Time variant nonquadratic optimal regulators

This paper, on the assumptions of convexity, proves that there exists closed-loop optimal control of time variant nonquadratic optimal regulator problems. The closed-loop solution is given by a nonlinear feedback u(t) = - R-1(t)B* (t)P(t,x(t)) in which P(t,x) is a normal solution of a quasi-Riccati equation. It is also proved that the nonlinear feedback operator P(t,x) can be explicitly expressed by solutions of the associated nonlinear algebraic equation and nonlinear integral equations for three cases corresponding to the nonquadratic cost functional of Mayer type, Lagrange type and Bolza type respectively.