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arXiv · 1608.08422

Optimal Control for a Class of Infinite Dimensional Systems Involving an $L^\infty$-term in the Cost Functional

Sébastien Court·Karl Kunisch·Laurent Pfeiffer
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Abstract

An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical control function, the time at which this maximum is reached is considered as a free parameter. The problem couples the behavior of the state and the control, with this time-parameter. A change of variable is introduced to derive first and second-order optimality conditions. This allows the implementation of a Newton method. Numerical simulations are developed, for selected ordinary differential equations and a partial differential equation, which illustrate the influence of the additional parameter and the original motivation.

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Sébastien Court, Karl Kunisch, Laurent Pfeiffer. 2016-08-30. Optimal Control for a Class of Infinite Dimensional Systems Involving an $L^\infty$-term in the Cost Functional. https://doi.org/10.1002/zamm.201600199

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