Stéphane Lafortune. August 2006
|
|
- Barnaby Wilkins
- 6 years ago
- Views:
Transcription
1 UNIVERSITY OF MICHIGAN DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE LECTURE NOTES FOR EECS 661 CHAPTER 1: INTRODUCTION TO DISCRETE EVENT SYSTEMS Stéphane Lafortune August 2006
2 References for Chapter 1: Textbook, Chapter 1: Section 1.3 A Multidisciplinary Area: Discrete Event Systems Operations Research Computer Science DES Systems & Control What: Discrete State Space (logical, symbolic variables) Event-driven Dynamics Why: Technological Systems, Computer Control Large, Complex Systems: they need to be analyzed, diagnosed, controlled, and optimized S. Lafortune - Last revision: August
3 Where: Inherently Discrete Systems: computer systems, communication networks, automated manufacturing systems (cell and factory levels), software systems. Systems with Continuous and Discrete Variables (hybrid systems), modeled as DES at a certain level of abstraction, e.g., for the higher level control logic: automated manufacturing systems (machine and cell levels), process control, transportation systems. Embedded systems ; networked systems. How: Mathematical Modeling, Analysis, Verification, Diagnosis, Controller Design, Optimization, Simulation S. Lafortune - Last revision: August
4 SUPERVISORY CONTROLLER COORDINATION REAL-TIME CONTROL DIAGNOSTICS FAILURE RECOVERY Conceptual Control System Architecture: Commands INTERFACE Observable events EQUIPMENT CONTROLLERS CONTROLLER SYSTEM S. Lafortune - Last revision: August
5 Some Examples The Heating System of a Heating, Ventilation, and Air Conditioning (HVAC) Unit FAN HTG. COIL VALVE PUMP BOILER CONTROLLER The operation of the unit is monitored by a set of sensors. The issue of interest: Fault Diagnosis. Specifically: diagnose occurrence of sharp faults during the on-line operation of the unit. Examples of faults: stuck failures of valves, on-off failures of pumps, controllers, sensors, etc. Implementation: diagnostics module in the control logic. S. Lafortune - Last revision: August
6 PUMP PON POFF P1 P2 PON VALVE V3 CV, OV POFF SO1 SO2 OV LOAD CV V1 V2 OV FOFF L0 FOFF CV SC1 SC2 S P I S P D S P I V4 L1 L2 CV, OV S P D Models of the Components of the HVAC System: FOFF F1 FON FOFF FAN CFOFF F2 FON FON C21 FOFF C22 FOFF BON B1 BOFF BOFF BOILER SPD C23 SPI SPD SPI C24 B2 BON FON S P I OV PON BON C1 C2 C3 C4 C5 C6 FOFF S P D S P I S P D CFON C10 BOFF C9 POFF C8 CV C7 C11 FON C12 SPI SPD C13 OV C14 PON C15 BON C16 SPD SPI C20 OV C19 PON C18 BON C17 CONTROLLER S. Lafortune - Last revision: August
7 1 N < FON, NF > Part of the Diagnoser for the Heating System (HVAC Unit) F1: SO F2: SC F3: CFON F4: CFOFF 7 N 8 F1 9 F2 37 F3 38 F1 F3 39 F2 F3 85 F4 86 F1 F4 87 F2 F4 10 N 11 F1 12 F2 40 F3 41 F1 F3 42 F2 F3 A < SPI, NF > 13 N 14 F1 43 F3 44 F1 F3 16 N 17 F1 46 F3 47 F1 F3 19 N 20 F1 58 F3 59 F1 F3 22 N 25 N 27 F2 < OV, NF > < PON, F > < BON, F > < SPD, F > < CV, N F > < POFF, NF > < BOFF, NF > 28 N 29 F1 30 F2 < SPI, NF > < FON, NF > B < FOFF, NF > < BON, F > 4 N 5 F1 6 F2 34 F3 35 F1 F3 36 F2 F3 82 F4 83 F1 F4 84 F2 F4 < SPD, NF > 28 N 29 F1 30 F2 49 F3 50 F1 F3 51 F2 F3 88 F4 89 F1 F4 90 F2 F4 < OV, NF > 52 F3 53 F1 F3 54 F2 F3 < PON, F > < BON, F > < SPI, F > < OV, F > < PON, F > < BON, F > C < SPD, F > 55 F3 56 F1 F3 67 F3 68 F1 F3 70 F3 71 F1 F3 73 F3 74 F1 F3 76 F3 77 F1 F3 46 F3 47 F1 F3 E < FON, NF > 1 N 2 F1 3 F2 79 F4 80 F1 F4 81 F2 F4 < FOFF, NF > < PON, NF > 57 F2 F3 69 F2 F3 72 F2 F3 75 F2 F3 < BON, NF > < SPI, NF > < OV, NF > < PON, NF > < BON, NF > 78 F2 F3 48 F2 F3 < BON, NF > < SPD, NF > D 7 N 8 F1 9 F2 < OV, NF > 1 N 2 F1 3 F2 58 F3 59 F1 F3 < OV, F > 60 F2 F3 < OV, NF > 10 N 11 F1 12 F2 < PON, F > 61 F3 62 F1 F3 < PON, F > 63 F2 F3 < PON, NF > 13 N 14 F1 < BON, F > 64 F3 65 F1 F3 66 F2 F3 16 N 17 F1 < SPD, F > 19 N 20 F1 < CV, N F > S. Lafortune - Last revision: August
8 A Small Telephone System The network has screening, forwarding, and multi-way calling capabilities. The issue of interest: Feature Interactions. Specifically: detection and resolution of logical conflicts (interactions) between options (features). Implementation: correct design of the (modular) software programs that run at the switches. S. Lafortune - Last revision: August
9 Model of User 0 in a Telephone System: Model of User 1 at Switch 0 in Telephone System: req00 FWD_TO_0 FWD_TO_1 req01 FWD_TO_2 req02 REQ fwd001 fwd002 fwd020 fwd021 nocon00 req00 fwd010 con01 nocon01 onh0 req01 fwd012 REQ_0 REQ_1 REQ_2 nocon0 nocon0 CON INIT offh0 con02 nocon02 fh0 dfh0 req02 nocon0 con10 nocon10 fwd101 fwd102 NOT_REQ onh1 INIT req10 offh1 fh1 dfh1 S. Lafortune - Last revision: August
