An optimal control model for the Lyapunov system of stability problem

Lyapunov theory is the key point of stability problems. In this paper, we consider the stability problem of a nonlinear system. First, we design the control function and prove that the Lyapunov function can be maximally reduced. Next, we treat the Lyapunov function as a state variable and formulate a dynamic system of Lyapunov function, where the control is the magnitude of original control function. After proving that there exist many control functions such that the Lyapunov function can be stabilized in finite time, we generate the optimal control problem to find the control function such that a given objective, which combines stabilize time and control cost, is minimized. Finally, we take the Lorenz system as a numerical example to illustrate the proposed method.