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Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control. (English) Zbl 1167.34357
Authors’ abstract: “A new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed. Based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions, an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable, i.e., these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values. This is called pragmatical generalized synchronization. Finally, two numerical examples are studied for two quantum-CNN oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double Duffing chaotic system as a goal system.”
MSC:
34D05Asymptotic stability of ODE
93D21Adaptive or robust stabilization
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C28Complex behavior, chaotic systems (ODE)