10 G C 0 G 0 A Control Architecture for Approaching this Problem:... S TCS... S OCS S POTS-4 S. Lafortune - Last revision: August
11 Other examples: Railway Connections and Time Tables 1 The network of railway connections is closed and each line has a fixed number of trains. The inter-station travel times are known and deterministic. The objective is to design satisfactory time tables for the trains. Specifications include: certain trains have to wait for one another to allow change overs. Constraints: want system to operate fast, but also want perturbations to completely disappear in finite time. Issues of interest: how do perturbations to the time table propagate, what limits the minimum operation time, where would it be helpful to add trains, etc. Approach: write equations for the departure times of the trains, using maximum and addition. 1 Example due to G. J. Olsder S. Lafortune - Last revision: August
12 Dispatching Control in an Elevator System 2 Events: hall call, car call, car arrives at floor i, etc. States: position of car k, number of passengers waiting at floor i, etc. (very large state space!) Control problem: which car to send where so as to achieve satisfactory performance? Performance measures: average waiting time (until car comes), average service time (until car delivers to desired floor), fraction of passengers waiting more (on average) than one minute, etc. Probabilistic formulation: passenger arrival rates at floors, probability distribution for destination floors, load times and travel times, etc. Common solution: threshold-based control, i.e., hold a car until a threshold is reached. The issue is then to determine this threshold and automatically adjust it in real-time, based on observed passenger arrival rates. 2 Example due to C. Cassandras S. Lafortune - Last revision: August
13 S. Lafortune - Last revision: August
14 S. Lafortune - Last revision: August
15 The Three Levels of Abstraction in Modeling DES Sample Paths of Discrete Event Systems x(t) x6 x5 x4 x3 x2 x1 t1 t2 t3 t4 t5 t6 t7 t e1 e2 e3 e4 e5 e6 e7 e Describe this sample path by the timed sequence of events that it contains: s t e = (e 1, t 1 )(e 2, t 2 )(e 3, t 3 )(e 4, t 4 )(e 5, t 5 )(e 6, t 6 )(e 7, t 7 ) S. Lafortune - Last revision: August
16 The behavior of a given DES is described as follows: Timed Language: set of all timed sequences of events that the DES can generate/execute Stochastic Timed Language: a timed language with a probability distribution function defined over it Language: a timed language where the timing information has been deleted, i.e., it is a set of sequences, or traces, of events. Formal language theory: Finite set of events E : {e 1, e 2,..., e n } s e = e 1 e 2 e 3 e 4 e 5 e 6 e 7 Set of all finite strings of event in E: E - Kleene-closure A language L is a subset of E : L E S. Lafortune - Last revision: August
17 This leads to the three complemetary levels of abstraction at which DES are studied. Logical level: the language model is used to study properties that concern event ordering only; e.g., consider the telephone system example, as well as the HVAC unit example (diagnosis). Priorities, mutual exclusion, deadlock, livelock, occurrence of unobservable events, etc. Temporal level: the timed language model is used to study properties that concern the timing of the events; e.g., consider the railway network example. Deadlines, cycle times, effect of perturbations, etc. Stochastic level: the stochastic timed language model is used to study properties that concern the expected behavior of the system under the given statistical information; e.g., consider the elevator example. Average delay, throughput, and other relevant performance measures. N.B.: Discrete Event Simulation usually refers to the stochastic level. Question: How to represent [(stochastic) timed] languages? S. Lafortune - Last revision: August
18 Discrete Event Modeling Formalisms Formal classes of models that represent [(stochastic) timed] languages State-based formalisms: define a state space and specify the state transition structure (i.e., (out state, event, in state) triples) that represents the language. Automata (or State Machines) and Petri Nets are widely used. Trace-based formalisms: use (recursive) algebraic equations on the events to represent the traces in the language (i.e., no explicit state ). Often referred to as Process Algebras. Communicating Sequential Processes (CSP) is a well-know formalism in this category. We will study: (untimed and timed) automata [modeling, analysis, diagnosis, supervisory control] (untimed and timed) Petri nets [modeling, analysis, some control] timed event graphs, a special case of timed Petri nets [analysis using max-plus algebra] We illustrate the above modeling formalisms for the (familiar) example of the dining philosophers. S. Lafortune - Last revision: August
