On‐line parameter estimation for a class of time‐varying continuous systems with bounded disturbances

Chen, Jie; Zhang, Guozhu; Li, Zhiping

doi:10.1002/acs.1188

Cited by 24 publications

(29 citation statements)

References 24 publications

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“…If

δ_{i} ((), {\overset{x}{true}}_{i}) = 1

, then becomes an external disturbance, which is bounded by an unknown constant

p_{i}^{*}

. This assumption has also been discussed in other works …”

Section: Adaptive Robust Control Lawmentioning

confidence: 92%

“…Consider the following second‐order plant, which is often used to represent the dynamics of a servo motor:

\begin{matrix} lefttrue \\ {\overset{x}{true}}_{1} = & x_{2} \\ {\overset{x}{true}}_{2} = & - θ_{1} (t) x_{2} - θ_{2} (t) S_{f} (x_{2}) + Ku + Δ (t) \\ y = & x_{1}, \end{matrix}

where θ 1 ( t ) = 2 + sin( t ) and θ 2 ( t ) = 3 + cos(0.5 πt ) are the unknown TV parameters; K = 10 is the high‐frequency gain; S f ( x 2 ) = 10 arctan (900 x 2 ) is the previously known smooth function; x 1 and x 2 are the states that are assumed to be available; u is the control input; Δ ( t ) = rand (1) − 0.5 is the external disturbance, which represents a zero‐mean random number whose magnitude is less than 0.5. This simulation example can be transformed into the standard form as , with g 1 = 1; g 2 = K ; f 1 = 0 ; f 2 = 0;

φ_{1} = {[\begin{matrix} center \\ 0 & 0 \end{matrix}]}^{T}

;

φ_{2} = {[\begin{matrix} center \\ - x_{2} & - S_{f} (x_{2}) \end{matrix}]}^{T}

;

θ = {[\begin{matrix} center \\ θ_{1} & θ_{2} \end{matrix}]}^{T}

; Δ 1 = 0 and Δ 2 = Δ ( t ).…”

Section: Simulation Studiesmentioning

confidence: 99%

“…Under the assumption that the driving signals satisfy the PE condition, Wu et al proposed a modified LS algorithm to estimate the TV parameters. A polynomial estimation method was further proposed in the work of Chen et al, where a direct LS scheme was used to estimate the coefficients of the used polynomial. Although it is proved that the estimated parameters converge to a neighborhood of the actual values, online test of the invertability for regressor matrix and the calculation of its inverse are required, which can result in a great amount of computation.…”

Section: Introductionmentioning

confidence: 99%

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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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“…If

δ_{i} ((), {\overset{x}{true}}_{i}) = 1

, then becomes an external disturbance, which is bounded by an unknown constant

p_{i}^{*}

. This assumption has also been discussed in other works …”

Section: Adaptive Robust Control Lawmentioning

confidence: 92%

“…Consider the following second‐order plant, which is often used to represent the dynamics of a servo motor:

\begin{matrix} lefttrue \\ {\overset{x}{true}}_{1} = & x_{2} \\ {\overset{x}{true}}_{2} = & - θ_{1} (t) x_{2} - θ_{2} (t) S_{f} (x_{2}) + Ku + Δ (t) \\ y = & x_{1}, \end{matrix}

φ_{1} = {[\begin{matrix} center \\ 0 & 0 \end{matrix}]}^{T}

;

φ_{2} = {[\begin{matrix} center \\ - x_{2} & - S_{f} (x_{2}) \end{matrix}]}^{T}

;

θ = {[\begin{matrix} center \\ θ_{1} & θ_{2} \end{matrix}]}^{T}

; Δ 1 = 0 and Δ 2 = Δ ( t ).…”

Section: Simulation Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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show abstract

“…Consider the following second-order model of a servomotor, which is nonlinear in states but linear in parameters 35 :…”

Section: Examplementioning

confidence: 99%

Online and stable parameter estimation based on normalized brain emotional learning model (NBELM)

