Abstract :
Under the assumption of convexity of nonquadratic time-variant criteria for a
linear time-variant control system, it is proved in this paper that the closed-loop
synthesis of the optimal control is given by a nonlinear feedback
u t.syRy1 t.B* t.P t, x t..,
in which P t, x.is the normal solution of a quasi-Riccati operator equation. It is
also shown that the nonlinear feedback operator P t, x.can be explicitly expressed
by solutions of the associated nonlinear algebraic equation and nonlinear integral
equations respectively in three cases corresponding to Mayer problems, Lagrange
problems, and Bolza problems.
