Recursive Subspace Identification of Continuous-Time Systems Using Generalized Poisson Moment Functionals

Yu, Miao; Liu, Jianchang; Guo, Ge; Zhang, Wenle

doi:10.1007/s00034-021-01871-x

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…Numerous identification approaches have been presented to address the aforementioned problems in order to acquire reliable models. Linear filtering, which includes Laguerre filters, generalized PMFs (GPMFs), and Poisson Moment Functionals (PMFs), is the first category [4][5][6]. In [7], a generalized singular-value decomposition (SVD) was used to compensate for the noise coloration for estimating the continuous-time system.…”

Section: Introductionmentioning

confidence: 99%

Closed-Loop Continuous-Time Subspace Identification with Prior Information

Yu,

Wang,

Wang

2023

Mathematics

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This paper presents a closed-loop continuous-time subspace identification method using prior information. Based on a rational inner function, a generalized orthonormal basis can be constructed, and the transformed noises have ergodicity features. The continuous-time stochastic system is converted into a discrete-time stochastic system by using generalized orthogonal basis functions. As is known to all, incorporating prior information into identification strategies can increase the precision of the identified model. To enhance the precision of the identification method, prior information is integrated through the use of constrained least squares, and principal component analysis is adopted to achieve the reliable estimate of the system. Moreover, the identification of open-loop models is the primary intent of the continuous-time system identification approaches. For closed-loop systems, the open-loop subspace identification methods may produce biased results. Principal component analysis, which reliably estimates closed-loop systems, provides a solution to this problem. The restricted least-squares method with an equality constraint is used to incorporate prior information into the impulse response following the principal component analysis. The input–output algebraic equation yielded an optimal multi-step-ahead predictor, and the equality constraints describe the prior information. The effectiveness of the proposed method is provided by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Closed-Loop Continuous-Time Subspace Identification with Prior Information

Yu,

Wang,

Wang

2023

Mathematics

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“…Ref. [16] proposed a continuous-time subspace identification method via generalized PMF, which fixed the size of the data matrices in the identification process. Based on the invariant subspace, ref.…”

Section: Introductionmentioning

confidence: 99%

Continuous-Time Subspace Identification with Prior Information Using Generalized Orthonormal Basis Functions

Yu,

Wang,

Wang

et al. 2023

Mathematics

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This paper presents a continuous-time subspace identification method utilizing prior information and generalized orthonormal basis functions. A generalized orthonormal basis is constructed by a rational inner function, and the transformed noises have ergodic properties. The lifting approach and the Hambo system transform are used to establish the equivalent nature of continuous and transformed discrete-time stochastic systems. The constrained least squares method is adopted to investigate the incorporation of prior knowledge in order to further increase the subspace identification algorithm’s accuracy. The input–output algebraic equation derives an optimal multistep forward predictor, and prior knowledge is expressed as equality constraints. In order to solve an optimization problem with equality constraints characterizing the prior knowledge, the proposed method reduces the computational burden. The effectiveness of the proposed method is provided by numerical simulations.

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“…A method of nuclear norm subspace identifcation based on Kalman flter for the stochastic continuous-time system is proposed in [13]. In [14], the recursive subspace identifcation method of continuous-time systems via generalized Poisson moment functional is presented.…”

Section: Introductionmentioning

confidence: 99%

Recursive Delta-Operator-Based Subspace Identification with Fixed Data Size

Yu,

Wang,

Wang

et al. 2023

Complexity

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This paper proposes a recursive delta-operator-based subspace identification method with fixed data size. The majority of existing subspace identification methods are constrained to discrete-time systems because of the disparity in Hankel matrices. Additionally, due to the storage cost, LQ-factorization and singular value decomposition in identification methods are best suited for batch processing rather than online identification. The continuous-time systems are transformed into state space models based on the delta-operator to address these issues. These models approach the original systems when the sampling interval approaches zero. The size of the data matrices is fixed to reduce the computing load. By fading the impact of past data on future data, the amount of data storage can be decreased. The effectiveness of the proposed method is illustrated by the continuous stirred tank reactor system.

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Recursive Subspace Identification of Continuous-Time Systems Using Generalized Poisson Moment Functionals

Cited by 3 publications

References 33 publications

Closed-Loop Continuous-Time Subspace Identification with Prior Information

Closed-Loop Continuous-Time Subspace Identification with Prior Information

Continuous-Time Subspace Identification with Prior Information Using Generalized Orthonormal Basis Functions

Recursive Delta-Operator-Based Subspace Identification with Fixed Data Size

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