Robust Mrac Of A Nonautonomous Parabolic System With Spatiotemporally Varying Coefficients And Bounded Disturbance

Yang, Kwangho; Hong, Keum‐Shik

doi:10.1111/j.1934-6093.2003.tb00127.x

Cited by 3 publications

(1 citation statement)

References 34 publications

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“…Compared to the finite dimensional systems, adaptive control techniques have been developed for only a few classes of partial differential equations. In the last several years, there has been an ever increasing effort devoted to the adaptive control of linear parabolic systems, see [1,[6][7][8][9][10][11][12], to name just a few.…”

Section: Introductionmentioning

confidence: 99%

A note on the model reference adaptive control of linear parabolic systems with constant coefficients

Jia

2011

J Syst Sci Complex

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The problem of constructing a model reference adaptive control law for an uncertain 1-dimensional parabolic system with one constant coefficient is considered in this paper. Adaptive control law are obtained by Lyapunov redesign method. The energy method for parabolic systems and the Agmon's inequality are applied in the analysis, which leads to a stronger result than that of Hong and Bentsman (Automatica, 1994).

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Section: Introductionmentioning

confidence: 99%

A note on the model reference adaptive control of linear parabolic systems with constant coefficients

Jia

2011

J Syst Sci Complex

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Boundary Control of an Axially Moving Steel Strip under a Spatiotemporally Varying Tension

Yang

Hong²,

Matsuno

2004

JSME Int. J., Ser. C

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In this paper, a vibration suppression scheme of an axially moving steel strip in the zinc galvanizing line is investigated. The moving steel strip is modeled as a moving beam, in which the tension applied to the strip is a spatiotemporally varying function. The transverse vibration of the strip is controlled by a hydraulic touch-roll actuator at the right boundary. The mathematical model of the system, which consists of a hyperbolic partial differential equation describing the dynamics of the moving beam and an ordinary differential equation describing the actuator dynamics, is derived by using the Hamilton's principle for the systems of changing mass. The Lyapunov method is employed to design a boundary control law for ensuring the vibration reduction of the system in the presence of a spatiotemporally varying tension. The exponential stability of the closed loop system under the boundary control is proved through the use of invariance principle and semigroup theory. Simulation results verify the effectiveness of the boundary control law proposed.

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Robust Adaptive Control of a Cantilevered Flexible Structure with Spatiotemporally Varying Coefficients and Bounded Disturbance

Yang

Hong²,

Matsuno

2004

JSME Int. J., Ser. C

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In this paper, a robust model reference adaptive control of a cantilevered flexible structure with unknown spatiotemporally varying coefficients and disturbance is investigated. Any mechanically flexible manipulators/structures are inherently distributed parameter systems whose dynamics are described by partial, rather than ordinary, differential equations. Robust adaptive control laws are derived by the Lyapunov redesign method on an infinite dimensional Hilbert space. Under the assumption that disturbances are uniformly bounded, the proposed robust adaptive scheme guarantees the boundedness of all signals in the closed loop system and the convergence of the state error near to zero. With an additional persistence of excitation condition, the parameter estimation errors are shown to converge near to zero as well.

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Robust Mrac Of A Nonautonomous Parabolic System With Spatiotemporally Varying Coefficients And Bounded Disturbance

Cited by 3 publications

References 34 publications

A note on the model reference adaptive control of linear parabolic systems with constant coefficients

A note on the model reference adaptive control of linear parabolic systems with constant coefficients

Boundary Control of an Axially Moving Steel Strip under a Spatiotemporally Varying Tension

Robust Adaptive Control of a Cantilevered Flexible Structure with Spatiotemporally Varying Coefficients and Bounded Disturbance

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