There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.

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Nonlinear Complementary Filters on the Special Orthogonal Group

The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.

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Handbook of Marine Craft Hydrodynamics and Motion Control: Fossen/Handbook of Marine Craft Hydrodynamics and Motion Control

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

Dissipative Systems Analysis and Control

Dissipative Systems Analysis and Control (second edition) presents a fully revised and expanded treatment of dissipative systems theory, constituting a self-contained, advanced introduction for graduate students, researchers and practising engineers. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional examples are also included. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. The theory is substantiated by experimental results and by reference to its application in illustrative physical cases (Lagrangian and Hamiltonian systems and passivity-based and adaptive controllers are covered thoroughly). The second edition is substantially reorganized both to accommodate new material and to enhance its pedagogical properties. Some of the changes introduced are: * Complete proofs of the main theorems and lemmas. * The Kalman-Yakubovich-Popov Lemma for non-minimal realizations, singular systems, and discrete-time systems (linear and nonlinear). * Passivity of nonsmooth systems (differential inclusions, variational inequalities, Lagrangian systems with complementarity conditions). * Sections on optimal control and H-infinity theory. * An enlarged bibliography with more than 550 references, and an augmented index with more than 500 entries. * An improved appendix with introductions to viscosity solutions, Riccati equations and some useful matrix algebra.

Dissipative Systems Analysis and Control: Theory and Applications

This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chained form. These systems are controllable but not asymptotically stabilizable by a smooth static-state feedback control law. In addition, exponential stability cannot be obtained with a smooth, time-varying feedback control law. Here, global, asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth, time-varying feedback control law. The control law depends, in addition to the state and time, on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state. The inputs are differentiable with respect to time and tend exponentially toward zero. For use in the analysis, a lemma on the exponential convergence of a stable time-varying nonlinear system perturbed by an exponentially decaying signal is presented. Simulation results are also shown. >

Exponential stabilization of nonholonomic chained systems

No parts of this publication may be reproduced by any means, transmitted, or translated into machine language without the written permission of the author. Requests for permisson to reproduce parts of the book should be adressed directly to Professor Olav Egeland, Preface Modeling and simulation of dynamic processes are very important subjects in control systems design. Most processes that are encountered in practical controller design are very well described in the engineering literature, and it is important that the control engineer is able to take advantage of this information. It is a problem that several books must be used to get the relevant modeling information of a particular process, and it may take a long time to go through all the necessary material. The idea of this book is to supply the control engineer with a sufficient modeling background to design controllers for a wide range of processes. In addition, the book provides a good starting point for going into the specialist literature of different engineering disciplines. In this connection the references indicate where to start. The book also contains more material than what will normally be covered in the lectures of a typical course, so that students may return to the book at a later stage and find additional information about a particular subject. This will be more efficient than to extract the required information from a series of other books. In this sense the book will be of great value for practising control engineers. The development of new products and systems is often done in a team of experts with different backgrounds. It is hoped that this book will help control engineers to communicate with other experts in this type of team. To achieve this we have been careful to use standard terminology and notation from the different engineering disciplines in question. Here we deliberately break the tradition evident in many books in the control literature where the emphasis is on having a unified formulation specific to automatic control. The selection of the material is based on the experience of the authors in teaching and research at the Norwegian University of Science and Technology. In addition to this, material has been selected on the basis of extensive industrial activity through research programs between university and industry, and product development in industry. In this activity there has been close cooperation with experts from other disciplines, and this has given …

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Modeling and simulation for automatic control

An adaptive control scheme for the attitude control of a rigid spacecraft is derived using a linear parameterization of the equation of motion. The tracking error is described with the Euler parameter vector. Global convergence of the tracking error to zero is shown using passivity theory. This allows for the use of time-varying positive-definite feedback gain matrices, and the results can easily be extended to other passive parameter update laws. >

Olav Egeland

Papers

Dissipative Systems Analysis and Control

Dissipative Systems Analysis and Control: Theory and Applications

Exponential stabilization of nonholonomic chained systems

Modeling and simulation for automatic control

Passivity-based adaptive attitude control of a rigid spacecraft