Hybrid Control and Switched Systems. Lecture #1 Hybrid systems are everywhere: Examples
|
|
- Regina Hicks
- 6 years ago
- Views:
Transcription
1 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. Thermostat 3. Transmission 4. Inverted pendulum swing-up 5. Multiple-tank 6. Server 7. Supervisory control 1
2 Example #1: Bouncing ball y g Free fall Collision c [0,1] energy reflected at impact Notation: given x : [0, ) R n piecewise continuous signal x at points t where x is continuous x(t) = x - (t) = x + (t) By convention we will generally assume right continuity, i.e., x(t) = x + (t) t 0 x x + Example #1: Bouncing ball x 1 ú y Free fall Collision for any c < 1, there are infinitely many transitions in finite time (Zeno phenomena) t x 1 = 0 & x 2 <0? guard or jump condition transition state reset x 2 ú c x 2 2
3 Example #2: Thermostat room goal regulate temperature around 75 o x mean temperature heater when heater is off: ( x 50 o ) when heater is on: ( x 100 o ) event-based control turn heater on turn heater off 73 o 77 o x Example #2: Thermostat x q = on off off off on on on turn heater off turn heater on guard condition x 73? discrete state or mode off mode t no reset on mode x(t) R continuous state q(t) { off, on } discrete state x 77? guard condition 3
4 η 1 η 2 η 3 η 4 Example #3: Transmission throttle u [-1,1] position θ g {1,2,3,4} gear ω velocity η k efficiency of the k th gear ω velocity [Hedlund, Rantzer 1999] Example #3: Automatic transmission ω ω 2? ω ω 3? ω ω 4? g = 1 g = 2 g = 3 g = 4 ω ϖ 1? ω ϖ 2? ω ϖ 3? g = 1 ω 2 ω 3 g = 2 ϖ 1 ϖ 2 g = 3 ω 4 g = 4 ϖ 3 4
5 Example #3: Semi-automatic transmission v(t) { up, down, keep } drivers input (discrete) v = up or ω ω 2? v = up or ω ω 3? v = up or ω ω 4? g = 1 g = 2 g = 3 g = 4 v = down or ω ϖ 1? v = down or ω ϖ 2? v = down or ω ϖ 3? ω 2 g = 1 ω 3 g = 2 ϖ 1 g = 3 ϖ 2 ω 4 g = 4 ϖ 3 Example #4: Inverted pendulum swing-up u [-1,1] θ goal drive θ to 0 (upright position) u [-1,1] force applied to the cart Total system energy Feedback linearization controller: try to make kinetic potential normalized to be zero at stationary upright position only in [-1,1] close to upright position (θ = ω = 0) [Astrom, Furuta 1999] 5
6 Example #4: Inverted pendulum swing-up u [-1,1] θ Hybrid controller: 1 st pump/remove energy into/from the system by applying maximum force, until E 0 (energy control) 2 nd wait until pendulum is close to the upright position 3 th next to upright position use feedback linearization controller remove energy E [ ε,ε]? E < ε? wait stabilize E>ε? pump energy E [ ε,ε]? ω + θ δ? Question: can you figure out a way to solve the problem ω(0) = 0, θ(0) = π? pump Example #5: Tank system goal prevent the tank from emptying or filling up * pump-on inflow λ constant outflow μ y δ delay between command is sent to pump and the time it is executed guard condition pump off τ δ? wait to off y y min? τ ú 0 state reset τ ú 0 wait to on τ δ? pump on y y max? How to choose y min and y max for given μ, λ, δ? 6
7 Example #5: Multiple-tank system y 1 y 1,min & y 2 y 2,max? τ ú 0 τ δ k? Initialized rectangular hybrid automata all differential equations have constant r.h.s. all jump cond. are of the form: state var. 1 fixed interval 1 & state var. 2 fixed interval 2 & etc. all resets have constant r.h.s. Most general class of hybrid systems for which there exist completely automated procedures to compute the set of reachable states Example #6: Switched server r 0 r 1 r 2 rates of incoming parts buffers server r > r 0 + r 1 + r 2 rate of service δ ij setup time needed to move from buffer i to j Scheduling algorithm (cyclic scheduling): 1. start in buffer 0 2. work on a buffer until empty 3. when buffer j is empty move to buffer j + 1 (mod 3) Often also an initialized rectangular hybrid automata 7
