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.

/pdf/linear-matrix-inequalities-in-system-and-control-theory-2q5cf0pqm2.pdf

Linear Matrix Inequalities in System and Control Theory

This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.

/pdf/supervisory-control-of-a-class-of-discrete-event-processes-45fsmhdhbo.pdf

Supervisory control of a class of discrete event processes

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.

Mathematical Control Theory: Deterministic Finite Dimensional Systems

A long-run equilibrium theory of turnover is presented and is shown to explain the important regularities that have been observed by empirical investigators. A worker's productivity in a particular job is not known ex ante and becomes known more precisely as the worker's job tenure increases. Turnover is generated by the existence of a nondegenerate distribution of the worker's productivity across different. The nondegeneracy is caused by the assumed variation in the quality of the worker-employer match.

Job Matching and the Theory of Turnover

A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence, at possibly unknown irregular intervals, of physical events. Such systems arise in a variety of contexts ranging from computer operating systems to the control of complex multimode processes. A control theory for the logical aspects of such DESs is surveyed. The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered. Automata and formal language models for DESs are surveyed. >

The control of discrete event systems

This paper introduces a new synthesis approach for the supervisory control of discrete-event systems (DES). Our algorithm, named S(mart)TCT after our software package CTCT hitherto in use, is much more efficient than CTCT. Efficiency is achieved by exploiting the modular composition of the plant and specification in DES, and its embodiment in integer decision diagrams (IDDs) as the basic data structure.

/pdf/stct-an-efficient-algorithm-for-supervisory-control-design-1az85yyvpp.pdf

STCT: An Efficient Algorithm for Supervisory Control Design

A geometric formulation of the state feedback triangular decoupling problem is given. Necessary and sufficient conditions for the existence of decoupling matrices are presented. A procedure is outlined for simultaneously realizing a triangular structure and assigning the poles of the closed-loop system transfer function matrix.

Triangular decoupling of linear multivariable systems

Stochastic problems in optimal control

With supervisory control theory it is possible to describe controllers which influence the behaviour of a system by disabling controllable events. But sometimes it is desirable to have a controller which not only disables controllable events but also chooses one among the enabled ones. This event can be interpreted as a command given to the plant. This idea is formalized in the concept of an implementation, which is a special supervisor, enabling at most one controllable event at a time. In this paper, some useful properties are introduced, which ensure, when met, that each implementation of a given DES is nonblocking. The approach is applied to a simple chemical batch process example.

/pdf/implementation-considerations-in-supervisory-control-4sb3brvfwv.pdf

Implementation Considerations in Supervisory Control

Stochastic saturating systems optimal control computation, considering attitude control and tracking system design by elliptical differential equation of dynamic programming

W. M. Wonham

Papers

STCT: An Efficient Algorithm for Supervisory Control Design

Triangular decoupling of linear multivariable systems

Stochastic problems in optimal control

Implementation Considerations in Supervisory Control

A computational approach to optimal control of stochastic saturating systems.