Analysis of the Hamilton--Jacobi Equation in Nonlinear Control Theory by Symplectic Geometry

Abstract

In this paper, the geometric property and structure of the Hamilton--Jacobi equation arising from nonlinear control theory are investigated using symplectic geometry. The generating function of symplectic transforms plays an important role in revealing the structure of the Hamilton--Jacobi equation. It is seen that many fundamental properties of the Riccati equation can be generalized in the Hamilton--Jacobi equation, and, therefore, the theory of the Hamilton--Jacobi equation naturally contains that of the Riccati equation.