Identification of linear time-varying systems using a modified least-squares algorithm

Lozano, Rogelio; Dimogianopoulos, Dimitrios; Mahony, Robert

doi:10.1016/s0005-1098(00)00010-8

Cited by 19 publications

(30 citation statements)

References 4 publications

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“…However, a complex online eigenvalue decomposition on a symmetric semidefinite positive matrix should be performed, which is disbenefit for the design of IARC. A modified LS algorithm was presented for LTV systems in the work of Lozano et al However, this algorithm needs the prior knowledge about the range of the TV parameters and its change ratio to optimize the design coefficients. Under the assumption that the driving signals satisfy the PE condition, Wu et al proposed a modified LS algorithm to estimate the TV parameters.…”

Section: Introductionmentioning

confidence: 99%

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Zhao

2018

Intl J Robust & Nonlinear

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Summary Without any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.

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Section: Introductionmentioning

confidence: 99%

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Zhao

2018

Intl J Robust & Nonlinear

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“…The following well-recognized assumptions to be used in the analysis are summarized as follow: [10], [14], [15], and they can be fulfilled in most practical applications. Specifically, the assumptions are less stringent than those used in [10], [15], where a priori knowledge on the upper bounds of the unknown time-varying parameters are required. In this paper, the upper bound parameter  in Assumption 2 is used for analysis only, and thus its true value is not necessarily known.…”

Section: Problem Formulationmentioning

confidence: 99%

“…On the other hand, the limitations of classical adaptive estimation algorithms have also stimulated several studies on investigating advanced adaptive estimation algorithms for time-varying parameters. On this topic, there have been two major ideas: 1) transform the systems with time-varying parameters to alternative systems with constant parameters and then use the gradient based algorithms [9]- [11]; 2) exploit the ability of gradient based algorithms and further tailor them for time-varying parameters [12]- [15].…”

Section: Introductionmentioning

confidence: 99%

“…As it is stated in [14], the non-recursive LS algorithms can retain robustness against bounded disturbances. Lozeno et al [15] proposed a modified LS algorithm with  -modification to address linear time-varying systems with bounded disturbances. These methods all require the upper bounds of the time-varying parameters and their derivatives, so that they can be used for slowly varying parameters only with a priori known knowledge.…”

Section: Introductionmentioning

confidence: 99%

“…, which is online calculated based on the adaptive laws to be proposed in the following (15) and (20). Now, we have the following fact: Lemma 3: For the variable given in (10) and 11…”

mentioning

confidence: 99%

See 2 more Smart Citations

Adaptive Estimation of Time-Varying Parameters With Application to Roto-Magnet Plant

Xing

Costa‐Castelló

2021

IEEE Trans. Syst. Man Cybern, Syst.

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This paper presents an alternative adaptive parameter estimation framework for nonlinear systems with time-varying parameters. Unlike existing techniques that rely on the polynomial approximation of time-varying parameters, the proposed method can directly estimate the unknown time-varying parameters. Moreover, this paper proposes several new adaptive laws driven by the derived information of parameter estimation errors, which achieve faster convergence rate than conventional gradient descent algorithms. In particular, the exponential error convergence can be rigorously proved under the well-recognized persistent excitation (PE) condition. The robustness of the developed adaptive estimation schemes against bounded disturbances is also studied. Comparative simulation results reveal that the proposed approaches can achieve better performance than several conventional estimation algorithms. Finally, the proposed parameter estimation methods are verified by conducting experiments based on a roto-magnet plant.

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Adaptive state observation of linear time‐varying systems with switching unknown parameters: Application to gain scheduling and event‐triggered control

Romero¹,

Ortega²

2023

Adaptive Control & Signal

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SummaryMotivated by its application in gain scheduling and event‐triggered controllers we propose in this paper an adaptive observer for linear time‐varying (LTV) systems with unknown switching parameters, but known switching time instants. To construct the observer we propose an extension to the generalized parameter estimation‐based observers (GPEBO), which we combine with the least‐squares plus dynamic regression extension and mixing (LS+DREM) estimator recently proposed. We prove that the system state and the parameters converge in finite time inside each switching sub‐interval, under the weak assumption of interval‐excitation (IE). The excellent performance of the proposed observer is illustrated with a practical and an academic example both reported in the literature.

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Identification of linear time-varying systems using a modified least-squares algorithm

Cited by 19 publications

References 4 publications

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Adaptive Estimation of Time-Varying Parameters With Application to Roto-Magnet Plant

Adaptive state observation of linear time‐varying systems with switching unknown parameters: Application to gain scheduling and event‐triggered control

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