19 Automata models of two philosophers (P1, P2) and two forks (F1, F2) P1 1T 1f1 1I1 1f 1f2 1E P2 2T 2f1 2I1 2f 2f2 2E 1f2 1I2 1f1 2f2 2I2 2f1 F1 1f1,2f1 F2 1f2,2f2 1A 1U 2A 2U 1f,2f 1f,2f S. Lafortune - Last revision: August
20 Composition of the four automata: P 1 P 2 F 1 F 2 1f (1T,2T,1A,2A) 1f1 1f2 1f1 2f1 1f2 1f2 2f1 (1E,2T,1U,2U) (1I2,2I1,1U,2U) 2f 2f2 2f2 1f1 2f2 (1I1,2I2,1U,2U) 2f1 (1T,2E,1U,2U) S. Lafortune - Last revision: August
21 Petri net model of one philosopher and two forks if2 if1 fork 2 available holding fork 2 if eating thinking if1 if2 holding fork 1 fork 1 available S. Lafortune - Last revision: August
22 Petri net model of two philosophers and two forks fork 2 available 1f2 1f1 2f1 2f2 1f 2f 1f1 1f2 2f2 2f1 fork 1 available philosopher 1 philosopher 2 S. Lafortune - Last revision: August
23 Recursive equation model of two philosophers and two forks P1 = (1f1 1f2 E1 1f2 1f1 E1) E1 = (1f P1) P2 = (2f1 2f2 E2 2f2 2f1 E2) E2 = (2f P2) F1 = (1f1 1f F1 2f1 2f F1) F2 = (1f2 1f F2 2f2 2f F2) SY STEM = P1 P2 F1 F2 In general, we get a set of equations of the form: X = f(x) Y = g(x) where X is a vector of processes and f must contain. S. Lafortune - Last revision: August
24 How to Compare Modeling Formalisms? Descriptive Power: Language complexity or class of languages that a (finite) model can represent. Finite-state automata: Regular Languages R Labeled Petri Nets: PN L R. Algebraic Structure: Formal operations that permit to build complex systems by interconnecting simple systems and that allow to manipulate a model for analysis and synthesis purposes. R has nice properties: closed under union, concatenation, intersection, parallel composition, complementation w.r.t. E. These operations can be implemented using finite-state automata. PN L does not enjoy such nice properties. However, Petri nets have intrinsically modular structure: e.g., system decomposition by means of place-bordered Petri nets. S. Lafortune - Last revision: August
Industrial Automation (Automação de Processos Industriais)
Industrial Automation (Automação de Processos Industriais) Discrete Event Systems http://users.isr.ist.utl.pt/~jag/courses/api1516/api1516.html Slides 2010/2011 Prof. Paulo Jorge Oliveira Rev. 2011-2015
More informationThe State Explosion Problem
The State Explosion Problem Martin Kot August 16, 2003 1 Introduction One from main approaches to checking correctness of a concurrent system are state space methods. They are suitable for automatic analysis
More informationSemi-asynchronous. Fault Diagnosis of Discrete Event Systems ALEJANDRO WHITE DR. ALI KARIMODDINI OCTOBER
Semi-asynchronous Fault Diagnosis of Discrete Event Systems ALEJANDRO WHITE DR. ALI KARIMODDINI OCTOBER 2017 NC A&T State University http://www.ncat.edu/ Alejandro White Semi-asynchronous http://techlav.ncat.edu/
More informationBridging the Gap between Reactive Synthesis and Supervisory Control
Bridging the Gap between Reactive Synthesis and Supervisory Control Stavros Tripakis University of California, Berkeley Joint work with Ruediger Ehlers (Berkeley, Cornell), Stéphane Lafortune (Michigan)
More informationIN THIS paper we investigate the diagnosability of stochastic
476 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL 50, NO 4, APRIL 2005 Diagnosability of Stochastic Discrete-Event Systems David Thorsley and Demosthenis Teneketzis, Fellow, IEEE Abstract We investigate
More informationSri vidya college of engineering and technology
Unit I FINITE AUTOMATA 1. Define hypothesis. The formal proof can be using deductive proof and inductive proof. The deductive proof consists of sequence of statements given with logical reasoning in order
More informationON DIAGNOSIS AND PREDICTABILITY OF PARTIALLY-OBSERVED DISCRETE-EVENT SYSTEMS
ON DIAGNOSIS AND PREDICTABILITY OF PARTIALLY-OBSERVED DISCRETE-EVENT SYSTEMS by Sahika Genc A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Electrical
More informationIntersection Based Decentralized Diagnosis: Implementation and Verification
Intersection Based Decentralized Diagnosis: Implementation and Verification Maria Panteli and Christoforos N. Hadjicostis Abstract We consider decentralized diagnosis in discrete event systems that are
More informationADVANCED ROBOTICS. PLAN REPRESENTATION Generalized Stochastic Petri nets and Markov Decision Processes
ADVANCED ROBOTICS PLAN REPRESENTATION Generalized Stochastic Petri nets and Markov Decision Processes Pedro U. Lima Instituto Superior Técnico/Instituto de Sistemas e Robótica September 2009 Reviewed April
