Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

2 1 The innovative transport systems and the CityMobil project 10 1.1 The research questions 10 2 The state of art in the field of automatic transport systems 12 2.1 Case studies and demand studies for innovative transport systems 12 3 The design and implementation of surveys 14 3.1 Definition of experimental design 14 3.2 Questionnaire design and delivery 16 3.3 First analyses on the collected sample 18 4 Calibration of Logit Multionomial demand models 21 4.1 Methodology 21 4.2 Calibration of the “full” model. 22 4.3 Calibration of the “final” model 24 4.4 The demand analysis through the final Multinomial Logit model 25 5 The analysis of interaction between the demand and socioeconomic attributes 31 5.1 Methodology 31 5.2 Application of Mixed Logit models to the demand 31 5.3 Analysis of the interactions between demand and socioeconomic attributes through Mixed Logit models 32 5.4 Mixed Logit model and interaction between age and the demand for the CTS 38 5.5 Demand analysis with Mixed Logit model 39 6 Final analyses and conclusions 45 6.1 Comparison between the results of the analyses 45 6.2 Conclusions 48 6.3 Answers to the research questions and future developments 52

The European commission

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

The continuous- and discrete-time H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMI-based parametrization of all H∞-suboptimal controllers, including reduced-order controllers.

The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMIs. Efficient convex optimization techniques are available to solve this system. Moreover, its solutions parametrize the set of H∞ controllers and bear important connections with the controller order and the closed-loop Lyapunov functions.

Thanks to such connections, the LMI-based characterization of H∞ controllers opens new perspectives for the refinement of H∞ design. Applications to cancellation-free design and controller order reduction are discussed and illustrated by examples.

A linear matrix inequality approach to H∞ control

This tutorial/survey paper: (1) provides a concise point of departure for researchers and practitioners alike wishing to assess the current state of the art in the control and monitoring of civil engineering structures; and (2) provides a link between structural control and other fields of control theory, pointing out both differences and similarities, and points out where future research and application efforts are likely to prove fruitful. The paper consists of the following sections: section 1 is an introduction; section 2 deals with passive energy dissipation; section 3 deals with active control; section 4 deals with hybrid and semiactive control systems; section 5 discusses sensors for structural control; section 6 deals with smart material systems; section 7 deals with health monitoring and damage detection; and section 8 deals with research needs. An extensive list of references is provided in the references section.

Structural control: past, present, and future

All controllers for the general H ∞ control problem: LMI existence conditions and state space formulas

This paper is yet another demonstration of the fact that enlarging the design space allows simpler tools to be used for analysis. It shows that several problems in linear systems theory can be solved by combining Lyapunov stability theory with Finsler’s Lemma. Using these results, the differential or difference equations that govern the behavior of the system can be seen as constraints. These dynamic constraints, which naturally involve the state derivative, are incorporated into the stability analysis conditions through the use of scalar or matrix Lagrange multipliers. No a priori use of the system equation is required to analyze stability. One practical consequence of these results is that they do not necessarily require a state space formulation. This has value in mechanical and electrical systems, where the inversion of the mass matrix introduces complicating nonlinearities in the parameters. The introduction of multipliers also simplify the derivation of robust stability tests, based on quadratic or parameter-dependent Lyapunov functions.

Stability tests for constrained linear systems

There is much theory for the use of covariance matrices in both identification and in state estimation. However, there exists no theory for the control of covariances. The need for a theory of covariance control may be argued from two points: 1) Many engineering systems have performance requirements which are naturally stated in terms of root-mean-square (RMS) values of the system states or outputs and 2) the various theories of identification, estimation, and model reduction use covariances as a measure of performance. Hence a theory on covariance control may help unify the modeling and control problem. This paper introduces a theory for designing linear feedback controllers so that the closed loop system achieves a specified state covariance.

A covariance control theory

http://www2.egr.uh.edu/~mece2hv/Papers/32.pdf

Robert E. Skelton

Papers

Structural control: past, present, and future

All controllers for the general H ∞ control problem: LMI existence conditions and state space formulas

Stability tests for constrained linear systems

A covariance control theory

Paper: Low-order control design for LMI problems using alternating projection methods