In this paper we present a time adaptive technique for the solution of optimal control problems where the dynamic is given by an evolutive semi linear PDE. The method is based on a model reduction using a POD approximation coupled with a Hamilton-Jacobi equation characterizing the value function of the corresponding control problem for the reduced system. The choice of the POD basis is updated according to the evaluation of a numerical indicator in order to guarantee a global accurate solution. This is obtained via a sub-division of the time horizon into sub-intervals where the residual is below a given threshold. Some numerical tests illustrate the main features of this approach. © IFAC.
A time-adaptive POD method for optimal control problems / Alla, A.; Falcone, M.. - 46:26(2013), pp. 245-250. (Intervento presentato al convegno 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2013 tenutosi a Paris, fra) [10.3182/20130925-3-FR-4043.00042].
A time-adaptive POD method for optimal control problems
Alla A.;
2013
Abstract
In this paper we present a time adaptive technique for the solution of optimal control problems where the dynamic is given by an evolutive semi linear PDE. The method is based on a model reduction using a POD approximation coupled with a Hamilton-Jacobi equation characterizing the value function of the corresponding control problem for the reduced system. The choice of the POD basis is updated according to the evaluation of a numerical indicator in order to guarantee a global accurate solution. This is obtained via a sub-division of the time horizon into sub-intervals where the residual is below a given threshold. Some numerical tests illustrate the main features of this approach. © IFAC.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
