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

There is an increasing demand for dynamic systems to become safer and more reliable This requirement extends beyond the normally accepted safety-critical systems such as nuclear reactors and aircraft, where safety is of paramount importance, to systems such as autonomous vehicles and process control systems where the system availability is vital It is clear that fault diagnosis is becoming an important subject in modern control theory and practice Robust Model-Based Fault Diagnosis for Dynamic Systems presents the subject of model-based fault diagnosis in a unified framework It contains many important topics and methods; however, total coverage and completeness is not the primary concern The book focuses on fundamental issues such as basic definitions, residual generation methods and the importance of robustness in model-based fault diagnosis approaches In this book, fault diagnosis concepts and methods are illustrated by either simple academic examples or practical applications The first two chapters are of tutorial value and provide a starting point for newcomers to this field The rest of the book presents the state of the art in model-based fault diagnosis by discussing many important robust approaches and their applications This will certainly appeal to experts in this field Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research The book is useful for both researchers in academia and professional engineers in industry because both theory and applications are discussed Although this is a research monograph, it will be an important text for postgraduate research students world-wide The largest market, however, will be academics, libraries and practicing engineers and scientists throughout the world

Robust Model-Based Fault Diagnosis for Dynamic Systems

1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

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Essentials of Robust Control

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material. The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback. Numerous examples emphasize the issues related to consistent and accurate system design. Key topics include loop-recovery techniques, frequency shaping, and controller reduction, for both scalar and multivariable systems. Self-contained appendixes cover matrix theory, linear systems, the Pontryagin minimum principle, Lyapunov stability, and the Riccati equation. Newly added to this Dover edition is a complete solutions manual for the problems appearing at the conclusion of each section.

Optimal Control: Linear Quadratic Methods

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

B = set of bus subsystem indices Dk = total amount of battery capacity discharged at the kth scheduling time step d = discharge vector dj = amount of battery capacity discharged by the jth mode f = vectorized generic function f = generic function i, j, k = generic indices I = set of the number of operating modes for each subsystem K, L = generic constants M = set of discrete times over a mission cycle mi = number of operating modes for the ith subsystem nSC = number of spacecraft subsystems P = set of payload subsystem indices p = index denoting the number of the payload subsystem Qk = number of prunings at the kth scheduling time step qj = amount of power consumed by the jth mode Rk = total amount of reward at the kth scheduling time step r = reward vector rj = amount of reward associated with the jth mode S = set of state vectors over the mission cycle s u = size of an object u tk = kth scheduling time step V = battery voltage v u = value of an object u X = field of state vectors xk = state vector at the kth scheduling time step xj = state of the jth mode Z = field of positive integers = th simulation time step = final time step index 8 = for each 2 = an element of

Reward-Lifetime Scheduling Approach to the Autonomous Spacecraft Power Management Problem

The dynamic stability of a swarm is an essential consideration in the design of autonomous formation flying spacecraft. In this paper, we begin by using an illustrative example to create a geometric framework utilizing spacecraft formations in Hill-Clohessy-Wiltshire frame. We use this geometric structure to develop theoretical results to analyze swarm stability in a general three-dimensional space and show how stable swarm members can lead to instabilities. We also discuss an adaptive key-component controller as a means to regulate relative error dynamics in highly sensed swarm environments where a fixed gain controller can be difficult to design. Finally, we use a simulation to present and validate our theoretical framework for swarm stability.

Mark J. Balas

Papers

Reward-Lifetime Scheduling Approach to the Autonomous Spacecraft Power Management Problem

A Theoretical Framework for the Stable Operation of Autonomous Spacecraft Formations in the Hill-Clohessy-Wiltshire Frame

Utilizing Direct Model Reference Adaptive Control to maintain control during failure of a second order plant

Adaptive flow control of rotating wind turbine blades based on the Beddoes-Leishman model using trailing-edge flaps

Some Conditions for Strict Positive Realness of Second Order Systems