More informationIntroduction: Computer Science is a cluster of related scientific and engineering disciplines concerned with the study and application of computations. These disciplines range from the pure and basic scientific
More informationSemi-asynchronous Fault Diagnosis of Discrete Event Systems
1 Semi-asynchronous Fault Diagnosis of Discrete Event Systems Alejandro White, Student Member, IEEE, Ali Karimoddini, Senior Member, IEEE Abstract This paper proposes a diagnostics tool for a Discrete-
More information7. Queueing Systems. 8. Petri nets vs. State Automata
Petri Nets 1. Finite State Automata 2. Petri net notation and definition (no dynamics) 3. Introducing State: Petri net marking 4. Petri net dynamics 5. Capacity Constrained Petri nets 6. Petri net models
More informationDesign and Analysis of Distributed Interacting Systems
Design and Analysis of Distributed Interacting Systems Organization Prof. Dr. Joel Greenyer April 11, 2013 Organization Lecture: Thursdays, 10:15 11:45, F 128 Tutorial: Thursdays, 13:00 13:45, G 323 first
More informationOn the Design of Adaptive Supervisors for Discrete Event Systems
On the Design of Adaptive Supervisors for Discrete Event Systems Vigyan CHANDRA Department of Technology, Eastern Kentucky University Richmond, KY 40475, USA and Siddhartha BHATTACHARYYA Division of Computer
More informationCS 154, Lecture 3: DFA NFA, Regular Expressions
CS 154, Lecture 3: DFA NFA, Regular Expressions Homework 1 is coming out Deterministic Finite Automata Computation with finite memory Non-Deterministic Finite Automata Computation with finite memory and
More informationDiscrete Event Systems
DI DIPARTIMENTO DI INGEGNERIA DELL INFORMAZIONE E SCIENZE MATEMATICHE Lecture notes of Discrete Event Systems Simone Paoletti Version 0.3 October 27, 2015 Indice Notation 1 Introduction 2 1 Basics of systems
More informationSafety and Reliability of Embedded Systems. (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Fault Tree Analysis Obscurities and Open Issues
(Sicherheit und Zuverlässigkeit eingebetteter Systeme) Fault Tree Analysis Obscurities and Open Issues Content What are Events? Examples for Problematic Event Semantics Inhibit, Enabler / Conditioning
More informationOptimal Non-blocking Decentralized Supervisory Control Using G-Control Consistency
Optimal Non-blocking Decentralized Supervisory Control Using G-Control Consistency Vahid Saeidi a, Ali A. Afzalian *b, Davood Gharavian c * Phone +982173932626, Fax +982177310425 a,b,c Department of Electrical
More informationDiagnosis of Dense-Time Systems using Digital-Clocks
Diagnosis of Dense-Time Systems using Digital-Clocks Shengbing Jiang GM R&D and Planning Mail Code 480-106-390 Warren, MI 48090-9055 Email: shengbing.jiang@gm.com Ratnesh Kumar Dept. of Elec. & Comp. Eng.
More informationIndustrial Automation (Automação de Processos Industriais)
Industrial Automation (Automação de Processos Industriais) (Sequential Function Chart) http://users.isr.ist.utl.pt/~jag/courses/api1415/api1415.html Slides 2010/2011 Prof. Paulo Jorge Oliveira Rev. 2011-2015
More informationPart I. Principles and Techniques
Introduction to Formal Methods Part I. Principles and Techniques Lecturer: JUNBEOM YOO jbyoo@konkuk.ac.kr Introduction Text System and Software Verification : Model-Checking Techniques and Tools In this
More informationDECENTRALIZED DIAGNOSIS OF EVENT-DRIVEN SYSTEMS FOR SAFELY REACTING TO FAILURES. Wenbin Qiu and Ratnesh Kumar
DECENTRALIZED DIAGNOSIS OF EVENT-DRIVEN SYSTEMS FOR SAFELY REACTING TO FAILURES Wenbin Qiu and Ratnesh Kumar Department of Electrical and Computer Engineering Iowa State University Ames, IA 50011, U.S.A.
More informationDiagnosis of Repeated/Intermittent Failures in Discrete Event Systems
Diagnosis of Repeated/Intermittent Failures in Discrete Event Systems Shengbing Jiang, Ratnesh Kumar, and Humberto E. Garcia Abstract We introduce the notion of repeated failure diagnosability for diagnosing
More informationCoordinated Decentralized Protocols for Failure Diagnosis of Discrete Event Systems
Discrete Event Dynamic Systems: Theory and Applications, 10, 33 86 (2000) c 2000 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. Coordinated Decentralized Protocols for Failure Diagnosis
More informationIndustrial Automation de Processos Industriais)
Industrial Automation (Automação de Processos Industriais) (Sequential Function Chart) http://users.isr.ist.utl.pt/~jag/courses/api1213/api1213.html Slides 2010/2011 Prof. Paulo Jorge Oliveira Rev. 2011-2013
More informationLet us first give some intuitive idea about a state of a system and state transitions before describing finite automata.
