L&lt;inf&gt;1&lt;/inf&gt; adaptive controller for multi-input multi-output systems in the presence of nonlinear unmatched uncertainties

Xargay, Enric; Hovakimyan, Naira; Cao, Chengyu

doi:10.1109/acc.2010.5530686

Cited by 48 publications

(60 citation statements)

References 4 publications

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“…As in the case of the system without quantization Xargay et al (2010), we introduce the following assumptions. Assumption 1.…”

Section: Problem Formulationmentioning

confidence: 99%

“…(Xargay et al (2010)). For the closed-loop reference system in (16), subject to the L 1 -norm condition (5), if…”

Section: Closed-loop Reference Systemmentioning

confidence: 99%

“…Lemma 3. (Xargay et al (2010)). Let the adaptation gain be lower bounded as in (26), and the projection be confined to the bounds in (27).…”

Section: Prediction Errormentioning

confidence: 99%

“…The performance bounds for the state and the control signal in (37) contain a term linear in the quantization parameter ∆. When ∆ goes to zero and there is no quantization, this term vanishes and the bounds reduce to the ones in Theorem 1 of Xargay et al (2010). Remark 6.…”

Section: Logarithmic Quantizationmentioning

confidence: 99%

“…The issues addressed are not only the extension from SISO to MIMO systems, but also from linear to nonlinear, and from systems with matched uncertainties to those with both matched and unmatched uncertainties. For that, we refer to Xargay et al (2010) for the general architecture of L 1 adaptive controller and analyze the performance bounds of this architecture in the presence of logarithmic as well as uniform quantization.…”

Section: Introductionmentioning

confidence: 99%

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L1 Adaptive Controller for Uncertain Nonlinear Multi-Input Multi-Output Systems with Input Quantization

Sun

Hovakimyan

Basar

2011

IFAC Proceedings Volumes

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Abstract:We address the problem of tracking for a general class of uncertain nonlinear MIMO systems with input quantization, without requiring any matching conditions. We consider the L 1 adaptive controller and analyze its performance bounds in the presence of input quantization. We study two common types of quantization, the uniform quantization and the logarithmic quantization. In both cases we provide the transient performance bounds, which are decoupled into two positive terms. One of these terms can be made arbitrarily small by increasing the rate of adaptation, while the other term can be made small by increasing the quantization density. The performance bounds imply that with sufficiently dense quantization and fast adaptation, the output of an uncertain MIMO nonlinear system can follow the desired reference input sufficiently closely. We notice that with L 1 adaptive control architecture fast adaptation does not lead to high-gain control and retains guaranteed time-delay margin, which is bounded away from zero. Simulations included in the paper illustrate the results.

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“…As in the case of the system without quantization Xargay et al (2010), we introduce the following assumptions. Assumption 1.…”

Section: Problem Formulationmentioning

confidence: 99%

“…(Xargay et al (2010)). For the closed-loop reference system in (16), subject to the L 1 -norm condition (5), if…”

Section: Closed-loop Reference Systemmentioning

confidence: 99%

“…Lemma 3. (Xargay et al (2010)). Let the adaptation gain be lower bounded as in (26), and the projection be confined to the bounds in (27).…”

Section: Prediction Errormentioning

confidence: 99%

Section: Logarithmic Quantizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

L1 Adaptive Controller for Uncertain Nonlinear Multi-Input Multi-Output Systems with Input Quantization

Sun

Hovakimyan

Basar

2011

IFAC Proceedings Volumes

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Comparison of architectures and robustness of model reference adaptive controllers and adaptive controllers

Kharisov

Hovakimyan

Åström

2013

Adaptive Control & Signal

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The paper compares direct and indirect model reference adaptive controllers (MRAC) with the L 1 adaptive controller. The architectures of the closed-loop systems are first compared in a simple setting that clarifies the similarities and differences of the controllers. The indirect MRAC and the L 1 controller have identical state predictors, but they differ in the computation of the control signal, which in L 1 is carried out by solving a feedback loop. The special case, where the controllers only adapt to a parameter representing input disturbances, is discussed. In this case, the closed-loop system is linear, so it may not be appropriate to call the controllers adaptive. The special case does, however, give good insight into similarities and differences of the controllers and the effects of various modifications. In particular, the analysis gives good understanding of the robustness properties.where x.t/ 2 R is the state of the system, u.t / 2 R is the control input, and a 2 R and b 2 R are unknown constants with known (conservative) bounds:jaj 6 a max , 0 < b min 6 b 6 b max .( 2 ) norm of a stable proper transfer function H.s/ with its impulse response h.t/ is defined as kH.s/k L1 D R 1 0 jh. /jd . || For a uniformly bounded signal a.t/ 2 R for t > 0, its L 1 norm is defined as kak L1 D sup t>0 ja.t/j. ** We have used the fact that for a stable proper transfer function H.s/ and a uniformly bounded input u.t/ 2 R, the output y.s/ D H.s/u.s/ can be uniformly bounded as follows: kyk L1 6 kH.s/k L1 kuk L1 .Bode plots of this transfer function for different adaptation gains are shown in Figure 4a. It is obvious that the Nyquist plot for L u 1 u 2 .s/ in Figure 4b never crosses the negative part of the real line; therefore, the closed-loop system has infinite gain margin (g m D 1). The gain crossover frequency ! gc can be computed from

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Command governor‐based adaptive control for dynamical systems with matched and unmatched uncertainties

Yayla

Arabi

Kutay

et al. 2018

Adaptive Control & Signal

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SummaryIn this paper, we propose a command governor‐based adaptive control architecture for stabilizing uncertain dynamical systems with not only matched but also unmatched uncertainties and achieving the desired command following performance of a user‐defined subset of the accessible states. In our proposed solution, online least‐squares solutions for the matched and unmatched parameters are obtained through integration method and they are employed in the adaptive control framework. Specifically, the matched uncertainty is identified and its effect upon the system behavior is entirely attenuated. Moreover, using the unmatched uncertainty approximation obtained through radial basis function neural networks, the command governor signal is designed to achieve the desired command following performance of the user‐defined subset of the accessible states. With this command governor‐based model reference adaptive control architecture, the tracking error of the selected states can be made arbitrarily small by judiciously tuning the design parameters. In addition to the analysis of the closed‐loop system stability using methods from the Lyapunov theory, our findings are also illustrated through numerical examples.

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L<inf>1</inf> adaptive controller for multi-input multi-output systems in the presence of nonlinear unmatched uncertainties

Cited by 48 publications

References 4 publications

L1 Adaptive Controller for Uncertain Nonlinear Multi-Input Multi-Output Systems with Input Quantization

L1 Adaptive Controller for Uncertain Nonlinear Multi-Input Multi-Output Systems with Input Quantization

Comparison of architectures and robustness of model reference adaptive controllers and adaptive controllers

Command governor‐based adaptive control for dynamical systems with matched and unmatched uncertainties

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