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Optimality criterion for singular controllers: Linear boundary conditions. (English) Zbl 0895.49013
The paper deals with the optimal control problem $$J(u)= \varphi(x(t_0), x(t_1))+ \int_T F(x,u,t)dt\to \min,$$ $$\dot x= f(x,u,t),\quad t\in T= [t_0,t_1],$$ $$L_0x(t_0)+ L_1x(t_1)- b=0;\quad u(t)\in U,\quad t\in T,$$ where $U$ is a compact set in $\bbfR^r$. It is supposed that $\text{rank}[L_0,L_1]= n$. 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.

49K15Optimal control problems with ODE (optimality conditions)
Full Text: DOI
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