Optimal control for a class of infinite dimensional systems involving an \(L^{\infty}\)-term in the cost functional. (English) Zbl 1538.49027
Summary: 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.
{© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim}
{© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim}
MSC:
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49K15 | Optimality conditions for problems involving ordinary differential equations |
| 49K21 | Optimality conditions for problems involving relations other than differential equations |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 90C46 | Optimality conditions and duality in mathematical programming |
Keywords:
optimality conditions; PDE-constrained optimization; transversality conditions; hybrid optimal control problemReferences:
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