Optimal control of a singular PDE modeling transient MEMS with control or state constraints

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Clason, Christian¹  Kaltenbacher, Barbara² 

[1] Karl Franzens Univ Graz, Inst Math & Sci Comp, A-8010 Graz, Austria

[2] Alpen Adria Univ Klagenfurt, Inst Math, A-9020 Klagenfurt, Austria

关键词: Optimal control of PDEs;    Control constraints;    State constraints;    Singular PDEs;    Microelectromechanical systems (MEMS);   

DOI  :  10.1016/j.jmaa.2013.08.058

来源: Elsevier

【 摘 要 】

A particular feature of certain microelectromechanical systems (MEMS) is the appearance of a so-called pull-in instability, corresponding to a singularity in the underlying PDE model. We here consider a transient MEMS model and its optimal control via the dielectric properties of the membrane and/or the applied voltage. In contrast to the static case, the control problem suffers from low dimensionality of the control compared to the state and hence requires different techniques for establishing first order optimality conditions. For this purpose, we here use a relaxation approach combined with a localization technique. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free