Sundarapandian Vaidyanathan

Computational Intelligence Applications in Modeling and Control

The development of computational intelligence (CI) systems was inspired by observable and imitable aspects of intelligent activity of human being and nature. The essence of the systems based on computational intelligence is to process and interpret data of various nature so that that CI is strictly connected with the increase of available data as well as capabilities of their processing, mutually supportive factors. Developed theories of computational intelligence were quickly applied in many fields of engineering, data analysis, forecasting, biomedicine and others. They are used in images and sounds processing and identifying, signals processing, multidimensional data visualization, steering of objects, analysis of lexicographic data, requesting systems in banking, diagnostic systems, expert systems and many other practical implementations. This book consists of 16 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of Control Systems, Power Electronics, Computer Science, Information Technology, modeling and engineering applications. Special importance was given to chapters offering practical solutions and novel methods for the recent research problems in the main areas of this book, viz. Control Systems, Modeling, Computer Science, IT and engineering applications. This book will serve as a reference book for graduate students and researchers with a basic knowledge of control theory, computer science and soft-computing techniques. The resulting design procedures are emphasized using Matlab/Simulink software.

Chaos Modeling and Control Systems Design

The development of computational intelligence (CI) systems was inspired by observable and imitable aspects of intelligent activity of human being and nature. The essence of the systems based on computational intelligence is to process and interpret data of various nature so that that CI is strictly connected with the increase of available data as well as capabilities of their processing, mutually supportive factors. Developed theories of computational intelligence were quickly applied in many fields of engineering, data analysis, forecasting, biomedicine and others. They are used in images and sounds processing and identifying, signals processing, multidimensional data visualization, steering of objects, analysis of lexicographic data, requesting systems in banking, diagnostic systems, expert systems and many other practical implementations. This book consists of 15 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of Control Systems, Power Electronics, Computer Science, Information Technology, modeling and engineering applications. Special importance was given to chapters offering practical solutions and novel methods for the recent research problems in the main areas of this book, viz. Control Systems, Modeling, Computer Science, IT and engineering applications. This book will serve as a reference book for graduate students and researchers with a basic knowledge of control theory, computer science and soft-computing techniques. The resulting design procedures are emphasized using Matlab/Simulink software.

Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems

This research work investigates the global chaos synchronization of Sprott’s jerk chaotic system using backstepping control method. Sprott’s jerk system (1997) is algebraically the simplest dissipative chaotic system consisting of five terms and a quadratic nonlinearity. Sprott’s chaotic system involves only five terms and one quadratic nonlinearity, while Rossler’s chaotic system (1976) involves seven terms and one quadratic nonlinearity. This work first details the properties of the Sprott’s jerk chaotic system. The phase portraits of the Sprott’s jerk system are described. The Lyapunov exponents of the Sprott’s jerk system are obtained as L 1 = 0.0525, L 2 = 0 and L 3 = −2.0727. The Lyapunov dimension of the Sprott’s jerk system is obtained as D L = 2.0253. Next, an active backstepping controller is designed for the global chaos synchronization of identical Sprott’s jerk systems with known parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict-feedback chaotic systems. Finally, an adaptive backstepping controller is designed for the global chaos synchronization of identical Sprott’s jerk systems with unknown parameters. MATLAB simulations are provided to validate and demonstrate the effectiveness of the proposed active and adaptive chaos synchronization schemes for the Sprott’s jerk systems.

Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities

This research work introduces a six-term novel 3-D polynomial chaotic system with three quadratic nonlinearities. Phase portraits and detailed qualitative analysis of the polynomial novel chaotic system are described. Lyapunov exponents and Lyapunov dimension for the novel chaotic system have been obtained. The maximal Lyapunov exponent (MLE) for the novel polynomial chaotic system has been found to have a large value, viz. L1 = 10.2234. Thus, the novel 3-D chaotic system exhibits strong chaotic behaviour. New results are derived for the adaptive control and adaptive synchronisation of the novel 3-D polynomial chaotic system with unknown parameters using Lyapunov stability theory. MATLAB plots have been shown to illustrate the phase portraits of the novel 3-D chaotic system and the adaptive results derived in this paper.

Analysis and Control of a 4-D Novel Hyperchaotic System

Hyperchaotic systems are defined as chaotic systems with more than one positive Lyapunov exponent. Combined with one null Lyapunov exponent along the flow and one negative Lyapunov exponent to ensure boundedness of the solution, the minimal dimension for a continuous hyperchaotic system is four. The hyperchaotic systems are known to have important applications in secure communications and cryptosystems. First, this work describes an eleven-term 4-D novel hyperchaotic system with four quadratic nonlinearities. The qualitative properties of the novel hyperchaotic system are described in detail. The Lyapunov exponents of the system are obtained as \( L_{1} = 0.7781,L_{2} = 0.2299,L_{3} = 0 \) and \( L_{4} = - 12.5062 \). The maximal Lyapunov exponent of the system (MLE) is \( L_{1} = 0.7781 \). The Lyapunov dimension of the novel hyperchaotic system is obtained as \( D_{L} = 3.0806 \). Next, the work describes an adaptive controller design for the global chaos control of the novel hyperchaotic system. The main result for the adaptive controller design has been proved using Lyapunov stability theory. MATLAB simulations are described in detail for all the main results derived in this work for the eleven-term 4-D novel hyperchaotic system with four quadratic nonlinearities.

Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity

In this research work, an eight-term 3-D novel chaotic system with an exponential nonlinearity has been derived. The basic qualitative properties of the 3-D chaotic system have been discussed in detail. The new chaotic system has only one equilibrium point, which is a saddle-point. Hence, the system has an unstable equilibrium. The Lyapunov exponents of the 3-D chaotic system are obtained as L1 = 14.0893, L2 = 0 and L3 = -33.9828. Since the maximal Lyapunov exponent of the novel chaotic system is L1 = 14.0893, which is a large value, the novel chaotic system has strong chaotic behaviour. The Lyapunov dimension of the chaotic system is obtained as DL = 2.4146. Next, an adaptive control law has been designed to stabilise the unstable chaotic system with unknown system parameters. The adaptive control result has been established using Lyapunov stability theory. MATLAB simulations have been shown in detail to illustrate the phase portraits and adaptive control results for the novel chaotic system.

Global Chaos Synchronization of WINDMI and Coullet Chaotic Systems using Adaptive Backstepping Control Design

In this paper, global chaos synchronization is investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems using adaptive backstep- ping control design based on recursive feedback control. Our theorems on synchronization for WINDMI and Coullet chaotic systems are established using Lyapunov stability the- ory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predeter- mined desired value. The adaptive backstepping control method is efiective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the ∞exibility to construct a control law and estimate the parameter values. Numeri- cal simulations are also given to illustrate and validate the synchronization results derived in this paper.

Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system

Synchronisation of chaotic systems is an important research problem in chaos theory. In this research work, a novel sliding mode control method is proposed for the global chaos synchronisation of identical chaotic systems. The general result derived using novel sliding mode control method is established using Lyapunov stability theory. As an application of the general result, the problem of global chaos synchronisation of identical Zhu chaotic systems (2010) is studied and a new sliding mode controller is derived. Numerical simulations have been shown to illustrate the phase portraits of Zhu chaotic system and the sliding mode controller design for the global chaos synchronisation of identical Zhu chaotic systems.

Anti-synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan–Madhavan Chaotic Systems

Anti-synchronization is an important type of synchronization of a pair of chaotic systems called the master and slave systems. The anti-synchronization characterizes the asymptotic vanishing of the sum of the states of the master and slave systems. In other words, anti-synchronization of master and slave system is said to occur when the states of the synchronized systems have the same absolute values but opposite signs. Anti-synchronization has applications in science and engineering. This work derives a general result for the anti-synchronization of identical chaotic systems using sliding mode control. The main result has been proved using Lyapunov stability theory. Sliding mode control (SMC) is well-known as a robust approach and useful for controller design in systems with parameter uncertainties. Next, as an application of the main result, anti-synchronizing controller has been designed for Vaidyanathan–Madhavan chaotic systems (2013). The Lyapunov exponents of the Vaidyanathan–Madhavan chaotic system are found as \(L_1 = 3.2226, L_2 = 0\) and \(L_3 = -30.3406\) and the Lyapunov dimension of the novel chaotic system is found as \(D_L = 2.1095\). The maximal Lyapunov exponent of the Vaidyanathan–Madhavan chaotic system is \(L_1 = 3.2226\). As an application of the general result derived in this work, a sliding mode controller is derived for the anti-synchronization of the identical Vaidyanathan–Madhavan chaotic systems. MATLAB simulations have been provided to illustrate the qualitative properties of the novel 3-D chaotic system and the anti-synchronizer results for the identical novel 3-D chaotic systems.

Generalised projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control

Generalised projective synchronisation (GPS) of chaotic systems is a general type of synchronisation, which includes known synchronisation types such as complete synchronisation, anti-synchronisation, hybrid synchronisation and projective synchronisation as special cases. This research work also introduces a novel 3-D chaotic system with an exponential non-linearity. Phase portraits of the strange chaotic attractor for the novel chaotic system are described. The novel chaotic system is a dissipative system with fractional Lyapunov dimension. The novel chaotic system has two saddle-foci equilibrium points, which are both unstable. Since the maximal Lyapunov exponent (MLE) for the novel chaotic system has a large value, viz. L1 = 15.4249, the novel 3-D chaotic system exhibits strong chaotic behaviour. New results are derived for the GPS of identical novel chaotic systems using Lyapunov stability theory. First, active control method is used for deriving new results for the GPS of novel chaotic systems with known parameters. Then, adaptive control method is used for derived new results for the GPS of novel chaotic systems with unknown system parameters. All the main results are established using Lyapunov stability theory. Numerical simulations are shown using MATLAB to validate and demonstrate the GPS results derived in this paper for the novel chaotic systems with an exponential non-linearity.