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Stability , Chaos Tests with Adaptive and Feedback Control Methods for 3D Discrete - Time Dynamical System

Maysoon M. Aziz; Omar M. Jihad
In this paper, a three dimensional non linear discrete - time dynamical system was introduced, The numerical solution was carried by Newton's Raphson method. The basic properties was investigated by mean of it's fixed points , bifurcation and numerical diagrams. Stability analysis measured by eigenvalues of the characteristic equation roots ، Lyapunov function and Jury's test which all show that the system is unstable . Chaos diagnose was calculated by Lyapunov exponent and binary test , the maximum value of Lyapunov exponent is obtain as (L_max= 3.8), Lyapunov dimension is obtain as (D_L= 2.0872) and binary test (0-1) is obtain as (k = 0.9942≈1), which all shows the system is highly chaotic. Finally, the system was controlled effectively by designed feedback and adaptive controllers , the results after controls were very good system trajectories are stable and regular.
Select Volume / Issues:
Year:
2021
Type of Publication:
Article
Keywords:
Stability; Chaotic System; Lyapunov Function; Lyapunov Exponent; Lyapunov Dimension; Adaptive Control; Feedback Control
Journal:
IJECCE
Volume:
12
Number:
2
Pages:
31-42
Month:
March
ISSN:
2249-071X
Hits: 213

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