On the controllability of trajectories in the optimal control problems with phase constraints (Q2771537)

For the optimal control problem NEWLINE\[NEWLINE\dot x=f(x,u,t), t\in[t_1^{*},t_2],\;t_1^{*}\leq t_2,\;u=(u_1,u_2),\;u_2(t)\in U_2\;\forall t,NEWLINE\]NEWLINE NEWLINE\[NEWLINER(x,u_1,t)\leq 0,\;G(x,t)\leq 0,\;K_1(p)\leq 0,\;K_2(p)=0,NEWLINE\]NEWLINE NEWLINE\[NEWLINEp=(x_1,x_2,t_2),\;x_1=x(t_1^{*}),\;x_2=x(t_2),NEWLINE\]NEWLINE NEWLINE\[NEWLINEJ(p,u)=K_0(p)+\int_{t_1^{*}}^{t_2}f^0(x,u,t) dt\to\minNEWLINE\]NEWLINE the controllability of trajectories with respect to phase constraints and its connection with nondegeneracy of Pontryagin's maximum principle are studied.NEWLINENEWLINEFor the entire collection see [Zbl 0949.00042].