Finite Automata Automata (singular: automation) are a particularly simple, but useful, model of computation. They were initially proposed as a simple model for the behavior of neurons. The concept of a
More informationMethods for the specification and verification of business processes MPB (6 cfu, 295AA)
Methods for the specification and verification of business processes MPB (6 cfu, 295AA) Roberto Bruni http://www.di.unipi.it/~bruni 08 - Petri nets basics 1 Object Formalization of the basic concepts of
More informationA new delay forecasting system for the Passenger Information Control system (PIC) of the Tokaido-Sanyo Shinkansen
Computers in Railways X 199 A new delay forecasting system for the Passenger Information Control system (PIC) of the Tokaido-Sanyo Shinkansen K. Fukami, H. Yamamoto, T. Hatanaka & T. Terada Central Japan
More information1 Modelling and Simulation
1 Modelling and Simulation 1.1 Introduction This course teaches various aspects of computer-aided modelling for the performance evaluation of computer systems and communication networks. The performance
More informationMethods for the specification and verification of business processes MPB (6 cfu, 295AA)
Methods for the specification and verification of business processes MPB (6 cfu, 295AA) Roberto Bruni http://www.di.unipi.it/~bruni 07 - Introduction to nets 1 Object Overview of the basic concepts of
More informationDecentralized Diagnosis of Discrete Event Systems using Unconditional and Conditional Decisions
Decentralized Diagnosis of Discrete Event Systems using Unconditional and Conditional Decisions Yin Wang, Tae-Sic Yoo, and Stéphane Lafortune Abstract The past decade has witnessed the development of a
More informationMasked Prioritized Synchronization for Interaction and Control of Discrete Event Systems
Masked Prioritized Synchronization for Interaction and Control of Discrete Event Systems Ratnesh Kumar Department of Electrical Engineering University of Kentucky Lexington, KY 40506-0046 Michael Heymann
More informationLecture Notes On THEORY OF COMPUTATION MODULE -1 UNIT - 2
BIJU PATNAIK UNIVERSITY OF TECHNOLOGY, ODISHA Lecture Notes On THEORY OF COMPUTATION MODULE -1 UNIT - 2 Prepared by, Dr. Subhendu Kumar Rath, BPUT, Odisha. UNIT 2 Structure NON-DETERMINISTIC FINITE AUTOMATA
More informationResolution of Initial-State in Security Applications of DES
Resolution of Initial-State in Security Applications of DES Christoforos N. Hadjicostis Abstract A non-deterministic labeled finite automaton is initial-state opaque if the membership of its true initial
More informationOverview. Discrete Event Systems Verification of Finite Automata. What can finite automata be used for? What can finite automata be used for?
Computer Engineering and Networks Overview Discrete Event Systems Verification of Finite Automata Lothar Thiele Introduction Binary Decision Diagrams Representation of Boolean Functions Comparing two circuits
More informationBusiness Processes Modelling MPB (6 cfu, 295AA)
Business Processes Modelling MPB (6 cfu, 295AA) Roberto Bruni http://www.di.unipi.it/~bruni 07 - Introduction to nets!1 Object Overview of the basic concepts of Petri nets Free Choice Nets (book, optional
More informationMotors Automation Energy Transmission & Distribution Coatings. Servo Drive SCA06 V1.5X. Addendum to the Programming Manual SCA06 V1.
Motors Automation Energy Transmission & Distribution Coatings Servo Drive SCA06 V1.5X SCA06 V1.4X Series: SCA06 Language: English Document Number: 10003604017 / 01 Software Version: V1.5X Publication Date:
More informationRobust Supervisory Control of a Spacecraft Propulsion System
1 Robust Supervisory Control of a Spacecraft Propulsion System Farid Yari, Shahin Hashtrudi-Zad*, and Siamak Tafazoli In this paper the theory of supervisory control of discrete-event systems is used to
More informationModelling of Railway Network Using Petri Nets
Modelling of Railway Network Using Petri Nets MANDIRA BANIK 1, RANJAN DASGUPTA 2 1 Dept. of Computer Sc. & Engg., National Institute of Technical Teachers' Training & Research, Kolkata, West Bengal, India
More informationMOST OF the published research on control of discreteevent
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 43, NO. 1, JANUARY 1998 3 Discrete-Event Control of Nondeterministic Systems Michael Heymann and Feng Lin, Member, IEEE Abstract Nondeterminism in discrete-event
More informationMethods for the specification and verification of business processes MPB (6 cfu, 295AA)
Methods for the specification and verification of business processes MPB (6 cfu, 295AA) Roberto Bruni http://www.di.unipi.it/~bruni 07 - Introduction to nets 1 Object Overview of the basic concepts of
More informationCMPSCI 250: Introduction to Computation. Lecture #22: From λ-nfa s to NFA s to DFA s David Mix Barrington 22 April 2013
CMPSCI 250: Introduction to Computation Lecture #22: From λ-nfa s to NFA s to DFA s David Mix Barrington 22 April 2013 λ-nfa s to NFA s to DFA s Reviewing the Three Models and Kleene s Theorem The Subset
More informationAnalysis and Optimization of Discrete Event Systems using Petri Nets
Volume 113 No. 11 2017, 1 10 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Analysis and Optimization of Discrete Event Systems using Petri Nets
More informationAutomata Theory. Lecture on Discussion Course of CS120. Runzhe SJTU ACM CLASS
Automata Theory Lecture on Discussion Course of CS2 This Lecture is about Mathematical Models of Computation. Why Should I Care? - Ways of thinking. - Theory can drive practice. - Don t be an Instrumentalist.
