Kavitha Madhavan

Adaptive control of a two-scroll novel chaotic system with a quartic nonlinearity

This paper proposes a two-scroll novel 3-D chaotic system with a quartic nonlinearity and devises an adaptive control law for globally stabilizing the system when the system parameters are unknown. First, this paper derives fundamental qualitative properties of the new chaotic system such as dissipativity, symmetry, invariance, Lyapunov exponents and Lyapunov dimension. The phase portraits of the novel chaotic system are shown using MATLAB. Next, this paper uses adaptive control theory and Lyapunov stability theory to derive an adaptive feedback control law for globally stabilizing the novel chaotic system for all initial conditions. The main result is proved with the help of Lyapunov stability theory. Adaptive control results are validated by MATLAB simulations.

Adaptive synchronization of two-scroll novel chaotic systems with a quartic nonlinearity

Synchronization of different types, control and regulation of chaotic systems are important areas of research in the control literature and various methods have been adopted for these research problems. Also, the discovery of novel chaotic systems in various applications, their qualitative properties and the control of such systems are also important research areas in chaos theory. This paper proposes a novel 3-D chaotic system and details its qualitative properties such as Lyapunov exponents and Lyapunov dimension. Next, the main result of this paper, namely, an adaptive feedback controller has been constructed for the drive-response synchronization of novel systems for all initial states when the system parameters are unknown. Phase orbits of the new chaotic system have been demonstrated using numerical simulations with MATLAB. Adaptive feedback results for the drive-response synchronization of the systems have been also illustrated using numerical simulations with MATLAB.

Exponential observers for nonlinear oscillators

In this paper, exponential observers are constructed using Sundarapandians observer design (2002) for the second order and third order nonlinear oscillators. The study of nonlinear oscillators has been very important in the study of dynamical systems. Nonlinear oscillators have many applications in areas such as mechanical engineering, electrical engineering, etc. Numerical examples and MATLAB plots have been shown to illustrate the main results derived in this paper.

Reduced order linear functional observers for large scale linear discrete-time control systems

For the last five decades, there has been great interest in the control literature in deriving reduced order models for large-scale linear control systems. Such reduced order models have great applications in science, engineering and industry. In this paper, we have studied the problem of designing linear functional observers for large-scale linear discrete-time control systems and derived some new results, viz. necessary and sufficient conditions for the reduced order linear functional observer for discrete-time linear control systems. We have also established a separation principle for implementation of an observer-based feedback stabilization scheme. A simple algorithm has been provided for the ready implementation of the proposed linear functional observer. A numerical example using MATLAB has been provided to illustrate the new design procedure.

A Novel Design of Reduced Order Controllers Using Exponential Observers for Large-Scale Linear Discrete-Time Control Systems

This paper discusses the design of observer-based reduced order controllers for the stabilization of large scale linear discrete-time control systems. This design is carried out via deriving a reduced-order model for the given linear plant using the dominant state of the linear plant. Using this reduced-order linear model, sufficient conditions are derived for the design of observer-based reduced order controllers. A separation principle has been established in this paper which demonstrates that the observer poles and controller poles can be separated and hence the pole-placement problem and observer design are independent of each other.

Stabilization of Large Scale Linear Discrete-Time Systems by Reduced Order Controllers

This paper investigates the stabilization of large scale discrete-time linear systems by reduced order controllers. Conditions are derived for the design of reduced order controllers for the discrete-time linear systems by obtaining a reduced order model of the original plant using the dominant state of the system. The reduced order controllers are assumed to use only the state of the reduced order model of the original plant.

Stabilization of Large Scale Discrete-Time Linear Control Systems by Observer-Based Reduced Order Controllers

This paper investigates the stabilization of large scale discrete-time linear control systems by observer-based reduced order controllers. Sufficient conditions are derived for the design of observer-based reduced order controllers for the large scale discrete-time linear control systems by obtaining a reduced order model of the original linear plant using the dominant state of the system. A separation principle has been established in this paper which shows that the observer poles and controller poles can be separated and hence the pole placement problem and observer design problem are independent of each other.