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Optimal control of Lorenz system during different time intervals. (English) Zbl 1036.49028
Summary: 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 application, it is shown that the equilibrium states of the Lorenz system are asymptotically stable. Graphical and numerical simulation studies for the obtained results are presented.
MSC:
49K20Optimal control problems with PDE (optimality conditions)
34D20Stability of ODE
76D05Navier-Stokes equations (fluid dynamics)
93D20Asymptotic stability of control systems
37D45Strange attractors, chaotic dynamics