An Lmi Approach To Stochastic Linear System Design Using Alternating Linearization

This book introduces multi-objective design methods to solve multi-objective optimization problems (MOPs) of linear/nonlinear dynamic systems under intrinsic random fluctuation and external disturbance. The MOPs of multiple targets for systems are all transformed into equivalent linear matrix inequality (LMI)-constrained MOPs. Corresponding reverse-order LMI-constrained multi-objective evolution algorithms are introduced to solve LMI-constrained MOPs using MATLAB®. All proposed design methods are based on rigorous theoretical results, and their applications are focused on more practical engineering design examples. Features: Discusses multi-objective optimization from an engineer’s perspective. Contains the theoretical design methods of multi-objective optimization schemes. Includes a wide spectrum of recent research topics in control design, especially for stochastic mean field diffusion problems. Covers practical applications in each chapter, like missile guidance design, economic and financial systems, power control tracking, minimization design in communication, and so forth. Explores practical multi-objective optimization design examples in control, signal processing, communication, and cyber-financial systems. This book is aimed at researchers and graduate students in electrical engineering, control design, and optimization.

This book shows how the use of S-variables (SVs) in enhancing the range of problems that can be addressed with the already-versatile linear matrix inequality (LMI) approach to control can, in many cases, be put on a more unified, methodical footing. Beginning with the fundamentals of the SV approach, the text shows how the basic idea can be used for each problem (and when it should not be employed at all). The specific adaptations of the method necessitated by each problem are also detailed. The problems dealt with in the book have the common traits that: analytic closed-form solutions are not available; and LMIs can be applied to produce numerical solutions with a certain amount of conservatism. Typical examples are robustness analysis of linear systems affected by parametric uncertainties and the synthesis of a linear controller satisfying multiple, often conflicting, design specifications. For problems in which LMI methods produce conservative results, the SV approach is shown to achieve greater accuracy. The authors emphasize the simplicity and easy comprehensibility of the SV approach and show how it can be implemented in programs without difficulty so that its power becomes readily apparent. The S-variable Approach to LMI-based Robust Control is a useful reference for academic control researchers, applied mathematicians and graduate students interested in LMI methods and convex optimization and will also be of considerable assistance to practising control engineers faced with problems of conservatism in their systems and controllers.

In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.

Although the problem of nonlinear controller design is as old as that of linear controller design, the systematic design methods framed in response are more sparse. Given the range and complexity of nonlinear systems, effective new methods of control design are therefore of significant importance. Dynamic Surface Control of Uncertain Nonlinear Systems provides a theoretically rigorous and practical introduction to nonlinear control design. The convex optimization approach applied to good effect in linear systems is extended to the nonlinear case using the new dynamic surface control (DSC) algorithm developed by the authors. A variety of problems – DSC design, output feedback, input saturation and fault-tolerant control among them – are considered. The inclusion of applications material demonstrates the real significance of the DSC algorithm, which is robust and easy to use, for nonlinear systems with uncertainty in automotive and robotics. Written for the researcher and graduate student of nonlinear control theory, this book will provide the applied mathematician and engineer alike with a set of powerful tools for nonlinear control design. It will also be of interest to practitioners working with a mechatronic systems in aerospace, manufacturing and automotive and robotics, milieux.

Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control.