Optimal control of Lorenz system during different time intervals

摘要

The problem of optimal control of the equilibrium states of the Lorenz system in both finite and infinite time intervals has been studied. The optimal control functions ensuring asymptotic stability of desired states in both cases are obtained as functions of the phase state and time. The squared Euclidean norm of the perturbed state of the Lorenz system in both cases is obtained as transcendental function of time. As an applications, it was shown that the equilibrium states of the Lorenz system are asymptotic stable. Graphical and numerical simulation studies for the obtained results are presented.