Шалби Лина Ахмед Сайед Хамис Стабилизация неустойчивых точек равновесия и циклов в нелинейных динамических системах / Stabilization of Unstable Equilibrium Points and Cycles in Non-linear Dynamical Systems

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Шалби Лина Ахмед Сайед Хамис Стабилизация неустойчивых точек равновесия и циклов в нелинейных динамических системах / Stabilization of Unstable Equilibrium Points and Cycles in Non-linear Dynamical Systems
ОГЛАВЛЕНИЕ ДИССЕРТАЦИИ
кандидат наук Шалби Лина Ахмед Сайед Хамис
Contents

Introduction

1 Dynamical Systems and Their Stability

1.1 Discrete-Time Dynamical Systems

1.2 Continuous-Time Dynamical Systems

1.3 Examples on Unstable Dynamical Systems

1.3.1 The Logistic Map

1.3.2 Henon Map

1.3.3 Lorenz Model

1.3.4 Rossler 4D Model

1.3.5 Restricted Three Body Problem

2 Stabilization of Unstable Systems by Predictive Feedback Control

2.1 PFC Method and Other Methods for

Discrete-Time Chaotic Systems

2.2 Extended PFC Method to Stabilize Chaotic Continuous-Time Systems

3 Stabilization by Optimal Control

3.1 Control with ^-Minimization Method

3.2 Application: Spacecraft Fuel Consumption

3.2.1 Fuel Optimal Control Strategy

3.2.2 Trajectory Control at Lagrangian Points

Conclusion

Bibliography