NON-QUADRATIC OPTIMAL REGULATORS AND SOLUTION OF QUASI-RICCATI EQUATIONS

<正> This paper, on the assumption of convexity, proves that there exists a closed-loop solution to non-quadratic optimal regulator problems with cost functions of final state type and integral state type respectively. The closed-loop solution is given by a nonlinear state feedback u（t） = —R-1B*. P(t,x（t）) in which P（t,x） is a solution of a quasi-Riccati equation. For the problem of final state type, P（t,x） is expressed by solution of a nonlinear algebraic equation. For the problem of integral state type, P（t,x） is expressed by solution of a nonlinear Fredhohn integral equation.