Stabilization And Synchronization Of Chaotic Systems Via Intermittent Control

Intermittent control is a straightforward engineering approach to process control ofany type—an approach that has been used for a variety of purposes in such engineeringfields as manufacturing, transportation, communication, and so on. This dissertationfocuses on intermittent control for chaos control and synchronization of classes ofchaotic systems. In this field, we studied stabilization of a memristor-based chaoticsystem, lag synchronization of chaotic neural networks with time-delay, lagsynchronization and projective synchronization of hyperchaotic systems,synchronization and lag synchronization of memristor-based chaotic systems,finite-time synchronization of chaotic neural networks with time-delay, finite-timesynchronization of memristor-based chaotic systems. The main contributions andoriginality contained in this dissertation are as follows:①Stabilization of a memristor-based chaotic system via intermittent controlThis dissertation investigates the problem of intermittent control of amemristor-based Chua’s oscillator and presents a memristor-based Chua’s oscillator asthe T-S fuzzy model system. Based on Lyapunov stability theory, we design anintermittent controller to guarantee the stability of the chaotic system.②Lag synchronization of chaotic neural networks with time-delayLag synchronization of coupled chaotic neural networks with time delay isinvestigated. Some sufficient conditions for lag synchronization will be derived byusing Lyapunov stability theory and intermittent control. Compared to exiting results,some less conservative conditions are derived to guarantee the stabilization of errorsystem. Because of parameter mismatches, complete lag synchronization cannot beachieved. In this dissertation, a lag quasi-synchronization scheme is proposed toguarantee that lag synchronization of coupled systems can be weakly achieved. We alsoestimate the error bound of the lag synchronization by rigorous theoretical analysis.Interestingly, we find that the error bound of lag synchronization depends on theswitching rate. If we select a larger switching rate, the error level of lagsynchronization can be smaller. Then，we investigate the problem of projective lagsynchronization of coupled chaotic neural networks with time delay. By means of theLyapunov stability theory, an intermittent controller is designed for achieving projectivelag synchronization between two identical chaotic neural networks systems. ③Lag synchronization and projective synchronization and of hyperchaoticsystemsLag synchronization of coupled hyperchaotic systems is investigated theoreticallyand numerically. Different from the most existing results, intermittent controllerschemes are designed to achieve lag synchronization of coupled hyperchaotic systemsand some results are proved theoretically using Lyapunov stability theory. Then, Weformulate the intermittent control system that governs the dynamics of the projectivesynchronization error, and derive the sufficient conditions for the exponential stabilityof intermittent control system by using Lyapunov stability theory, and finally establishthe periodically intermittent controller based on the stability criterion by which theprojective synchronization is expected to achieve.④Discontinuous Control for memristor-based systemsA memristor-based five-dimensional (5-D) hyperchaotic Chua’s circuit is proposed.Based on the Lyapunov stability theorem, the controllers are designed to realize thesynchronization and lag synchronization between the hyperchaotic memristor-basedChua’s circuits under different initial values respectively.⑤Finite-time synchronization of chaotic systemsA finite-time lag synchronization of coupled chaotic neural networks with timedelay is investigated. By means of the Lyapunov stability theory, a feedback controlleris designed for achieving lag synchronization between two delayed chaotic neuralnetworks systems in finite time. Paper extends some basic results from the area of finitetime to time-delay systems. And, based on the Lyapunov stability theory and finite-timestability theory, the controller is designed to realize the finite-time synchronizationbetween the hyperchaotic memristor-based circuits under different initial valuesrespectively.