Abdellatif Ben Makhlouf - Böcker

This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative.

This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modelled by a fractional differential equation carried with a non-integer derivative.

This book discusses various methods for designing different kinds of observers, such as the Luenberger observer, unknown input observers, discontinuous observers, sliding mode observers, observers for impulsive systems, observers for nonlinear Takagi-Sugeno fuzzy systems, and observers for electrical machines.

This book discusses various methods for designing different kinds of observers, such as the Luenberger observer, unknown input observers, discontinuous observers, sliding mode observers, observers for impulsive systems, observers for nonlinear Takagi-Sugeno fuzzy systems, and observers for electrical machines.

This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal forthe stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).

This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal forthe stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).

This proceedings volume convenes works within the field of fractional calculus and its applications, presented at the International Conference on Fractional Differentiation and its Applications (ICFCA), held in Sousse, Tunisia, from December 26th to 30th, 2024.In its first rendition, the ICFCA gathers papers from several countries such as Algeria, Lebanon, Qatar, Tunisia, Türkiye, and United Arab Emirates, among others. It aims to provide a unique platform for researchers engaged in fractional calculus in a mathematical context. Covered topics range from foundational aspects, such as fractional differential equations, stability analysis, boundary value problems, and inverse problems, to more applied aspects such as fractional control systems, and the use of fractional calculus tools and techniques in physics, engineering, biology, and more.This volume fills a gap in the fractional calculus landscape by covering theoretical developments and applications in various fields while showcasing the recent findings of a new generation of researchers.

This book provides an in-depth exploration of novel fractional-order memristor-based discrete chaotic maps, examining their stability and chaotic behavior, investigating their complex dynamics, and exploring their applications in synchronization control using theoretical, numerical, and analog methods. It offers valuable insights for scholars, researchers, engineers, and professionals in the fields of applied mathematics, electrical engineering, and computational science. The main topics of this book include fractional calculus, discrete memristors, and their integration into well-known discrete systems. It focuses on developing novel fractional-order memristor-based chaotic discrete systems and investigating chaos theory, including initial conditions, complexity, and multistability dynamics. Detailed chapters also cover the experimental verification of these phenomena and explore their unique applications in synchronization control.