Frequency-limited adaptive control architecture for transient response improvement

Yucelen, Tansel; Torre, Gerardo De La; Johnson, Eric N.

doi:10.1109/acc.2013.6580880

Cited by 16 publications

(20 citation statements)

References 8 publications

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“…In the adaptive feedback case, although the parameter drift problem has been resolved, the ability to adjust closed‐loop bandwidth is a nontrivial problem . In general, filtering has been shown not to be effective and even detrimental, save for some recent approaches given in . Based on the similarities between adaptive feedback control and AILC, similar results are likely to be encountered in the iterative case.…”

Section: Resultsmentioning

confidence: 99%

Rohrs' Example Revisited: On the Robustness of Adaptive Iterative Learning Control

Altın

Barton

2018

Asian Journal of Control

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Adaptive feedback based methods in iterative learning control (ILC) have garnered much interest from researchers for some time now. Much as in adaptive feedback control, most of these methods use Lyapunov functions and positive real transfer functions to prove convergence and boundedness of system signals updated through iterative estimations. While Rohrs et al. have motivated further research on the design of robust adaptive feedback controllers, by demonstrating in the early 1980's that the algorithms of the time were not robust in the presence of unmodeled dynamics, the topic of robustness has not been studied much in the adaptive iterative learning control (AILC) literature. Inspired by Rohrs' counterexample, we use a model reference AILC scheme to show the lack of robustness to unmodeled dynamics in AILC. We rigorously define the concept of stability in ILC via  2 space concepts, and demonstrate the existence of unstable learning operators. We put forth linear systems arguments to explain how conditions leading to instability can occur, and support heuristic arguments with simulation examples. Our findings indicate that the shortcomings of AILC in terms of robustness are no different than those of adaptive feedback, with the robustness issue more severe in certain cases, and further research is necessary to design robust AILC schemes.

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Section: Resultsmentioning

confidence: 99%

Rohrs' Example Revisited: On the Robustness of Adaptive Iterative Learning Control

Altın

Barton

2018

Asian Journal of Control

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“…It is not difficult to show that the robust invariance requirement for is satisfied if the following MI condition Specifically, (23) states that P V .t/ 6 0, which derives from the stability conditions introduced in (16) and (17). Condition (24) defines the region external to the boundary @ and descends from (20); conditions (25) and (26) define the admissible values for the adaptive weights and filtered adaptive weight errors and descend from (13). Finally, (27) expresses the componentwise bounds on the uncertainty and descends from (14).…”

Section: Proofmentioning

confidence: 99%

“…The proposed methodology was applied for the performance verification of the wing rock aircraft nonlinear model that was used as benchmark for the study of adaptive systems also in [24][25][26][27] Ä P…”

Section: Application To a Case Studymentioning

confidence: 99%

Set theoretic performance verification of low‐frequency learning adaptive controllers

Fravolini

Yucelen

Campa

2014

Adaptive Control & Signal

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Although adaptive control has been used in numerous applications, the ability to obtain a predictable transient and steady-state closed-loop performance is still a challenging problem from the verification and validation standpoint. To that end, we considered a recently developed robust adaptive control methodology called low-frequency learning adaptive control and utilized a set of theoretic analysis to show that the transitory performance of this approach can be expressed, analyzed, and optimized via a convex optimization problem based on linear matrix inequalities. This key feature of this design and analysis framework allows one to tune the adaptive control parameters rigorously so that the tracking error components of the closedloop nonlinear system evolve in a priori specified region of the state space whose size can be minimized by selecting a suitable cost function. Simulation examples are provided to demonstrate the efficacy of the proposed verification and validation architecture showing the possibility of performing parametric studies to analyze the interplay between the size of the tracking error residual set and important design parameters such as the adaptation rate and the low-pass filters time constant of the weights adaptation algorithm. Copyright where f 2 R s s is a positive-definite filter gain matrix and Proj. / denotes the projection operator [21] that is used to guarantee uniform boundedness of the closed-loop tracking error, weight update

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“…Then, the controller adapts feedback gains to suppress this error using the information received from the update law. From a practical standpoint, the output (resp., state) of the uncertain dynamical system can be far different from the output (resp., state) of the reference model during transient time (learning phase) and this difference can lead to poor transient performance, although a model reference adaptive control scheme can guarantee that this system error vanishes asymptotically 3,4 .…”

Section: Introductionmentioning

confidence: 98%

A Direct Uncertainty Minimization Framework in Model Reference Adaptive Control

Yucelen

Gruenwald

Muse

2015

AIAA Guidance, Navigation, and Control Conference

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This paper considers stabilization and command following of uncertain dynamical systems and presents a new adaptive control approach with improved system performance. The proposed framework consists of a novel architecture involving modification terms in the adaptive controller and the update law. Specifically, these terms are activated when the system error between an uncertain dynamical system and a given reference model, which captures a desired closed-loop dynamical system behavior, is nonzero and vanishes as the system reaches its steady-state. This key feature of our framework allows to suppress the effect of system uncertainty on the transient system response through a gradient minimization procedure, and hence, leads to improved system performance. We further show that by automatically adjusting the design parameter of the added terms in response to system variations, we can enforce system error to approximately stay in a priori given, userdefined error performance bounds. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

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Frequency-limited adaptive control architecture for transient response improvement

Cited by 16 publications

References 8 publications

Rohrs' Example Revisited: On the Robustness of Adaptive Iterative Learning Control

Rohrs' Example Revisited: On the Robustness of Adaptive Iterative Learning Control

Set theoretic performance verification of low‐frequency learning adaptive controllers

A Direct Uncertainty Minimization Framework in Model Reference Adaptive Control

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