Uma formulação variacional do tipo mínimos quadrados para equações diferenciais ordinárias aplicável ao tratamento numérico de problemas de controle ótimo

Abstract

The equivalence between an initial value problem described by ordinary differential equations and the extremum of a least square type functional is showed to happen under certain regularity condition hypothesis. This allows the formulation of a numerical procedure for optimal control problems with control discontinuites. This procedure is based on the substitution of differential constraints of the optimal control problems by a accessory variational problem. The construction of the least square functional can be interpreted as an exactly penalization technique for the differential constraints creating a natural means for the Ritz Method application on the differential equations that are present on the optimal control problems. The procedure is illustrated by mean of numerically solved examples.