Optimal control of ODE systems involving a rate independent variational inequality

By M. Brokate, P. Krejčí. 2012

108 citations recorded by the source corpus.

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.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/86e3f31099be8a9bc4c95a7f3bd375a56308bf70

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In Civil and Structural Engineering

In Computational Theory and Mathematics

Citations in the corpus

On optimal control of a sweeping process coupled with an ordinary differential equation (2014, methodology): “Although the main result of article [5] was the development of necessary optimality conditions, several of the proven auxiliary results can be also used to derive their discretized–version counterparts.”
Optimal control of the sweeping process over polyhedral controlled sets (2015, background): “In the other line of development we mention the recent paper [8] and its subsequent extension [2], which address a different class of optimal control problems for an equivalent variational inequality description of the sweeping process of the rate-independent hysteresis type, where the convex moving”
Optimality conditions for a controlled sweeping process with applications to the crowd motion model (2015, background): “Namely, [11] deals with controls only in perturbations addressing existence and relaxation issues for optimal solutions, while [1, 4] apply controls in associated differential equations with deriving necessary optimality conditions for discrete-time [1] and continuous-time [4] systems.”