8 Example #7: Server system with congestion control incoming rate r q max q Additive increase/multiplicative decrease congestion control (AIMD): while q < q max increase r linearly when q reaches q max instantaneously multiply r by γ (0,1) guard condition q q max? server B rate of service (bandwidth) q(t) r ú γ r state reset no longer an initialized rectangular hybrid automata t Example #8: Supervisory control supervisor logic that selects which controller to use bank of controllers σ controller 1 controller 2 u process y σ switching signal taking values in the set {1,2} 2 1 σ 8
9 E.g. #8 a): Vision-based control of a flexible manipulator flexible manipulator m tip u b base I base θ base θ tip goal drive θ tip to zero, using feedback from θ base θ tip encoder at the base machine vision (needed to increase the damping of the flexible modes in the presence of noise) To achieve high accuracy in the measurement of θ tip the camera must have a small field of view output feedback output: E.g. #8 a): Vision-based control of a flexible manipulator controller 1 controller 2 u manipulator y controller 1 optimized for feedback from θ base and θ tip and controller 2 optimized for feedback only from θ base E.g., LQG controllers that minimize 9
10 E.g. #8 a): Vision-based control of a flexible manipulator feedback connection with controller 1 (θ base and θ tip available) feedback connection with controller 2 (only θ base available) E.g. #8 a): Vision-based control of a flexible manipulator 5 no switching (feedback only from θ base ) 0 θ tip (t) with switching (close to 0 feedback also from θ tip ) 0 θ tip (t) θ max =
11 Example #8 b): Adaptive supervisory control supervisor bank of controllers σ process can either be: controller 1 controller 2 u process y Goal: stabilize process, regardless of which is the actual process model Supervisor must try to determine which is the correct process model by observing u and y select the appropriate controller Next class 1. Formal models for hybrid systems: Finite automata Differential equations Hybrid automata Open hybrid automaton 2. Nondeterministic vs. stochastic systems Non-deterministic automata and differential inclusions Markov chains and stochastic processes 11
Hybrid Control and Switched Systems. Lecture #8 Stability and convergence of hybrid systems (topological view)
Hybrid Control and Switched Systems Lecture #8 Stability and convergence of hybrid systems (topological view) João P. Hespanha University of California at Santa Barbara Summary Lyapunov stability of hybrid
More informationHybrid Control and Switched Systems. Lecture #9 Analysis tools for hybrid systems: Impact maps
Hybrid Control and Switched Systems Lecture #9 Analysis tools for hybrid systems: Impact maps João P. Hespanha University of California at Santa Barbara Summary Analysis tools for hybrid systems Impact
More informationHybrid Control and Switched Systems. Lecture #4 Simulation of hybrid systems
Hybrid Control and Switched Systems Lecture #4 Simulation of hybrid systems João P. Hespanha University of California at Santa Barbara Summary 1. Numerical simulation of hybrid automata simulations of
More informationStochastic Hybrid Systems: Applications to Communication Networks
research supported by NSF Stochastic Hybrid Systems: Applications to Communication Networks João P. Hespanha Center for Control Engineering and Computation University of California at Santa Barbara Deterministic
More informationControlo Switched Systems: Mixing Logic with Differential Equations. João P. Hespanha. University of California at Santa Barbara.
