Abstract
This study deals with a nonlinear T_∞ state feedback control problem. The solvable condition of this problem is given by the Hamilton-Jacobi equality(HJE) or the Hamilton-Jacobi inequality (HJI). Recently, the study of the control design using the viscosity solution of HJE has been proposed. But, the viscosity solution is not partial differentiable, so the solution must be approximated to design control laws. It is unknown what kind of nonlinear systems have the viscosity solution of HJE or HJI. In this paper, the control object is limited to bilinear system. And it is shown that HJE or HJI of the nonlinear H_∞ state feedback control problem have the viscosity solution by the dynamic programming approach. And also, we propose the method to approximate the viscosity solution for control designs.
