On Iterative Learning From Different Tracking Tasks in the Presence of Time-Varying Uncertainties

Xu, Jian‐Xin; Xu, Jing

doi:10.1109/tsmcb.2003.818433

Cited by 192 publications

(151 citation statements)

References 21 publications

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“…In other words, the learning process remains effective even if the desired trajectory (or the reference model) is changing from iteration to iteration. This is one important advantage of this Lyapunov-based framework with respect to the traditional contraction mapping-based frameworks (see, for instance, Reference [13]). …”

Section: Proofmentioning

confidence: 99%

Model reference adaptive iterative learning control for linear systems

Tayebi

2006

Adaptive Control & Signal

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SUMMARYIn this paper, we propose a model reference adaptive control (MRAC) strategy for continuous-time singleinput single-output (SISO) linear time-invariant (LTI) systems with unknown parameters, performing repetitive tasks. This is achieved through the introduction of a discrete-type parametric adaptation law in the 'iteration domain', which is directly obtained from the continuous-time parametric adaptation law used in standard MRAC schemes. In fact, at the first iteration, we apply a standard MRAC to the system under consideration, while for the subsequent iterations, the parameters are appropriately updated along the iteration-axis, in order to enhance the tracking performance from iteration to iteration. This approach is referred to as the model reference adaptive iterative learning control (MRAILC). In the case of systems with relative degree one, we obtain a pointwise convergence of the tracking error to zero, over the whole finite time interval, when the number of iterations tends to infinity. In the general case, i.e. systems with arbitrary relative degree, we show that the tracking error converges to a prescribed small domain around zero, over the whole finite time interval, when the number of iterations tends to infinity. It is worth noting that this approach allows: (1) to extend existing MRAC schemes, in a straightforward manner, to repetitive systems; (2) to avoid the use of the output time derivatives, which are generally required in traditional iterative learning control (ILC) strategies dealing with systems with high relative degree; (3) to handle systems with multiple tracking objectives (i.e. the desired trajectory can be iteration-varying). Finally, simulation results are carried out to support the theoretical development.

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Section: Proofmentioning

confidence: 99%

Model reference adaptive iterative learning control for linear systems

Tayebi

2006

Adaptive Control & Signal

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“…In the sequel, the period of Â 1 is l 1 , where l 1 is the least common multiple of l 1 and l. The upper bound of Â 1 .t / is also defined accordingly. Following a similar procedure in [36], we can prove the asymptotic convergence under the switching PAC design.…”

Section: Remarkmentioning

confidence: 99%

A switching periodic adaptive control approach for time‐varying parameters with unknown periodicity

Huang

2015

Adaptive Control & Signal

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Periodic variations are encountered in many real systems, which can exist in the system parameters, as a disturbance or as the tracking objective. However, there exist a great number of situations where the periodicity is not known in advance. Hence, how to compensate for the effects of time-varying parameters with unknown periodicity remains a challenge for the controller design. In this paper, we proposed a switching periodic adaptive control approach for continuous-time nonlinear parametric systems with periodic uncertainties in which the period and bound are not known in advance. We utilized a fully saturated periodic adaptation law to identify the unknown periodic parameters in a pointwise manner. In addition, we provided a logic-based switching scheme to estimate the unknown period and bound online simultaneously. By virtue of Lyapunov stability analysis, we show that the asymptotic convergence can be guaranteed irrespective of the initial conditions. Finally, we carried out numerical simulations to demonstrate the efficacy of the switching periodic adaptive control algorithm. The proposed approach can be applied to parametric nonlinear systems with time-varying parameters of unknown periodicity irrespective of the types of periodic uncertainties.

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“…It is unnecessary to still apply second-order ILC law to all parameters, especially to those iteration-invariant ones which can be dealt with simply by first-order learning scheme, for example in [17,22], etc.…”

Section: Extension To Unknown Time-varying Input Gain and Mixed Umentioning

confidence: 99%

“…For the part concerning uncertainty /, the method used in [17] is similarly applied here. As a special case of second-order internal model, the proof of / can also be considered as direct application of the framework established in Theorem 1.…”

Section: Extension To Unknown Time-varying Input Gain and Mixed Umentioning

confidence: 99%

An ILC scheme for a class of nonlinear continuous‐time systems with time‐iteration‐varying parameters subject to second‐order internal model

Yin

Hou

2010

Asian Journal of Control

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In this paper, a new iterative learning control (ILC) scheme is proposed to deal with unknown time-iteration-varying parameters for a class of nonlinear continuous-time systems. The parametric non-repetitiveness in the iteration domain is described by a second-order internal model, which includes systems with iteration-invariant parameters as a subset. By incorporating the internal model into the parametric learning law, the proposed ILC scheme can handle more generic systems with parametric uncertainties, and includes existing ILC schemes as a special case with the first-order internal model. The conditions under which the new ILC scheme can guarantee learning convergence are delicately explored. Utilizing the information of the previous two iterations and the method of composite energy function (CEF), it is able to derive pointwise convergence along the time axis and asymptotic convergence along the iteration axis. The controller design is further extended to the case for systems with mixed parameters and unknown time-varying input gain.

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On Iterative Learning From Different Tracking Tasks in the Presence of Time-Varying Uncertainties

Cited by 192 publications

References 21 publications

Model reference adaptive iterative learning control for linear systems

Model reference adaptive iterative learning control for linear systems

A switching periodic adaptive control approach for time‐varying parameters with unknown periodicity

An ILC scheme for a class of nonlinear continuous‐time systems with time‐iteration‐varying parameters subject to second‐order internal model

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