Abstract
The shallow water model is one of the important models in dynamical systems. This paper investigates the adaptive chaos control and synchronization of the shallow water model. First, adaptive control laws are designed to stabilize the shallow water model. Then adaptive control laws are derived to chaos synchronization of the shallow water model. The sufficient conditions for the adaptive control and synchronization have been analyzed theoretically, and the results are proved using a Barbalat's Lemma.
Highlights
A dynamical system is a system that changes over time
Chaotic systems are dynamical systems that are highly sensitive to initial conditions
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems
Summary
Chaotic systems are dynamical systems that are highly sensitive to initial conditions. An atmospheric model is a set of equations that describes behavior of the atmosphere. Shallow water model is the set of the equations of motion that describes the evolution of a horizontal structure, hydrostatic homogeneous, and incompressible flow on the sphere 1. The control of chaotic systems is to design state feedback control laws that stabilize the chaotic systems. Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. Synchronizing two chaotic systems is seemingly a very challenging problem in chaos literature 2–6.
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