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IMA Journal of Mathematical Control and Information 1988 5(3):169-186; doi:10.1093/imamci/5.3.169
© 1988 by Institute of Mathematics and its Applications
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Monotone Control of a Damped Oscillator Under Random Perturbations

MIN SUN and JOSÉ-LUIS MENALDI

Department of Mathematics, Wayne State University Detroit, Michigan 48202, U.S.A.

Monotone controls of a class of nonlinear random oscillation problems, which can be reduced to so-called degenerate monotone-follower problems in R2, are studied by the method of dynamic programming and variational inequalities. Our aim is to minimize an expected integral cost which measures the mean deviation from the rest position over a finite horizon, with a possible resource constraint. After presenting some general analytic results on the optimal-cost functions, we will specialize to a randomly excited linear damped harmonic oscillator and obtain more specific results that have been known to us in scalar systems.


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