# American Institute of Mathematical Sciences

March  2013, 18(2): 331-348. doi: 10.3934/dcdsb.2013.18.331

## Optimal control of ODE systems involving a rate independent variational inequality

 1 Fakultät für Mathematik, TU München, Boltzmannstr. 3, D 85747 Garching bei München, Germany 2 Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1

Received  December 2011 Revised  April 2012 Published  November 2012

This paper is concerned with an optimal control problem for a system of ordinary differential equations with rate independent hysteresis modelled as a rate independent evolution variational inequality with a closed convex constraint $Z\subset \mathbb{R}^m$. We prove existence of optimal solutions as well as necessary optimality conditions of first order. In particular, under certain regularity assumptions we completely characterize the jump behaviour of the adjoint.
Citation: Martin Brokate, Pavel Krejčí. Optimal control of ODE systems involving a rate independent variational inequality. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 331-348. doi: 10.3934/dcdsb.2013.18.331
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