Controlo 00 5 th Portuguese Conference on Automatic Control University of Aveiro,, September 5-7, 5 00 Switched Systems: Mixing Logic with Differential Equations João P. Hespanha University of California
More informationDiscontinuous Systems
Discontinuous Systems Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline Simple Examples Bouncing ball Heating system Gearbox/cruise control Simulating Hybrid Systems
More informationSwitched Systems: Mixing Logic with Differential Equations
research supported by NSF Switched Systems: Mixing Logic with Differential Equations João P. Hespanha Center for Control Dynamical Systems and Computation Outline Logic-based switched systems framework
More informationHybrid Control and Switched Systems. Lecture #2 How to describe a hybrid system? Formal models for hybrid system
Hyrid Control nd Switched Systems Lecture #2 How to descrie hyrid system? Forml models for hyrid system João P. Hespnh University of Cliforni t Snt Brr Summry. Forml models for hyrid systems: Finite utomt
More informationHybrid Control and Switched Systems. Lecture #3 What can go wrong? Trajectories of hybrid systems
Hybrid Conrol and Swiched Sysems Lecure #3 Wha can go wrong? Trajecories of hybrid sysems João P. Hespanha Universiy of California a Sana Barbara Summary 1. Trajecories of hybrid sysems: Soluion o a hybrid
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 informationLecture 1. Introduction. The importance, ubiquity, and complexity of embedded systems are growing
Lecture 1 Introduction Karl Henrik Johansson The importance, ubiquity, and complexity of embedded systems are growing tremendously thanks to the revolution in digital technology. This has created a need
More informationEE291E Lecture Notes 3 Autonomous Hybrid Automata
EE9E Lecture Notes 3 Autonomous Hybrid Automata Claire J. Tomlin January, 8 The lecture notes for this course are based on the first draft of a research monograph: Hybrid Systems. The monograph is copyright
More informationStochastic Hybrid Systems: Modeling, analysis, and applications to networks and biology
research supported by NSF Stochastic Hybrid Systems: Modeling, analysis, and applications to networks and biology João P. Hespanha Center for Control Engineering and Computation University of California
More informationHYBRID AND SWITCHED SYSTEMS ECE229 WINTER 2004
HYBRID AND SWITCHED SYSTEMS ECE229 WINTER 2004 Course description As computers, digital networks, and embedded systems become ubiquitous and increasingly complex, one needs to understand the coupling between
More informationHybrid Systems - Lecture n. 3 Lyapunov stability
OUTLINE Focus: stability of equilibrium point Hybrid Systems - Lecture n. 3 Lyapunov stability Maria Prandini DEI - Politecnico di Milano E-mail: prandini@elet.polimi.it continuous systems decribed by
More informationNetworked Control System Protocols Modeling & Analysis using Stochastic Impulsive Systems
Networked Control System Protocols Modeling & Analysis using Stochastic Impulsive Systems João P. Hespanha Center for Control Dynamical Systems and Computation Talk outline Examples feedback over shared
More informationEmbedded Systems 5. Synchronous Composition. Lee/Seshia Section 6.2
Embedded Systems 5-1 - Synchronous Composition Lee/Seshia Section 6.2 Important semantic model for concurrent composition Here: composition of actors Foundation of Statecharts, Simulink, synchronous programming
More informationStochastic Hybrid Systems: Applications to Communication Networks
research supported by NSF Stochastic Hybrid Systems: Applications to Communication Networks João P. Hespanha Center for Control Engineering and Computation University of California at Santa Barbara Talk
More informationHybrid Control and Switched Systems. Lecture #6 Reachability
