This book makes more widely accessible the text of Lyapunov's major memoir of the general problem of the stability of motion. Translated by A. T. Fuller (University of Cambridge), the work is now available for the first time in the English language, and marked the centenary of the Russian publication in the late 1800s. Including a biography of Lyapunov and a comprehensive bibliography of his work, this excellent volume will prove to be of fundamental interest to all those concerned with the concept of the stability of motion, boundaries of stability, and with nonlinear dynamics.

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field

Mathematics in Science and Engineering, Volume 30: Stability of Motion deals with the problem of stability of motion. This volume investigates the problem of stability of the unperturbed motion in cases such as the system of differential equations for the perturbed motion is autonomie and the characteristic equation of the linear system that gives the first approximation has a double zero root. When the order of the system is larger than two (n > 2), all the remaining roots have negative real parts. The double root corresponds to a multiple elementary divisor of the characteristic matrix. This book is a good reference for mathematicians, students, and specialists conducting work on the stability of motion.

In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.

This book studies selected advanced flight control schemes for an uncertain quadrotor unmanned aerial vehicle (UAV) systems in the presence of constant external disturbances, parametric uncertainties, measurement noise, time-varying external disturbances, and random external disturbances. Furthermore, in all the control techniques proposed in this book, it includes the simulation results with comparison to other nonlinear control schemes recently developed for the tracking control of a quadrotor UAV. The main contributions of the present book for quadrotor UAV systems are as follows: (i) the proposed control methods are based on the high-order sliding mode controller (SMC) and hybrid control algorithm with an optimization method. (ii) the finite-time control schemes are developed by using fast terminal SMC (FTSMC), nonsingular FTSMC (NFTSMC), global time-varying SMC, and adaptive laws. (iii) the fractional-order flight control schemes are developed by using the fractional-order calculus theory, super twisting algorithm, NFTSMC, and the SMC. This book covers the research history and importance of quadrotor system subject to system uncertainties, external wind disturbances, and noise measurements, as well as the research status of advanced flight control methods, adaptive flight control methods, and flight control based on fractional-order theory. The book would be interesting to most academic undergraduate, postgraduates, researchers on flight control for drones and applications of advanced controllers in engineering field. This book presents a must-survey for advanced finite-time control for quadrotor system. Some parts of this book have the potential of becoming the courses for the modelling and control of autonomous flying machines. Readers (academic researcher, undergraduate student, postgraduate student, MBA/executive, and education practitioner) interested in nonlinear control methods find this book an investigation. This book can be used as a good reference for the academic research on the control theory, drones, terminal sliding mode control, and related to this or used in Ph.D. study of control theory and their application in field engineering.

This book includes selected contributions by lecturers at the third annual Formation d’Automatique de Paris. It provides a well-integrated synthesis of the latest thinking in nonlinear optimal control, observer design, stability analysis and structural properties of linear systems, without the need for an exhaustive literature review. The internationally known contributors to this volume represent many of the most reputable control centers in Europe.

Dynamics and Advanced Motion Control of Unmanned Ground Off-Road Vehicles details both theoretical concepts such as planning and perception when working with UGVs, as well as more practical, hands-on aspects such as torque vectoring control. The book also covers related technologies such as intelligent and electrification of ground vehicles. After an introduction, initial chapters include an exploration of wheel-soil and track-soil interaction mechanisms, motion stability, motion control, fault detection and identification, and fault tolerance control. This book offers readers a detailed understanding of Unmanned Ground Vehicles by combining theory, applications and further developments. Topics are covered in such a way that readers will be well versed on the current field of UGVs and will be able to implement future design and research in a feasible and effective way. - Gives a comprehensive analysis and introduction to the dynamics and advanced motion control of unmanned ground off-road vehicles - Covers key related technology concepts, such as intelligent and electrification of ground vehicles - Details the entire control framework of off-road UGVs and the implementation of controller design