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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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\textit{A. El-Gohary} and \textit{F. Bukhari}, Appl. Math. Comput. 144, No. 2--3, 337--351 (2003; Zbl 1036.49028)

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