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 presents a general discrete-event system (DES)-based hard periodic real-time task model. Based on supervisory control theory (SCT), an optimal priority-free real-time scheduling technique is proposed to process all the tasks running in uniprocessor or multiprocessor real-time systems (RTS). The preemption relation in this paper generalizes priority-based preemption. First, regular languages are utilized to describe the processor behavior related to each task’s execution. Thereafter, the languages are represented by DES generators. Finally, the global processor behavior is generated as the synchronous product of these DES generators. By discarding the priorities, a novel preemption policy, namely conditional-preemption, is developed. Two sets of conditional-preemption specifications are developed, on the processor level and task level, respectively. Moreover, in order to control the system to be nonblocking and also limit the worst-case response time of the tasks, two corresponding sets of specifications are presented. After generating the global specification as the synchronous product, by implementing SCT the calculated supervisor can provide all the safe real-time execution sequences. The supervisor calculation can be sped up by a three-step algorithm. Finally, the real-time scheduling is implemented for real-world examples.

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Optimal Priority-Free Conditionally-Preemptive Real-Time Scheduling of Periodic Tasks Based on DES Supervisory Control

The vector discrete-event system (VDES) is a compact serial discrete-event system model, in which the system state is represented by a vector with integer components and the transitions by integer vector addition. Continuing the study of VDES, we introduce in this paper concurrent VDES, extending the base VDES model to capture strict concurrency, or possible simultaneity of events. We characterize the effect of strict concurrency on control, and show how to synthesize nondeterministic controllers allowing maximal concurrency of a controlled VDES plant. >

Concurrent vector discrete-event systems

In this paper, a method for the specification of a supervisor for a discrete event system in terms of a legal constraint language which is defined in terms of illegal states and event sequences is proposed This is a natural manner for the specification of mutual exclusion and synchronization requirements A procedure for the synthesis of a supervisor which enforces the legal constraint language is also discussed

Supervisor specification and synthesis for discrete event systems

This paper presents supervisory control of a dynamic flow controller (DFC) based on the discrete-event systems (DES) theory. A DFC can be considered as a flexible AC transmission system controller and includes a mechanically-switched phase-shifting transformer, a multimodule thyristor-switched capacitor, a multimodule thyristor-switched reactor, and a mechanically switched capacitor. Owing to the inherent discrete switching nature of a DFC, its components are modeled as finite automata; then, a DES supervisory control is designed to implement the control logic of the DFC system in different modes of operation (i.e., ldquoautomaticrdquo and ldquoauto/manualrdquo). It is shown that the specifications are controllable and the synthesized supervisors are nonblocking in both modes and the modular supervisors nonconflict in auto/manual mode.

W. M. Wonham

Papers

Optimal Priority-Free Conditionally-Preemptive Real-Time Scheduling of Periodic Tasks Based on DES Supervisory Control

Concurrent vector discrete-event systems

Supervisor specification and synthesis for discrete event systems

Discrete-Event Systems Supervisory Control for a Dynamic Flow Controller

Supervision localization of timed discrete-event systems