Quantum Mechanical Theory of Nonlinear Control

Abstract

We propose a new method to deal with the nonlinear Hamilton-Jacobi equation in a linear theory framework. A superposable wave represented by a wave function ??? and a new design constant HR characterizing the strength of such a wave are introduced. Using a Hamiltonian operator Ĥ, a linear wave equation, ???, is set up. Its real part then leads to a generalization of the Hamilton-Jacobi equation. We call this a quantum Hamilton-Jacobi equation. A quantum cost in this new equation is analyzed theoretically. Numerical simulation is also given for a typical nonlinear control system. Accordingly, this paper puts forward an idea for a linear theory approach to the nonlinear optimal feedback control.