Hbrid Control and Switched Stem Lecture #6 Reachabilit João P. Hepanha Univerit of California at Santa Barbara Summar Review of previou lecture Reachabilit tranition tem reachabilit algorithm backward
More informationAn Introduction to Hybrid Systems Modeling
CS620, IIT BOMBAY An Introduction to Hybrid Systems Modeling Ashutosh Trivedi Department of Computer Science and Engineering, IIT Bombay CS620: New Trends in IT: Modeling and Verification of Cyber-Physical
More informationHybrid Systems Course Lyapunov stability
Hybrid Systems Course Lyapunov stability OUTLINE Focus: stability of an equilibrium point continuous systems decribed by ordinary differential equations (brief review) hybrid automata OUTLINE Focus: stability
More informationHybrid systems and computer science a short tutorial
Hybrid systems and computer science a short tutorial Eugene Asarin Université Paris 7 - LIAFA SFM 04 - RT, Bertinoro p. 1/4 Introductory equations Hybrid Systems = Discrete+Continuous SFM 04 - RT, Bertinoro
More informationHybrid Control and Switched Systems. Lecture #11 Stability of switched system: Arbitrary switching
Hybrid Control and Switched Systems Lecture #11 Stability of switched system: Arbitrary switching João P. Hespanha University of California at Santa Barbara Stability under arbitrary switching Instability
More informationHybrid Control and Switched Systems. Lecture #7 Stability and convergence of ODEs
Hybrid Control and Switched Systems Lecture #7 Stability and convergence of ODEs João P. Hespanha University of California at Santa Barbara Summary Lyapunov stability of ODEs epsilon-delta and beta-function
More informationONR MURI AIRFOILS: Animal Inspired Robust Flight with Outer and Inner Loop Strategies. Calin Belta
ONR MURI AIRFOILS: Animal Inspired Robust Flight with Outer and Inner Loop Strategies Provable safety for animal inspired agile flight Calin Belta Hybrid and Networked Systems (HyNeSs) Lab Department of
More informationLMI Methods in Optimal and Robust Control
LMI Methods in Optimal and Robust Control Matthew M. Peet Arizona State University Lecture 20: LMI/SOS Tools for the Study of Hybrid Systems Stability Concepts There are several classes of problems for
More informationCommunication constraints and latency in Networked Control Systems
Communication constraints and latency in Networked Control Systems João P. Hespanha Center for Control Engineering and Computation University of California Santa Barbara In collaboration with Antonio Ortega
More informationABSTRACT. Kevin Roy Kefauver, Ph.D., Hybrid dynamical systems are common throughout the physical and computer world, and
ABSTRACT Title of Dissertation: OPTIMAL FEEDBACK CONTROL FOR HYBRID SYSTEMS, WITH APPLICATION TO VEHICLE DYNAMICS. Kevin Roy Kefauver, Ph.D., Dissertation Directed By: Dr. William Levine, Professor, Department
More informationmodels, languages, dynamics Eugene Asarin PIMS/EQINOCS Workshop on Automata Theory and Symbolic Dynamics LIAFA - University Paris Diderot and CNRS
models, s, LIAFA - University Paris Diderot and CNRS PIMS/EQINOCS Workshop on Automata Theory and Symbolic Dynamics Context A model for verification of real-time systems Invented by Alur and Dill in early
More informationLab 6d: Self-Erecting Inverted Pendulum (SEIP)
Lab 6d: Self-Erecting Inverted Pendulum (SEIP) Arthur Schopen- Life swings like a pendulum backward and forward between pain and boredom. hauer 1 Objectives The goal of this project is to design a controller
More informationVerification of Nonlinear Hybrid Systems with Ariadne
Verification of Nonlinear Hybrid Systems with Ariadne Luca Geretti and Tiziano Villa June 2, 2016 June 2, 2016 Verona, Italy 1 / 1 Outline June 2, 2016 Verona, Italy 2 / 1 Outline June 2, 2016 Verona,
More informationEE 144/244: Fundamental Algorithms for System Modeling, Analysis, and Optimization Fall 2016
