A NECESSARY AND SUFFICIENT CONDITION FOR THE EXISTENCE OF THE STABILIZING SOLUTION OF THE HAMILTON-JACOBI EQUATION IN NONLINEAR CONTROL THEORY

摘要

A necessary and sufficient condition for the existence of the stabilizing solution of the Hamilton-Jacobi equation arising from nonlinear control theory is presented. First, a method of solving the Hamilton-Jacobi equation is outlined usingcontact and symplectic geometries. It is shown that to solve the Hamilton-Jacobi equation all one has to do is solve ordinary differential equations and/or integrate a completely integrable Pfaffian system. Next, a necessary and sufficient condition ofthe existence of the stabilizing solution is given in terms of the flow of the Hamiltonian vector field associated with the Hamilton-Jacobi equation.