Title

Hybrid Synchronization Control of Dynamical Chaotic Networks with Uncertain Parameters

Abstract

Hybrid synchronization control of dynamical Chaotic networks with uncertain parameters has increasing importance for the last two decades. A key motivation for this research comes from the fact that chaotic systems pose challenging circumstances for control design engineers. Chaotic systems are very sensitive to their initial conditions, a slight perturbation in the initial conditions leads to a very significant variation in the steady-state response of these systems. The hybrid synchronization of these kinds of systems in an interconnected network is of significant interest from a control point of view.

In this thesis, the hybrid synchronization control problem of the dynamical networks in the presence of uncertain parameters is investigated using adaptive integral sliding mode control (ISMC) and smooth super twisting algorithm (SSTA). To apply the adaptive ISMC, the error system is transformed into a special arrangement comprising of a nominal portion and a few unknown items. The unknown items are gauged adaptively. The error system is stabilized using ISMC. The designed controller for the error system comprises of both the nominal and compensatory control. Lyapunov stability theorem is employed to derive the adapted laws and compensator controllers.

The first part of the thesis deals with the hybrid synchronization control of a dynamical network of non-identical and identical chaotic systems connected in the ring topology by assuming the unknown parameters. The proposed control algorithm is employed onto a network of three different chaotic systems and then it is applied to a dynamical network of four identical dynamical systems. In the second part of this thesis, hybrid synchronization control is investigated for the dynamical network of complex chaotic systems connected in a ring topology. The proposed control algorithm is employed onto complex chaotic permanent magnet synchronous motors. In the last part of this thesis, Hybrid synchronization control is investigated for neural networks by assuming the uncertain parameters. The proposed control algorithm is applied to a 3-cell cellular neural network.

This dissertation primarily focuses on the design and application of adaptive ISMC and SSTA to investigate hybrid synchronization of dynamical networks of chaotic systems in the presence of unknown parameters. For this purpose, control laws are formulated using Lyapunov stability analysis. In all the cases, errors dynamics are converging to zero. The convergence of error dynamics to zero yields the convergence of systems states i.e the states of all the chaotic systems connected in the network are synchronized for synchronization scenario and are anti-synchronized for the anti-synchronization scenario. Moreover, the uncertain parameters are converging to their true values. Numerical simulations results support the validation of the proposed control algorithms.

Download full paper