Special solutions in singular optimization problems (Q1076332)

Dynamic systems with generalized controls are studied. Such systems occur in various problems of space navigation, heat engineering and from other domains. If the control u(t) is allowed to belong to the space \(L^ 1\), then it is not possible to find the state in the class of ordinary functions. The concept of generalized solution is based on generalized functions of zero order (measures \(u(t)=da(t)/dt\), where a(t) is a vector function of bounded variation). For such a solution to be unique, the usual concept of weak convergence of measures is slightly modified. The maximum principle is applied and a singular optimal control is derived.