Synthesis of time-variant optimal control with nonquadratic criteria

[摘要] 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) = -R-1(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. (C) 1997 Academic Press.

[发布日期] 1997-05-15