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

Yayla, Metehan; Arabi, Ehsan; Kutay, Ali Türker; Yucelen, Tansel

doi:10.1002/acs.2891

Cited by 14 publications

(19 citation statements)

References 31 publications

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“…Hence, based on Barbalat's Lemma, 3 Moreover, according to analysis given in References 24,27, we can calculate the integration of both sides of inequality (43), and then verify that 0 < V(e,W) ≤ V(e 0 ,W 0 )e − ≤ ( max (P)‖e 0 ‖ 2 2 + max (Γ −1 )‖W 0 ‖ 2 F )e − . This together with the facts min (P)‖e(t)‖ 2 2 ≤ V(e,W) and min (Γ −1 )‖W(t)‖ 2 F ≤ V(e,W) indicates the tracking error bound given by (39) and the estimation error bound given by (40). Clearly, compared with the error bounds of the standard MRAC scheme given by (12) and (13), the error bounds given by (39) and (40) can be vanishing rapidly since an exponentially decreasing term e − t is included.…”

Section: Lemma 6 61827mentioning

confidence: 97%

Robust model reference adaptive control for transient performance enhancement

Yang

Gao

2020

Intl J Robust & Nonlinear

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To circumvent the potentially poor transient response induced by nonlinear uncertain dynamics in the adaptive control system, this article proposes a new model reference adaptive control design scheme to improve its transient control response. We first construct a compensator to online extract the undesired dynamics in the online learning, which is incorporated into the reference model and control simultaneously. Then, an error feedback term is incorporated into the reference model to speed up the convergence of both the compensator and tracking error. Moreover, a new leakage term containing the estimation error is constructed and then added in the adaptive law to guarantee the convergence of both the estimation error and tracking error. To further reveal the mechanisms behind these proposed methods, a new methodology to analyze the transient error bounds based on L 2-norm and Cauchy-Schwartz inequality is also developed. Based on the analysis results, we find that the proposed methods can effectively reduce the bound of the tracking error and thus achieve an improved transient control performance without violating the system stability even with high-gain adaptation. In addition, the frequency-domain analysis is resorted to show the comparative responses of different adaptive laws, which indicate that the proposed adaptive law can maintain the stability margin even with a high-gain learning rate. A numerical example is given to demonstrate improved control responses of these proposed schemes.

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Section: Lemma 6 61827mentioning

confidence: 97%

Robust model reference adaptive control for transient performance enhancement

Yang

Gao

2020

Intl J Robust & Nonlinear

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“…34,35 For other specific systems where this condition is not fulfilled, neural networks or fuzzy logic systems can be adopted to approximate these unknown dynamics. [25][26][27][28][29][30][36][37][38][39] In this case, the formulation (6) is still feasible, though the tracking error dynamics given by (16) is slightly modified owing to the inherent bounded approximation error. Consequently, the stability analysis of the control system to be presented in Section 3.3 does not change.…”

Section: Problem Statementmentioning

confidence: 99%

Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence

Yang

Gao

2019

Adaptive Control & Signal

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This paper provides a modified model reference adaptive control (MRAC) scheme to achieve better transient control performance for systems with unknown unmatched dynamics, where an adaptive law with guaranteed convergence is introduced. We first revisit the standard MRAC system and analyze the tracking error bound by using L 2 -norm and Cauchy-Schwartz inequality.Based on this analysis, we suggest a feasible way to compensate the undesired transient dynamics induced by the gradient descent-based adaptive laws subject to sluggish convergence or even parameter drift. Then, a modified adaptive law with an alternative leakage term containing the parameter estimation error is developed. With this adaptive law, the convergence of both the estimation error and tracking error can be proved simultaneously. This enhanced convergence property can contribute to deriving smoother control signal and improved control response. Moreover, this paper provides a simple and numerically feasible approach to online verify the well-known persistent excitation condition by testing the positive definiteness of an introduced auxiliary matrix. Comparative simulations based on a benchmark 3-DOF helicopter model are given to validate the effectiveness of the proposed MRAC approach and show the improved performance over several other MRAC schemes. KEYWORDS model reference adaptive control (MRAC), parameter estimation, persistent excitation, transient response 1868

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“…The equations of motion for this system are defined as follows, where m 11 , m 12 , m 22 The equations of motion for this system are defined as follows, where m 11 , m 12 , m 22 …”

Section: Disk-on-disk Systemmentioning

confidence: 99%

“…12 Besides IDA-PBC, a sliding-mode-control formulation was proposed in the work of Martinez et al 13 for underactuated mechanical systems with Coulomb friction of known amplitude. 21,22 Additionally, differently from friction, constant disturbances do not vanish at equilibrium. Initial results in this respect were presented in the works of Teo et al 16 and Ryalat et al,17 where integral control was overlaid to IDA-PBC in order to compensate constant matched disturbances (ie, only affecting the actuated joints).…”

Section: Introductionmentioning

confidence: 99%

“…More sophisticated integral IDA-PBC designs for underactuated mechanical systems with matched disturbances, constant or bounded, were proposed in the works of Donaire et al 18 and Haddad et al 19 The extension of integral IDA-PBC to the case of unmatched disturbances for mechanical systems with constant inertia matrix was investigated in the work of Ferguson et al 20 In this respect, it must be highlighted that unmatched disturbances represent a particularly challenging condition even for linear systems, since control input and disturbances are not linearly dependent. 21,22 Additionally, differently from friction, constant disturbances do not vanish at equilibrium. As a result, the control of underactuated mechanical systems with constant unmatched disturbances remains an active area of research.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

Franco

2018

Adaptive Control & Signal

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This work investigates the control of nonlinear underactuated mechanical systems with matched and unmatched constant disturbances. To this end, a new control strategy is proposed, which builds upon the interconnection-anddamping-assignment passivity-based control, augmenting it with an additional term for the purpose of disturbance compensation. In particular, the disturbances are estimated adaptively and then accounted for in the control law employing a new matching condition of algebraic nature. Stability conditions are discussed, and for comparison purposes, an alternative controller based on partial feedback linearization is presented. The effectiveness of the proposed approach is demonstrated with numerical simulations for three motivating examples: the inertia wheel pendulum, the disk-on-disk system, and the pendulum-on-cart system. KEYWORDS adaptive control, matched and unmatched disturbances, nonlinear control, underactuated mechanical systems Int J Adapt Control Signal Process. 2019;33:1-15.wileyonlinelibrary.com/journal/acs

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

Cited by 14 publications

References 31 publications

Robust model reference adaptive control for transient performance enhancement

Robust model reference adaptive control for transient performance enhancement

Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence

Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

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