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Optimality criterion for singular controllers: Linear boundary conditions. (English) Zbl 0895.49013

The paper deals with the optimal control problem

J(u)=φ(x(t 0 ),x(t 1 ))+ T F(x,u,t)dtmin,
x ˙=f(x,u,t),tT=[t 0 ,t 1 ],
L 0 x(t 0 )+L 1 x(t 1 )-b=0;u(t)U,tT,

where U is a compact set in r . It is supposed that rank[L 0 ,L 1 ]=n. The authors examine the situation with the appearance of singular controllers and derive a second-order increment formula for the functional J. They also prove a second-order optimality criterion and illustrate it by a number of model examples.

MSC:
49K15Optimal control problems with ODE (optimality conditions)