الفهرس 
Control and Anti-control of ChaosOnly 14 pages are availabe for public view
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Abstract
Dynamic chaos is a very interesting non-linear effect, which has been intensively studied since Lorenz found the first canonical chaotic attractor in 1963. The effect is very common, it has been detected in a large number of dynamic systems of various physical natures, so it always says ”Most” physical systems are chaotic. In practice, chaos may be desirable or undesirable depending on the applications. In combustion application, chaos is desirable because it enhances mixing of air and fuel and hence leads to better performance. More over it has been utilized in many other practical applications such as increasing the power of lasers, synchronizing the output of electronic circuits, increasing the heat exchange, improving the performance of mobile robot and encode electronic messages for secure communications On the other hand, in aerodynamic and hydrodynamic applications, chaos (turbulence) is undesirable because it dramatically increases the drag of vehicles and results in increased operational cost. In mechanical and structural systems chaos may lead to irregular operation and fatigue failure. More over chaos can restrict the operating range of many mechanical and electronic devices. A chaotic system is a highly complex dynamic nonlinear system that possesses some special features like excessive sensitivity to initial conditions, transitivity and it possesses a dense set of bounded but typically unstable periodic orbits (UPO), which a non-chaotic nonlinear system generally does not have. As a result of its dependence on initial conditions, one can conclude that chaos control is not possible. Thus, to take advantage of chaos, controlling a chaotic orbit to reach a particular UPO is beneficial some engineering applications. This motivates the current research in controlling UPO of chaotic systemsChaos control, in a broader sense, can be divided into two categories:
• Suppress the chaotic dynamical behavior where chaotic behavior is
irregular, complex and generally undesirable.
• Generate or enhance chaos in nonlinear systems to be used in the above
mentioned applications such as secure communications.
The main objective of this thesis is to design a controller that is able to
mitigating or eliminating the chaos behavior of nonlinear systems that
experiencing such phenomenon. Three approaches are proposed for chaos
control. The first is ”Controlling chaotic systems via time-delayed control”.
Based on Lyapunov stabilization theory a proportional plus integral timedelayed
controller is proposed to stabilize UPOs embedded in chaotic
attractors.The second is ”Adaptive sliding mode control for a class of chaotic
systems”. An Adaptive Sliding Mode Controller (ASMC) is presented based on
Lyapunov stability theory. The robustness of the proposed scheme is proved,
even in the presence of parametric uncertainties. The third is ”An adaptive
feedback control for a class of chaotic systems”. A new scheme of adaptive
control based on predetermined control signal to stabilize UPOs embedded in
chaotic attractors is proposed. The predetermined control signal is constructed
based on time-delayed. The adaptation law is derived based on Lyapunov
stabilization theory.
This thesis is constructed of seven chapters, the first chapter describes the
meaning of chaos, the difference between chaos and randomness, the properties
of chaotic systems and finally answers the question that say, why chaos
control? The answer is provided with real applications of chaos control, which
include chaotic mobile robot, chaotic mixing, secure communication, and other
applications. Three conventional control techniques for chaos control including
dislocation, enhancing and speed feedback is discussed in chapter two.
Adaptive time delay control for chaotic systems is discussed in chapter three.
At first, advantages and disadvantages of time delay feedback control isdiscussed then varies control techniques based on time delayed for chaos is
discussed such as ”Adaptive Iterative Learning strategy”, ”repetitive Learning
strategy”, ”successive dislocation feedback strategy and then Proportional plus
integral strategy”. Integrity control of chaotic systems in the case of sensors
failure only is discussed in chapter four. This controller is considered as a type
of fault tolerant control of chaos. Sliding mode control (SMC) and adaptive
sliding mode control (ASMC) are discussed in chapter five. At first, the main
concepts of SMC is given then varies control techniques are given for chaos
control based on SMC and ASMC such as, ”proportional plus integral sliding
surface”, ”adaptive sliding mode control”, ”global adaptive sliding mode
control”, ”adaptive proportional-integral switching surface” and then ”sliding
surface based on delayed feedback”. Two methods of chaos control is
discussed in chapter six, the first is dealing only with the linearized chaotic
systems that satisfy certain form but the second dealing with a form that
satisfied by almost chaotic systems. In the two methods, a predetermined
control signal is considered, and then the feedback control gains are obtained.
Some conclusions are given in chapter seven, followed by future works then all
published, accepted and submitted papers related to chaos control and
synchronization are listed in the last..