EE 144/244: Fundamental Algorithms for System Modeling, Analysis, and Optimization Fall 2016 Discrete Event Simulation Stavros Tripakis University of California, Berkeley Stavros Tripakis (UC Berkeley)
More informationHybrid Routhian Reduction of Lagrangian Hybrid Systems
Hybrid Routhian Reduction of Lagrangian Hybrid Systems Aaron D. Ames and Shankar Sastry Department of Electrical Engineering and Computer Sciences University of California at Berkeley Berkeley, CA 94720
More informationZeno Behavior in Electromechanical Hybrid Systems: From Theory to Experimental Validation
Zeno Behavior in Electromechanical Hybrid Systems: From Theory to Experimental Validation Shishir Nadubettu Yadukumar, Bhargav Kothapalli and Aaron D. Ames Abstract The goal of this paper is to assess
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 informationELEC4631 s Lecture 2: Dynamic Control Systems 7 March Overview of dynamic control systems
ELEC4631 s Lecture 2: Dynamic Control Systems 7 March 2011 Overview of dynamic control systems Goals of Controller design Autonomous dynamic systems Linear Multi-input multi-output (MIMO) systems Bat flight
More informationHMM part 1. Dr Philip Jackson
Centre for Vision Speech & Signal Processing University of Surrey, Guildford GU2 7XH. HMM part 1 Dr Philip Jackson Probability fundamentals Markov models State topology diagrams Hidden Markov models -
More informationVerification of Hybrid Systems with Ariadne
Verification of Hybrid Systems with Ariadne Davide Bresolin 1 Luca Geretti 2 Tiziano Villa 3 1 University of Bologna 2 University of Udine 3 University of Verona An open workshop on Formal Methods for
More informationAnalysis and Design of Control Systems in the Time Domain
Chapter 6 Analysis and Design of Control Systems in the Time Domain 6. Concepts of feedback control Given a system, we can classify it as an open loop or a closed loop depends on the usage of the feedback.
More informationEl péndulo invertido: un banco de pruebas para el control no lineal. XXV Jornadas de Automática
El péndulo invertido: un banco de pruebas para el control no lineal Javier Aracil and Francisco Gordillo Escuela Superior de Ingenieros Universidad de Sevilla XXV Jornadas de Automática Ciudad Real, 8-1
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 informationControl Synthesis of Discrete Manufacturing Systems using Timed Finite Automata
Control Synthesis of Discrete Manufacturing Systems using Timed Finite utomata JROSLV FOGEL Institute of Informatics Slovak cademy of Sciences ratislav Dúbravská 9, SLOVK REPULIC bstract: - n application
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 informationHybrid Dynamical Systems: An Introduction to Control and Verification
Foundations and Trends R in Systems and Control Vol. 1, No. 1 (2014) 1 172 c 2014 H. Lin and P.J. Antsaklis DOI: 10.1561/2600000001 Hybrid Dynamical Systems: An Introduction to Control and Verification
More informationLogic Model Checking
Logic Model Checking Lecture Notes 10:18 Caltech 101b.2 January-March 2004 Course Text: The Spin Model Checker: Primer and Reference Manual Addison-Wesley 2003, ISBN 0-321-22862-6, 608 pgs. the assignment
More informationExercise 4: Markov Processes, Cellular Automata and Fuzzy Logic
Exercise 4: Markov Processes, Cellular Automata and Fuzzy Logic Formal Methods II, Fall Semester 2013 Distributed: 8.11.2013 Due Date: 29.11.2013 Send your solutions to: tobias.klauser@uzh.ch or deliver
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 informationDynamic logic for Hybrid systems
Differential Dynamic Logic for Verifying Parametric Hybrid Systems by Andre Platzer presented by Hallstein Asheim Hansen 15th April 2008 Hallstein Asheim Hansen Slide 1 An example of a hybrid system: Thermostat
More informationEmbedded Systems 2. REVIEW: Actor models. A system is a function that accepts an input signal and yields an output signal.
