Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions

William G. Litvinov

doi:10.3934/jimo.2011.7.291

Article Contents

2011, Volume 7, Issue 2: 291-315. Doi: 10.3934/jimo.2011.7.291

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Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions

William G. Litvinov^1,

1.
Institute of Mathematics, University of Augsburg, Universitätsstr. 14, D-86159 Augsburg

Received: June 30, 2010

Revised: October 31, 2010

Published: March 2011

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Abstract

The operation of the electrorheological clutch is simulated by a nonlinear parabolic equation which describes the motion of electrorheological fluid in the gap between the driving and driven rotors. In this case, the velocity of the driving rotor is prescribed on one part of the boundary. Nonlocal nonlinear boundary condition is given on a part of the boundary, which corresponds to the driven rotor A problem on optimal control of acceleration or braking of the driven rotor is formulated and studied. Functions of time of the angular velocity of the driving rotor and of the voltages are considered to be controls. In the case that the clutch acts as an accelerator, the energy consumed in the acceleration of the driven rotor is minimized under the restriction that at some instant, the angular velocity and the acceleration of the driven rotor are localized within given regions. In the case of braking, the energy production is maximized. The existence of a solution of optimal control problem is proved and necessary optimality conditions are established.

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Mathematics Subject Classification: Primary: 49J20, 35K60, 76A05; Secondary: 35B65, 76W05.

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