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

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.

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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 considers complex systems whose complexity is the result of the interactions of a number of subsystems. For such systems, a modular approach is presented to check the controllability of a specification with respect to a plant. This reduces the space complexity of checking the controllability from O(IXG'I"IXSI) to O(nIXG')IXSI). The paper also presents an online modular approach to suprema1 supervisor synthesis.

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Online supervision of discrete event systems

In this paper a modelling and analysis paradigm for multiprocess discrete event systems is presented within the formal language and automata settings. The proposed modelling structure features explicit representation of the system components as well as their interaction constraints. The model is then extended for hierarchical multilevel systems.

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Interacting DES: modelling and analysis

This paper identifies a property of delay-robustness in distributed supervisory control by supervisor localization of discrete-event systems (DES) with communication delays. In previous work a distributed supervisory control problem has been investigated on the assumption that inter-agent communications take place with negligible delay. From an applications viewpoint it is desirable to relax this constraint and identify communicating distributed controllers which are delay-robust, namely logically equivalent to their delay-free counterparts. For this we introduce interagent channels modelled as 2-state automata, compute the overall system behaviour, and then present an effective computational test for delay-robustness. From the test it typically results that the given delay-free distributed control is delay-robust with respect to certain communicated events, but not for all, thus distinguishing events which are not delay-critical from those that are. The approach is illustrated by a work-cell model with three communicating agents.

Checking delay-robustness of distributed supervisors of discrete-event systems

We study supervisor localization for real-time discrete-event systems (DES) in the Brandin-Wonham timed supervisory control framework. We view a real-time DES as comprised of asynchronous agents which are coupled through imposed logical and temporal specifications; the essence of supervisor localization is the decomposition of monolithic (global) control action into local control strategies for the individual agents. This study extends our previous work on supervisor localization for untimed DES, in that monolithic timed control action typically includes not only disabling action as in the untimed case, but also “clock preempting” action which enforces prescribed temporal behavior. The latter action is executed by a class of special events, called “forcible” events; and accordingly, we localize monolithic preemptive action with respect to these events. We demonstrate the new features of timed supervisor localization on a manufacturing cell case study, and discuss a distributed control implementation.

Supervision localization of timed discrete-event systems

Fixed-time regulator problem with time invariant feedback control and unspecified-time regulator problem with bounded control

W. M. Wonham

Papers

Online supervision of discrete event systems

Interacting DES: modelling and analysis

Checking delay-robustness of distributed supervisors of discrete-event systems

Supervision localization of timed discrete-event systems

On a problem of Letov in optimal control