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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:

49K20 Optimality conditions for problems involving partial differential equations
34D20 Stability of solutions to ordinary differential equations
76D05 Navier-Stokes equations for incompressible viscous fluids
93D20 Asymptotic stability in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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