More informationRanking Verification Counterexamples: An Invariant guided approach
Ranking Verification Counterexamples: An Invariant guided approach Ansuman Banerjee Indian Statistical Institute Joint work with Pallab Dasgupta, Srobona Mitra and Harish Kumar Complex Systems Everywhere
More informationCourse on Hybrid Systems
Course on Hybrid Systems Maria Prandini Politecnico di Milano, Italy Organizer and lecturer: Maria Prandini Politecnico di Milano, Italy maria.prandini@polimi.it Additional lecturers: CONTACT INFO Goran
More informationRegular Expressions. Definitions Equivalence to Finite Automata
Regular Expressions Definitions Equivalence to Finite Automata 1 RE s: Introduction Regular expressions are an algebraic way to describe languages. They describe exactly the regular languages. If E is
More informationState-Space Exploration. Stavros Tripakis University of California, Berkeley
EE 144/244: Fundamental Algorithms for System Modeling, Analysis, and Optimization Fall 2014 State-Space Exploration Stavros Tripakis University of California, Berkeley Stavros Tripakis (UC Berkeley) EE
More informationLecture 3: Nondeterministic Finite Automata
Lecture 3: Nondeterministic Finite Automata September 5, 206 CS 00 Theory of Computation As a recap of last lecture, recall that a deterministic finite automaton (DFA) consists of (Q, Σ, δ, q 0, F ) where
More informationDES. 4. Petri Nets. Introduction. Different Classes of Petri Net. Petri net properties. Analysis of Petri net models
4. Petri Nets Introduction Different Classes of Petri Net Petri net properties Analysis of Petri net models 1 Petri Nets C.A Petri, TU Darmstadt, 1962 A mathematical and graphical modeling method. Describe
More informationAlgebra Performance Level Descriptors
Limited A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Algebra. A student at this level has an emerging ability to A student whose performance
More informationCS 154, Lecture 2: Finite Automata, Closure Properties Nondeterminism,
CS 54, Lecture 2: Finite Automata, Closure Properties Nondeterminism, Why so Many Models? Streaming Algorithms 0 42 Deterministic Finite Automata Anatomy of Deterministic Finite Automata transition: for
More informationLET S CONTROL EVERYTHING!
LET S CONTROL EVERYTHING! C. G. Cassandras Boston University cgc@bu.edu http://vita.bu.edu/cgc LET S CONTROL LET S EVERYTHING LET CONTROL EVERYTHING CENTRAL THEMES OF THIS TALK... CONTROL is pervasive
More informationIntroduction to Model Checking. Debdeep Mukhopadhyay IIT Madras
Introduction to Model Checking Debdeep Mukhopadhyay IIT Madras How good can you fight bugs? Comprising of three parts Formal Verification techniques consist of three parts: 1. A framework for modeling
More informationIntroduction to Modelling and Simulation
Introduction to Modelling and Simulation Prof. Cesar de Prada Dpt. Systems Engineering and Automatic Control EII, University of Valladolid, Spain prada@autom.uva.es Digital simulation Methods and tools
More informationfakultät für informatik informatik 12 technische universität dortmund Petri nets Peter Marwedel Informatik 12 TU Dortmund Germany
12 Petri nets Peter Marwedel Informatik 12 TU Dortmund Germany Introduction Introduced in 1962 by Carl Adam Petri in his PhD thesis. Focus on modeling causal dependencies; no global synchronization assumed
More informationLectures on Medical Biophysics Department of Biophysics, Medical Faculty, Masaryk University in Brno. Biocybernetics
Lectures on Medical Biophysics Department of Biophysics, Medical Faculty, Masaryk University in Brno Norbert Wiener 26.11.1894-18.03.1964 Biocybernetics Lecture outline Cybernetics Cybernetic systems Feedback
More informationHRML: a hybrid relational modelling language. He Jifeng
HRML: a hybrid relational modelling language He Jifeng Hybrid Systems Systems are composed by continuous physical component and discrete control component The system state evoles over time according to
More informationSupervisory Control of Hybrid Systems
X.D. Koutsoukos, P.J. Antsaklis, J.A. Stiver and M.D. Lemmon, "Supervisory Control of Hybrid Systems, in Special Issue on Hybrid Systems: Theory and Applications, Proceedings of the IEEE, P.J. Antsaklis,
More informationAbstractions and Decision Procedures for Effective Software Model Checking
Abstractions and Decision Procedures for Effective Software Model Checking Prof. Natasha Sharygina The University of Lugano, Carnegie Mellon University Microsoft Summer School, Moscow, July 2011 Lecture
More informationEECS 579: Logic and Fault Simulation. Simulation
EECS 579: Logic and Fault Simulation Simulation: Use of computer software models to verify correctness Fault Simulation: Use of simulation for fault analysis and ATPG Circuit description Input data for
More informationCOM364 Automata Theory Lecture Note 2 - Nondeterminism
COM364 Automata Theory Lecture Note 2 - Nondeterminism Kurtuluş Küllü March 2018 The FA we saw until now were deterministic FA (DFA) in the sense that for each state and input symbol there was exactly
More informationHybrid Control and Switched Systems. Lecture #1 Hybrid systems are everywhere: Examples
Hybrid Control and Switched Systems Lecture #1 Hybrid systems are everywhere: Examples João P. Hespanha University of California at Santa Barbara Summary Examples of hybrid systems 1. Bouncing ball 2.