Akhormeh

Roshanian

MoradiMaryamnegari

et al. 2019

Adaptive Control & Signal

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Recently, a computational model of Amygdala based on the brain emotional learning is presented by psychologists. This brain emotional learning model (BELM) that has a neuro-inspired architecture is utilized to train the weights which are in Amygdala and Orbitofrontal. In this paper, unknown parameters of dynamic systems are estimated by developing the normalized BELM (NBELM).To this end, after proving the stability of the model output, the sufficient condition for weights convergence is extracted while the sensitivity analysis is applied for this model. In order to evaluate the performance of NBELM, in the first example, the matrices of a twin rotor MIMO system are estimated and compared with the equation error method (EEM). In the second example, the nonlinear model of a servomotor is utilized as a case study. In the third example, the performance of the NBELM in experimental systems is validated using a reaction wheel with a DC motor. An important feature of the brain emotional system is its fast response, leading the NBELM to have a high speed performance in estimating the parameters of dynamic systems. A few number of adjustable parameters and low computing complexity also cause the NBELM to be an appropriate method for online estimation of the unknown parameters of dynamic systems. KEYWORDSAmygdala computing model, BEL model, dynamic system parameter estimation, online and stable estimation Parameters of a large number of industrial systems need to be monitored online for various reasons, ranging from adaptive controls 1 to fault detection systems. 2,3 As a consequence, many research studies have been devoted to introducing novel parameters identification algorithms able to insure the stability of the system. Additionally, the proposed techniques must converge to real values as fast as possible in order to be applicable to engineering systems while high accuracy in the converging process is an evitable need in any novel method. The low complexity of the new algorithm is another challenge, leading the system identification method to be implemented with less effort and become wider. For mentioned challenges to be addressed, various investigations create new frameworks in terms of problem formulation, methodology development, theoretical foundation, software tools, and hardware modules. 4Int J Adapt Control Signal Process. 2019;33:1047-1065.wileyonlinelibrary.com/journal/acs

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“…Moreover, the disturbances and the potential approximation errors are not considered in [13]. Following this framework, the authors of [14] proposed an alternative polynomial approximation-based estimation, where the direct LS scheme is used to estimate the coefficients of the employed polynomials. Although it was proved that the parameter estimates converge to a neighborhood of their true values, the online test of the invertability for the regressor matrix and the calculation of its inverse should be conducted online.…”

mentioning

confidence: 99%

Robust adaptive estimation of nonlinear system with time‐varying parameters

Yang

Ren

et al. 2014

Adaptive Control & Signal

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The vast majority of available parameter estimation methods assume that the parameters to be estimated are constant or slowly time-varying and mainly depend on a predictor or observer design so that a large adaptive gain must be used to achieve fast adaptation; this may result in high-frequency oscillations when the system subjects to a large source of uncertainties or disturbances. This paper is concerned with adaptive online estimation of time-varying parameters for two kinds of linearly parameterized nonlinear systems. By dividing the time into small intervals, the time-varying parameters are approximated in terms of polynomials with unknown coefficients. Then a novel adaptive law design methodology is developed to estimate those constant coefficients, for which the parameter estimation error information is explicitly derived and used to drive the adaptations. To guarantee the continuity of the parameter estimation for all time, a parameter resetting scheme is introduced at the beginning of each interval. Finite-time estimation convergence and the robustness against disturbances are all proved. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms for estimating time-varying parameters.In practical systems, time-varying behavior of the plant parameters may be unavoidable due to the complex mechanisms, the model-plant mismatch, or unmeasured inputs that affect the system dynamics [7,8]. Consequently, the estimation of such time-varying behaviors is of great importance for the control system design. To address this issue, some efforts have been advanced to exploit the ability of gradient algorithms and LS algorithms to estimate time-varying parameters. In particular, various well-known approaches, for example, gradient, recursive/nonrecursive LS algorithms and modified LS algorithms with constant/variable forgetting factor, are reviewed and compared in terms of performance and robustness [9]. It is shown in [9] that the nonrecursive algorithms are more robust to disturbances under slowly time-varying parameters. In [10], the application of a local regression of a time-related polynomial for the RLS algorithm with a forgetting factor is validated to reduce the mean-square estimation error. However, these algorithms all assume that the parameters to be estimated are slowly time-varying, that is, they may fail to retain their properties for fast time-varying parameters.It is well-known that a continuous time-varying function can be locally approximated by polynomials with constant coefficients. Following this idea, with the assumption that the time-varying parameters can be precisely represented as a linear combination of known functions and unknown constants [11,12], conventional LS estimation has been adopted for time-varying systems. In [13], a local Taylor expansion of a time-related polynomial is used to approximate time-varying parameters, and the induced constant Taylor series coefficients are estimated by using standard LS approach. It is noted that such approxima...

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On‐line parameter estimation for a class of time‐varying continuous systems with bounded disturbances

Cited by 24 publications

References 24 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

Online and stable parameter estimation based on normalized brain emotional learning model (NBELM)

Robust adaptive estimation of nonlinear system with time‐varying parameters

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