A new on-line exponential parameter estimator without persistent excitation

Korotina, Marina; Romero, José Guadalupe; Aranovskiy, Stanislav; Bobtsov, Alexey A.

doi:10.1016/j.sysconle.2021.105079

Cited by 15 publications

(57 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This does not satisfy the objective (10). To this end, to achieve (10), the adaptive law is to be derived on the basis of one of the known approaches [13], [15]- [17], which relax…”

Section: B Adaptive Lawmentioning

confidence: 99%

Exponentially Stable Adaptive Control of MIMO Systems with Unknown Control Matrix

Glushchenko¹,

Lastochkin²

2022

Preprint

View full text Add to dashboard Cite

The scope of this research is a problem of the direct model reference adaptive control of linear time-invariant multi-input multi-output (MIMO) plants without any a priori knowledge about system matrices. To handle it, a new method is proposed, which includes three main stages. Firstly, using the well-known DREM procedure, the plant parametrization is made to obtain the linear regressions, in which the plant matrices and state initial conditions are the unknown parameters. Secondly, such regressions are substituted into the known equations for the controller parameters calculation. Thirdly, the controller parameters are identified using the novel adjustment law with the exponential rate of convergence. To the best of the authors' knowledge, such a method is the first one to provide the following features simultaneously: 1) it is applicable for the generic completely unknown MIMO systems (e.g. without any information about state or control allocation matrices, the sign of the latter, etc.); 2) it guarantees the exponential convergence of both the parameter and tracking errors under the mild requirement of the regressor finite excitation; 3) it ensures element-wise monotonicity of the transient curves of the control law parameters matrices. The results of the conducted experiments with the model of a rubber and ailerons control of a small passenger aircraft corroborate all the theoretical results.

show abstract

“…This does not satisfy the objective (10). To this end, to achieve (10), the adaptive law is to be derived on the basis of one of the known approaches [13], [15]- [17], which relax…”

Section: B Adaptive Lawmentioning

confidence: 99%

Exponentially Stable Adaptive Control of MIMO Systems with Unknown Control Matrix

Glushchenko¹,

Lastochkin²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…• ensure exponential convergence of the parameter error to zero under weak regressor excitation requirements 1,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] ;…”

Section: Introductionunclassified

“…Another way to provide exponential convergence is to filter the RE using different filters with the integral or strong inertial properties [7][8][9][10][11][12][13][14] . Also, recently the energy pumping-and-damping injection principle 32 has been successfully applied to generate the PE regressor from the IE one 18,19 . In contrast to the above-considered adaptive laws, which require the data stack processing, this approach does not use offline operations, but, like the schemes [7][8][9][10][11][12][13][14] , has strong inertial properties.…”

Section: Introductionmentioning

confidence: 99%

“…However, the laws [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] have been developed only to solve the identification problems of the RE time-invariant parameters. Their applicability to estimate the piecewise constant parameters is usually tested in numerical experiments only and, with a number of exceptions like 13,14,20 , does not have a sufficiently rigorous analytical proof.…”

Section: Introductionmentioning

confidence: 99%

“…Adaptive laws [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] have difficulties in solving problems of piecewise constant unknown parameters identification due to imperfect data storage/filtering procedures and inertial characteristics of filters, which are used for the RE processing. The point is that when the data on RE, which parameters are not time-invariant, are stored in the data stack or the regression with piecewise constant parameters is filtered with integral-based filters, then the combined/composite adaptive laws lose their ability to track true values of the unknown parameters.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Glushchenko¹,

Lastochkin²

2022

Preprint

View full text Add to dashboard Cite

The scope of this research is the identification of piecewise constant parameters of linear regression equations under the finite excitation condition. Such an equation is considered as a switched system, which identification usually consists of three main steps: a switching time instant detection, choice of the most appropriate model from the known set or generation of a new one, online adjustment of the chosen model parameters. Compared to the known methods, to make the computational burden lower and simplify the stability analysis, we use only one model to identify all switching states of the regression. So, the proposed identification procedure includes only two main approaches. The first one is a new estimation algorithm to detect switching time and preserve time alertness, which is based on a well-known DREM procedure and ensures adjustable detection delay. Unlike existing solutions, it does not involve an offline operation of data monitoring and stacking. The second one is the adaptive law, which provides element-wise monotonous exponential convergence of the regression parameters to their true values over the time range between two consecutive switches. Its convergence condition is that the regressor is finitely exciting somewhere inside such time interval. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved.Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second-order plant model are used.

show abstract

Unknown piecewise constant parameters identification with exponential rate of convergence

Glushchenko

Lastochkin

2022

Adaptive Control & Signal

View full text Add to dashboard Cite

Summary The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one model to identify all switching states of the regression is used in the developed procedure with the following two‐fold contribution. First of all, we propose a new truly online estimation algorithm based on a well‐known DREM approach to detect switching time and preserve time alertness with adjustable detection delay. Second, despite the fact that a switching signal function is unknown, the adaptive law is derived that provides global exponential convergence of the regression parameters estimates to their true values in case the regressor is finitely exciting somewhere inside the time interval between two consecutive parameters switches. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved. Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second‐order plant model are used.

show abstract

A new on-line exponential parameter estimator without persistent excitation

Cited by 15 publications

References 16 publications

Exponentially Stable Adaptive Control of MIMO Systems with Unknown Control Matrix

Exponentially Stable Adaptive Control of MIMO Systems with Unknown Control Matrix

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Unknown piecewise constant parameters identification with exponential rate of convergence

Contact Info

Product

Resources

About