More informationAn Algebraic Generalization for Graph and Tensor-Based Neural Networks
An Algebraic Generalization for Graph and Tensor-Based Neural Networks CIBCB 2017 Manchester, U.K. Ethan C. Jackson 1, James A. Hughes 1, Mark Daley 1, and Michael Winter 2 August 24, 2017 The University
More informationActive Diagnosis of Hybrid Systems Guided by Diagnosability Properties
Active Diagnosis of Hybrid Systems Guided by Diagnosability Properties Application to autonomous satellites Louise Travé-Massuyès 5 February 29 Motivation Control and autonomy of complex dynamic systems
More informationFinite-State Model Checking
EECS 219C: Computer-Aided Verification Intro. to Model Checking: Models and Properties Sanjit A. Seshia EECS, UC Berkeley Finite-State Model Checking G(p X q) Temporal logic q p FSM Model Checker Yes,
More informationAlan Bundy. Automated Reasoning LTL Model Checking
Automated Reasoning LTL Model Checking Alan Bundy Lecture 9, page 1 Introduction So far we have looked at theorem proving Powerful, especially where good sets of rewrite rules or decision procedures have
More informationClosure Properties of Regular Languages. Union, Intersection, Difference, Concatenation, Kleene Closure, Reversal, Homomorphism, Inverse Homomorphism
Closure Properties of Regular Languages Union, Intersection, Difference, Concatenation, Kleene Closure, Reversal, Homomorphism, Inverse Homomorphism Closure Properties Recall a closure property is a statement
More informationConcatenation. The concatenation of two languages L 1 and L 2
Regular Expressions Problem Problem Set Set Four Four is is due due using using a late late period period in in the the box box up up front. front. Concatenation The concatenation of two languages L 1
More informationEquivalence of DFAs and NFAs
CS 172: Computability and Complexity Equivalence of DFAs and NFAs It s a tie! DFA NFA Sanjit A. Seshia EECS, UC Berkeley Acknowledgments: L.von Ahn, L. Blum, M. Blum What we ll do today Prove that DFAs
More informationPlasma: A new SMC Checker. Axel Legay. In collaboration with L. Traonouez and S. Sedwards.
Plasma: A new SMC Checker Axel Legay In collaboration with L. Traonouez and S. Sedwards. 1 Plasma Lab A PLAtform for Statistical Model Analysis A library of statistical model-checking algorithms (Monte-Carlo,
More informationSupervisory Control: Advanced Theory and Applications
Supervisory Control: Advanced Theory and Applications Dr Rong Su S1-B1b-59, School of EEE Nanyang Technological University Tel: +65 6790-6042, Email: rsu@ntu.edu.sg EE6226, Discrete Event Systems 1 Introduction
More informationEfficient diagnosability assessment via ILP optimization: a railway benchmark
Efficient diagnosability assessment via LP optimization: a railway benchmark 23rd EEE nternational Conference on Emerging Technologies and Factory Automation (ETFA 2018) F. Basile1, A. Boussif2, Gianmaria
More informationFinite Automata and Languages
CS62, IIT BOMBAY Finite Automata and Languages Ashutosh Trivedi Department of Computer Science and Engineering, IIT Bombay CS62: New Trends in IT: Modeling and Verification of Cyber-Physical Systems (2
More informationClosure under the Regular Operations
Closure under the Regular Operations Application of NFA Now we use the NFA to show that collection of regular languages is closed under regular operations union, concatenation, and star Earlier we have
More informationSimulation of Discrete Event Systems
Simulation of Discrete Event Systems Unit 1 Introduction to Discrete Event Systems Fall Winter 2017/2018 Prof. Dr.-Ing. Dipl.-Wirt.-Ing. Sven Tackenberg Chair and Institute of Industrial Engineering and
More informationFailure Diagnosis of Discrete Event Systems With Linear-Time Temporal Logic Specifications
Failure Diagnosis of Discrete Event Systems With Linear-Time Temporal Logic Specifications Shengbing Jiang and Ratnesh Kumar Abstract The paper studies failure diagnosis of discrete event systems with
More informationAchieving Fault-tolerance and Safety of Discrete-event Systems through Learning
2016 American Control Conference (ACC) Boston Marriott Copley Place July 6-8, 2016. Boston, MA, USA Achieving Fault-tolerance and Safety of Discrete-event Systems through Learning Jin Dai, Ali Karimoddini,
More informationA Brief Introduction to Model Checking
A Brief Introduction to Model Checking Jan. 18, LIX Page 1 Model Checking A technique for verifying finite state concurrent systems; a benefit on this restriction: largely automatic; a problem to fight:
More informationConstructions on Finite Automata
Constructions on Finite Automata Informatics 2A: Lecture 4 Mary Cryan School of Informatics University of Edinburgh mcryan@inf.ed.ac.uk 24 September 2018 1 / 33 Determinization The subset construction
More informationDecentralized Failure Diagnosis of Discrete Event Systems
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS PART A: SYSTEMS AND HUMANS, VOL., NO., 2005 1 Decentralized Failure Diagnosis of Discrete Event Systems Wenbin Qiu, Student Member, IEEE, and Ratnesh Kumar,
More informationUNIT-II. NONDETERMINISTIC FINITE AUTOMATA WITH ε TRANSITIONS: SIGNIFICANCE. Use of ε-transitions. s t a r t. ε r. e g u l a r
