bilinear state as a linear function of input-output data. Multiple representations of this kind are derived, making it possible to develop an intersection subspace algorithm for the identification of discrete-time bilinear models. The technique first recovers the bilinear state by intersecting two vector spaces that are defined solely in terms of input-output data. The new input-output-to-state relationships are also used to extend the Equivalent Linear Model method for bilinear system identification. Among the benefits of the proposed approach, it does not require data from multiple experiments, and it does not impose specific restrictions on the form of input excitation.

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Section: Mixed-anticausal Representationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linear state representations for identification of bilinear discrete-time models by interaction matrices

et al. 2014

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“…20 Marzocca et al 21 analytically determined the Volterra kernels corresponding to a two-dimensional aeroelastic system in linear unsteady incompressible flow with nonlinear stiffness and damping terms in the heave and pitch degrees of freedom of the structure. In connection to the Volterra series expansion for nonlinear systems, the ERA has been used for the identification of nonlinear systems by a bilinear model, 22 but no application to aerodynamic or aeroelastic systems has been done yet.…”

Section: Introductionmentioning

confidence: 99%

An input-independent method for solving weakly nonlinear partial differential equations in the frequency domain: application to the Euler equations

Quero

2019

AIAA Aviation 2019 Forum

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In this work a novel approach in determining the first and second order frequencydomain Volterra kernels for weakly nonlinear partial differential equations (PDEs) in semidiscrete form based on the application of the harmonic probing (HP) method is presented. This represents a formal extension of the linearized-frequency domain (LFD) methods to a nonlinear framework, leading to a so-called LFD2 method. The method allows for the representation of weak nonlinearities by solving two input-independent linear algebraic systems of equations in the frequency domain and thus circumvents the solution of the nonlinear PDE by numerical integration for each different input, representing a nonlinear reduced-order model (ROM) for the physical phenomena. The general form of the equations is derived and an application to the well known viscous Burgers' equation to show its suitability in representing the nonlinear convective term is shown. Next, an application to the compressible quasi one-dimensional unsteady flow described by the Euler equations is presented. The proposed method overcomes two constraints present in other methods for the solution of nonlinear PDEs, namely, the consideration of exclusively periodic solutions as in the harmonic balance (HB) method and the dependency of the kernels with the input signal as in the Volterra kernel identification methods.

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“…However, much work remains to be done for the realization of nonlinear models that represent the majority of physical systems (Pacheco and Steffen, 2002;Prazenica and Kurdila, 2004;Feldman et al, 2009), in particular the bilinear systems (Bruni et al, 1971(Bruni et al, , 1974Elliott, 1999). Juang (2005) presented a method using a combination of pulses via multiple experiments to identify a continuous-time bilinear system model that is a universal approximator for a class of nonlinear systems (Svoronos et al, 1980;Rugh, 1981;Lee and Juang, 2010). Following an idea similar to the original one (Juang, 2005), a different algorithm was proposed (Majji et al, 2009) to ease some computational complexity.…”

Section: Introductionmentioning

confidence: 99%

System identification for a general class of observable and reachable bilinear systems

Lee

Juang

2013

Journal of Vibration and Control

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A novel method is developed incorporating a special input sequence for a general class of observable and reachable bilinear system identification. An order reduction scheme is introduced to determine the system matrices. This method makes a significant improvement to its predecessors by removing the observability requirement for the linear part of the bilinear systems. Numerical examples are given to demonstrate the method developed in this paper.

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Nonlinear System Identification — A Continuous-Time Bilinear State Space Approach

Cited by 11 publications

References 22 publications

Linear state representations for identification of bilinear discrete-time models by interaction matrices

Linear state representations for identification of bilinear discrete-time models by interaction matrices

An input-independent method for solving weakly nonlinear partial differential equations in the frequency domain: application to the Euler equations

System identification for a general class of observable and reachable bilinear systems

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