Embedded Systems 2 REVIEW: Actor models A system is a function that accepts an input signal and yields an output signal. The domain and range of the system function are sets of signals, which themselves
More information540 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 43, NO. 4, APRIL Algorithmic Analysis of Nonlinear Hybrid Systems
540 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 43, NO. 4, APRIL 1998 Algorithmic Analysis of Nonlinear Hybrid Systems Thomas A. Henzinger, Pei-Hsin Ho, Howard Wong-Toi Abstract Hybrid systems are digital
More informationLecture 1: Pragmatic Introduction to Stochastic Differential Equations
Lecture 1: Pragmatic Introduction to Stochastic Differential Equations Simo Särkkä Aalto University, Finland (visiting at Oxford University, UK) November 13, 2013 Simo Särkkä (Aalto) Lecture 1: Pragmatic
More informationHybrid Systems Techniques for Convergence of Solutions to Switching Systems
Hybrid Systems Techniques for Convergence of Solutions to Switching Systems Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel Abstract Invariance principles for hybrid systems are used to derive invariance
More informationNetworking = Plumbing. Queueing Analysis: I. Last Lecture. Lecture Outline. Jeremiah Deng. 29 July 2013
Networking = Plumbing TELE302 Lecture 7 Queueing Analysis: I Jeremiah Deng University of Otago 29 July 2013 Jeremiah Deng (University of Otago) TELE302 Lecture 7 29 July 2013 1 / 33 Lecture Outline Jeremiah
More informationI. D. Landau, A. Karimi: A Course on Adaptive Control Adaptive Control. Part 9: Adaptive Control with Multiple Models and Switching
I. D. Landau, A. Karimi: A Course on Adaptive Control - 5 1 Adaptive Control Part 9: Adaptive Control with Multiple Models and Switching I. D. Landau, A. Karimi: A Course on Adaptive Control - 5 2 Outline
More informationTrajectory tracking & Path-following control
Cooperative Control of Multiple Robotic Vehicles: Theory and Practice Trajectory tracking & Path-following control EECI Graduate School on Control Supélec, Feb. 21-25, 2011 A word about T Tracking and
More informationA Light Weight Rotary Double Pendulum: Maximizing the Domain of Attraction
A Light Weight Rotary Double Pendulum: Maximizing the Domain of Attraction R. W. Brockett* and Hongyi Li* Engineering and Applied Sciences Harvard University Cambridge, MA 38, USA {brockett, hongyi}@hrl.harvard.edu
More informationTimed Automata VINO 2011
Timed Automata VINO 2011 VeriDis Group - LORIA July 18, 2011 Content 1 Introduction 2 Timed Automata 3 Networks of timed automata Motivation Formalism for modeling and verification of real-time systems.
More informationANALYSIS OF ZENO STABILITY IN HYBRID SYSTEMS USING SUM-OF-SQUARES PROGRAMMING CHAITANYA MURTI
ANALYSIS OF ZENO STABILITY IN HYBRID SYSTEMS USING SUM-OF-SQUARES PROGRAMMING BY CHAITANYA MURTI Submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering
More informationReinforcement Learning In Continuous Time and Space
Reinforcement Learning In Continuous Time and Space presentation of paper by Kenji Doya Leszek Rybicki lrybicki@mat.umk.pl 18.07.2008 Leszek Rybicki lrybicki@mat.umk.pl Reinforcement Learning In Continuous
More informationTHE objective of this paper is to synthesize switching. Synthesis of Reactive Switching Protocols from Temporal Logic Specifications
Synthesis of Reactive Switching Protocols from Temporal Logic Specifications Jun Liu, Member, IEEE, Necmiye Ozay, Member, IEEE, Ufuk Topcu, Member, IEEE, and Richard M Murray, Fellow, IEEE Abstract We
More informationRecent results on Timed Systems
Recent results on Timed Systems Time Petri Nets and Timed Automata Béatrice Bérard LAMSADE Université Paris-Dauphine & CNRS berard@lamsade.dauphine.fr Based on joint work with F. Cassez, S. Haddad, D.