Syllabus R9 Regulation UNIT-II NONDETERMINISTIC FINITE AUTOMATA WITH ε TRANSITIONS: In the automata theory, a nondeterministic finite automaton (NFA) or nondeterministic finite state machine is a finite
More informationCONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. XV - Modeling of Discrete Event Systems - Stéphane Lafortune
CONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. XV - Modeling of Discrete Event Systes - Stéphane Lafortune MODELING OF DISCRETE EVENT SYSTEMS Stéphane Lafortune The University of Michigan, USA Keywords:
More informationEmbedded Systems 6 REVIEW. Place/transition nets. defaults: K = ω W = 1
Embedded Systems 6-1 - Place/transition nets REVIEW Def.: (P, T, F, K, W, M 0 ) is called a place/transition net (P/T net) iff 1. N=(P,T,F) is a net with places p P and transitions t T 2. K: P (N 0 {ω})
More informationCPS 220 Theory of Computation REGULAR LANGUAGES
CPS 22 Theory of Computation REGULAR LANGUAGES Introduction Model (def) a miniature representation of a thing; sometimes a facsimile Iraq village mockup for the Marines Scientific modelling - the process
More informationCausality in Concurrent Systems
Causality in Concurrent Systems F. Russo Vrije Universiteit Brussel Belgium S.Crafa Università di Padova Italy HaPoC 31 October 2013, Paris Causality in Concurrent Systems software, hardware or even physical
More informationCHURCH SYNTHESIS PROBLEM and GAMES
p. 1/? CHURCH SYNTHESIS PROBLEM and GAMES Alexander Rabinovich Tel-Aviv University, Israel http://www.tau.ac.il/ rabinoa p. 2/? Plan of the Course 1. The Church problem - logic and automata. 2. Games -
More informationAbstract. 1 Introduction
The max-plus algebra approach to railway timetable design R.M.P. Goverde Faculty of Civil Engineering and Geo Sciences, Delft University o/ Tec/mob^ f 0 Boz ^% ggoo G^ De% 7/^e A^e^er/a^^ email: goverde@ct.tudelft.nl
More informationColoured Petri Nets Based Diagnosis on Causal Models
Coloured Petri Nets Based Diagnosis on Causal Models Soumia Mancer and Hammadi Bennoui Computer science department, LINFI Lab. University of Biskra, Algeria mancer.soumia@gmail.com, bennoui@gmail.com Abstract.
More informationIntroduction to mcrl2
Introduction to mcrl2 Luís S. Barbosa DI-CCTC Universidade do Minho Braga, Portugal May, 2011 mcrl2: A toolset for process algebra mcrl2 provides: a generic process algebra, based on Acp (Bergstra & Klop,
More informationFormal Methods in Software Engineering
Formal Methods in Software Engineering Modeling Prof. Dr. Joel Greenyer October 21, 2014 Organizational Issues Tutorial dates: I will offer two tutorial dates Tuesdays 15:00-16:00 in A310 (before the lecture,
More informationDISTINGUING NON-DETERMINISTIC TIMED FINITE STATE MACHINES
DISTINGUING NON-DETERMINISTIC TIMED FINITE STATE MACHINES Maxim Gromov 1, Khaled El-Fakih 2, Natalia Shabaldina 1, Nina Yevtushenko 1 1 Tomsk State University, 36 Lenin Str.. Tomsk, 634050, Russia gromov@sibmail.com,
More informationFinite Automata Part Two
Finite Automata Part Two DFAs A DFA is a Deterministic Finite Automaton A DFA is defined relative to some alphabet Σ. For each state in the DFA, there must be exactly one transition defined for each symbol
More informationVerification and Anomaly Detection for Event-Based Control of Manufacturing Systems
Verification and Anomaly Detection for Event-Based Control of Manufacturing Systems by Lindsay Victoria Allen A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor
More informationFailure Diagnosis of Discrete Event Systems: A Temporal Logic Approach
Failre Diagnosis of Discrete Event Systems: A Temporal Logic Approach Shengbing Jiang Electrical & Controls Integration Lab General Motors R&D 1 Otline Introdction Notion of Diagnosability in Temporal
More informationNECESSARY AND SUFFICIENT CONDITIONS FOR DEADLOCKS IN FLEXIBLE MANUFACTURING SYSTEMS BASED ON A DIGRAPH MODEL
Asian Journal of Control, Vol. 6, No. 2, pp. 217-228, June 2004 217 NECESSARY AND SUFFICIENT CONDITIONS FOR DEADLOCKS IN FLEXIBLE MANUFACTURING SYSTEMS BASED ON A DIGRAPH MODEL Wenle Zhang, Robert P. Judd,
More informationAutomata-theoretic analysis of hybrid systems
Automata-theoretic analysis of hybrid systems Madhavan Mukund SPIC Mathematical Institute 92, G N Chetty Road Chennai 600 017, India Email: madhavan@smi.ernet.in URL: http://www.smi.ernet.in/~madhavan
More informationCSC173 Workshop: 13 Sept. Notes
CSC173 Workshop: 13 Sept. Notes Frank Ferraro Department of Computer Science University of Rochester September 14, 2010 1 Regular Languages and Equivalent Forms A language can be thought of a set L of
More informationCOMP-330 Theory of Computation. Fall Prof. Claude Crépeau. Lec. 10 : Context-Free Grammars
COMP-330 Theory of Computation Fall 2017 -- Prof. Claude Crépeau Lec. 10 : Context-Free Grammars COMP 330 Fall 2017: Lectures Schedule 1-2. Introduction 1.5. Some basic mathematics 2-3. Deterministic finite
More informationHybrid Systems Modeling, Analysis and Control
Hybrid Systems Modeling, Analysis and Control Radu Grosu Vienna University of Technology Lecture 6 Continuous AND Discrete Systems Control Theory Continuous systems approximation, stability control, robustness
More information