The optimal control of delay control systems with restricted state right endpoint (Q1389961)

In this paper, for the delay control system \[ \begin{cases} x'(t)= f(x(t), x(t-1), u(t), t),\quad t\in [t_0,t_1]\\ x(t)= \psi(t),\quad t\in [t_0- 1,t_0]\end{cases} \] with the state in the right endpoint restricted by conditions \(\psi_k(x(t_1))= 0\) \((k= 1,2,\dots,l)\), a necessary condition such that \(u^*(t)\) and \(x(t)\) to be the optimal control and the locus about the payoff functional \(J= Cx(t_1)\) is given. For the multidelay control systems, this result is possible to remain true. Finally, a simple example is presented.