More informationc 2011 Kyoung-Dae Kim
c 2011 Kyoung-Dae Kim MIDDLEWARE AND CONTROL OF CYBER-PHYSICAL SYSTEMS: TEMPORAL GUARANTEES AND HYBRID SYSTEM ANALYSIS BY KYOUNG-DAE KIM DISSERTATION Submitted in partial fulfillment of the requirements
More informationCongestion Control. Need to understand: What is congestion? How do we prevent or manage it?
Congestion Control Phenomenon: when too much traffic enters into system, performance degrades excessive traffic can cause congestion Problem: regulate traffic influx such that congestion does not occur
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 informationAutomatic Control 2. Nonlinear systems. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Nonlinear systems Prof. Alberto Bemporad University of Trento Academic year 2010-2011 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 2010-2011 1 / 18
More informationMCE503: Modeling and Simulation of Mechatronic Systems
MCE503: Modeling and Simulation of Mechatronic Systems Lecture 1: Introduction Cleveland State University Mechanical Engineering Hanz Richter, PhD MCE503 p.1/11 What is Mechatronics? Term understood in
More informationZeno Behavior in Electromechanical Hybrid Systems: From Theory to Experimental Validation
Zeno Behavior in Electromechanical Hybrid Systems: From Theory to Experimental Validation Shishir Nadubettu Yadukumar, Bhargav Kothapalli and Aaron D. Ames Abstract This paper studies existence of Zeno
More informationLecture 6: Control Problems and Solutions. CS 344R: Robotics Benjamin Kuipers
Lecture 6: Control Problems and Solutions CS 344R: Robotics Benjamin Kuipers But First, Assignment 1: Followers A follower is a control law where the robot moves forward while keeping some error term small.
More informationThe Discrete EVent System specification (DEVS) formalism
The Discrete EVent System specification (DEVS) formalism Hans Vangheluwe The DEVS formalism was conceived by Zeigler [Zei84a, Zei84b] to provide a rigourous common basis for discrete-event modelling and
More informationEECS 144/244: System Modeling, Analysis, and Optimization
EECS 144/244: System Modeling, Analysis, and Optimization Continuous Systems Lecture: Hybrid Systems Alexandre Donzé University of California, Berkeley April 5, 2013 Alexandre Donzé: EECS 144/244 Hybrid
More informationStochastic Petri Nets. Jonatan Lindén. Modelling SPN GSPN. Performance measures. Almost none of the theory. December 8, 2010
Stochastic Almost none of the theory December 8, 2010 Outline 1 2 Introduction A Petri net (PN) is something like a generalized automata. A Stochastic Petri Net () a stochastic extension to Petri nets,
More informationCALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems
CDS 101 1. Åström and Murray, Exercise 1.3 2. Åström and Murray, Exercise 1.4 3. Åström and Murray, Exercise 2.6, parts (a) and (b) CDS 110a 1. Åström and Murray, Exercise 1.4 2. Åström and Murray, Exercise
More informationDecidability Results for Probabilistic Hybrid Automata
Decidability Results for Probabilistic Hybrid Automata Prof. Dr. Erika Ábrahám Informatik 2 - Theory of Hybrid Systems RWTH Aachen SS09 - Probabilistic hybrid automata 1 / 17 Literatur Jeremy Sproston:
More informationLecture 10: Semi-Markov Type Processes
Lecture 1: Semi-Markov Type Processes 1. Semi-Markov processes (SMP) 1.1 Definition of SMP 1.2 Transition probabilities for SMP 1.3 Hitting times and semi-markov renewal equations 2. Processes with semi-markov
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 informationDiscrete Event Systems Exam
Computer Engineering and Networks Laboratory TEC, NSG, DISCO HS 2016 Prof. L. Thiele, Prof. L. Vanbever, Prof. R. Wattenhofer Discrete Event Systems Exam Friday, 3 rd February 2017, 14:00 16:00. Do not
More informationUnderstanding Deadlock and Livelock Behaviors in Hybrid Control Systems
Understanding Deadlock and Livelock Behaviors in Hybrid Control Systems Alessandro Abate a,d, Alessandro D Innocenzo b,c, Maria Domenica Di Benedetto c, Shankar Sastry d a Department of Aeronautics and
More informationCISC 4090: Theory of Computation Chapter 1 Regular Languages. Section 1.1: Finite Automata. What is a computer? Finite automata
CISC 4090: Theory of Computation Chapter Regular Languages Xiaolan Zhang, adapted from slides by Prof. Werschulz Section.: Finite Automata Fordham University Department of Computer and Information Sciences
More informationModeling & Control of Hybrid Systems. Chapter 7 Model Checking and Timed Automata
Modeling & Control of Hybrid Systems Chapter 7 Model Checking and Timed Automata Overview 1. Introduction 2. Transition systems 3. Bisimulation 4. Timed automata hs check.1 1. Introduction Model checking
More informationReglerteknik, TNG028. Lecture 1. Anna Lombardi
Reglerteknik, TNG028 Lecture 1 Anna Lombardi Today lecture We will try to answer the following questions: What is automatic control? Where can we nd automatic control? Why do we need automatic control?
