Adaptive feedback linearization of nonlinear MIMO systems using ES-MRAC

Haghi, Poorya; Ariyur, Kartik B.

doi:10.1109/acc.2013.6580101

Cited by 11 publications

(14 citation statements)

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“…Similar ideas of merging model-based control and MES has been proposed in [12], [21], [22], [4], [5], [6], [7], [8], [10]. For instance in [12], [21] extremum seeking is used to complement a model-based controller, under linearity of the model assumption in [12] (in the direct adaptive control setting, where the controllers gains are estimated), or in the indirect adaptive control setting, under the assumption of linear parametrization of the control in terms of the uncertainties in [21].…”

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confidence: 88%

Learning-based modular indirect adaptive control for a class of nonlinear systems

Benosman

Farahmand

Xia

2016

2016 American Control Conference (ACC)

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We study in this paper the problem of adaptive trajectory tracking control for a class of nonlinear systems with parametric uncertainties. We propose to use a modular approach, where we first design a robust nonlinear state feedback which renders the closed loop input-to-state stable (ISS), where the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed-loop output tracking error. Next, we augment this robust ISS controller with a model-free learning algorithm to estimate the model uncertainties. We implement this method with two different learning approaches. The first one is a model-free multi-parametric extremum seeking (MES) method and the second is a Bayesian optimization-based method called Gaussian Process Upper Confidence Bound (GP-UCB). The combination of the ISS feedback and the learning algorithms gives a learning-based modular indirect adaptive controller. We show the efficiency of this approach on a two-link robot manipulator example. I. INTRODUCTIONClassical adaptive methods can be classified into two main approaches; 'direct approaches', where the controller is updated to adapt to the process, and 'indirect approaches', where the model is updated to better reflect the actual process. Many adaptive methods have been proposed over the years for linear and nonlinear systems, we could not possibly cite here all the design and analysis results that have been reported, instead we refer the reader to e.g., [1], [2] and the references therein for more details. Of particular interest to us is the indirect modular approach to adaptive nonlinear control, e.g., [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. In this approach, first the controller is designed by assuming that all the parameters are known and then an identifier is used to guarantee certain boundedness of the estimation error. The identifier is independent of the designed controller and thus the approach is called 'modular'. For example, a modular approach has been proposed in [3] for adaptive neural control of pure-feedback nonlinear systems, where the input-to-state stability (ISS) modularity of the controller-estimator is achieved and the closed-loop stability is guaranteed by the small-gain theorem (see also [13], [14]).

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confidence: 88%

Learning-based modular indirect adaptive control for a class of nonlinear systems

Benosman

Farahmand

Xia

2016

2016 American Control Conference (ACC)

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“…Consider the system (3), under Assumptions 1 to 5, where Δb(t, (t)) satisfies (20). If we apply to (3) the feedback controller (14), where u n is given by (9) and u r is given by (21), then the closed-loop system (22) is ISS from the estimation errors input e Δ (t) ∈ R m 2 to the tracking errors state z(t) ∈ R n .…”

Section: Lyapunov Reconstruction-based Iss Controllermentioning

confidence: 99%

“…For example, it has been shown in the work of Benosman and Atinc 34 that the model-based gradient descent filters failed to estimate simultaneously multiple parameters in the case of the electromagnetic actuators example. For instance, in comparison with the MES-based indirect adaptive controller of Haghi and Ariyur, 22 the modular approach does not rely on the parameters mutual exhaustive assumption, ie, each element of the control vector needs to be linearly dependent on at least one element of the uncertainties vector. More specifically, we consider here the following case: Δ(1, 1) = 1.5, Δ(1, 2) = 1, and Δ(2, i) = 0, i = 1, 2.…”

Section: Two-link Manipulator Examplementioning

confidence: 99%

“…In this case, the uncertainties' effect on the accelerationq 1 cannot be differentiated, and thus, the application of the model-based X-swapping method to estimate the actual values of both uncertainties at the same time is challenging. Similarly, the method in the aformentioned work 22 cannot be readily applied because the second control 2 is not linearly depend on the uncertainties, which only affects 1 . However, we show next that, by using the modular ISS-based controller, we manage to estimate the actual values of the uncertainties simultaneously and improve the tracking performance.…”

Section: Two-link Manipulator Examplementioning

confidence: 99%

“…* For instance, extremum seeking is used to complement a model-based controller, under the linearity of the model assumption in the work of Haghi and Ariyur 21 (in the direct adaptive control setting, where the controllers gains are estimated) or in the indirect adaptive control setting, under the assumption of linear parametrization of the control in terms of the uncertainties in the work of Haghi and Ariyur. 22 The modular design idea of using a model-based controller with input-to-sate stable (ISS) guarantee, complemented with an MES-based module can be found in other works, 25,26,[30][31][32] where the MES was used to estimate the model parameters, and in the works of Benosman and Atinc, 24,46 where feedback gains were tuned using MES algorithms. The work of this paper falls in this class of ISS-based modular indirect adaptive controllers.…”

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Learning‐based iterative modular adaptive control for nonlinear systems

Benosman

Farahmand

Xia

2018

Adaptive Control & Signal

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In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed-loop input-to-state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed-loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data-driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data-driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization-based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data-driven learning algorithms gives a learning-based modular indirect adaptive controller. We show the efficiency of this approach on a two-link robot manipulator numerical example. INTRODUCTIONClassical adaptive methods can be classified into two main approaches: "direct" approaches, where the controller is updated to adapt to the process, and "indirect" approaches, where the model is updated to better reflect the actual process. Many adaptive methods have been proposed over the years for linear and nonlinear systems; we cannot possibly cite them all. Instead, we refer the reader to, eg, other works 1-4 and the references therein for more details. Of particular interest to us is the indirect modular approach to adaptive nonlinear control, eg, see the work of Krstić et al. 3 In this approach, first the controller is designed by assuming that all the parameters are known, and then, an identifier is used to guarantee boundedness or asymptotic convergence of the estimation error. When the identifier is based on a data-driven learning algorithm, which is independent of the designed controller, the approach is called "learning-based," eg, see the work of Benosman, 5 In this line of research in adaptive control we, can cite the following references, eg, see other works. For example, in the neural network (NN)-based modular adaptive control design, the idea is to write the model of the system as a combination of a known part and an unknown part (a.k.a. the disturbance part). The NN is then used to Int J Adapt Control Signal Process. 2019;33:335-355. wileyonlinelibrary.com/journal/acs © 2018 John Wiley & Sons, Ltd. 335 336 BENOSMAN ET AL.approximate the unknown part of the model. Finally, a controller based on both the known and the NN-estimate of the unknown part is determined to realize some desired regulation or tracking performance, eg, see other works. 8,10,13 In this work, we build upon this type of modular learning-based adaptive design and provide a framework that combines...

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Call for papers: Special Issue of International Journal of Adaptive Control and Signal Processing: Learning‐based Adaptive Control: Theory and Applications

2016

Adaptive Control & Signal

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Adaptive feedback linearization of nonlinear MIMO systems using ES-MRAC

Cited by 11 publications

References 10 publications

Learning-based modular indirect adaptive control for a class of nonlinear systems

Learning-based modular indirect adaptive control for a class of nonlinear systems

Learning‐based iterative modular adaptive control for nonlinear systems

Call for papers: Special Issue of International Journal of Adaptive Control and Signal Processing: Learning‐based Adaptive Control: Theory and Applications

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