More informationHybrid Systems: Foundations, advanced topics and applications
This is page i Printer: Opaque this Hybrid Systems: Foundations, advanced topics and applications John Lygeros, Shankar Sastry, and Claire Tomlin(order tbd) February 1, 2012 This material is under copyright
More informationTimed Automata. Chapter Clocks and clock constraints Clock variables and clock constraints
Chapter 10 Timed Automata In the previous chapter, we have discussed a temporal logic where time was a discrete entities. A time unit was one application of the transition relation of an LTS. We could
More informationQueuing Networks: Burke s Theorem, Kleinrock s Approximation, and Jackson s Theorem. Wade Trappe
Queuing Networks: Burke s Theorem, Kleinrock s Approximation, and Jackson s Theorem Wade Trappe Lecture Overview Network of Queues Introduction Queues in Tandem roduct Form Solutions Burke s Theorem What
More informationAppendix A Prototypes Models
Appendix A Prototypes Models This appendix describes the model of the prototypes used in Chap. 3. These mathematical models can also be found in the Student Handout by Quanser. A.1 The QUANSER SRV-02 Setup
More informationIs there Life after Zeno?
Is there Life after Zeno? Taking Executions Past the Breaking (Zeno) Point Aaron D. Ames, Haiyang Zheng, Robert D. Gregg and Shankar Sastry Department of Electrical Engineering and Computer Sciences University
More informationOptimal Control. McGill COMP 765 Oct 3 rd, 2017
Optimal Control McGill COMP 765 Oct 3 rd, 2017 Classical Control Quiz Question 1: Can a PID controller be used to balance an inverted pendulum: A) That starts upright? B) That must be swung-up (perhaps
More informationSwinging-Up and Stabilization Control Based on Natural Frequency for Pendulum Systems
9 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June -, 9 FrC. Swinging-Up and Stabilization Control Based on Natural Frequency for Pendulum Systems Noriko Matsuda, Masaki Izutsu,
More informationWhy Should I Care About. Stochastic Hybrid Systems?
Research Supported by NSF & ARO Why Should I Care About Stochastic Hybrid Systems? João Hespanha 1 Why Care Should I Care About SHSs? Eamples Feedback over shared networks Estimation using remote sensors
More informationThe algorithmic analysis of hybrid system
The algorithmic analysis of hybrid system Authors: R.Alur, C. Courcoubetis etc. Course teacher: Prof. Ugo Buy Xin Li, Huiyong Xiao Nov. 13, 2002 Summary What s a hybrid system? Definition of Hybrid Automaton
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 informationCyber-Physical Systems Modeling and Simulation of Hybrid Systems
Cyber-Physical Systems Modeling and Simulation of Hybrid Systems Matthias Althoff TU München 05. June 2015 Matthias Althoff Modeling and Simulation of Hybrid Systems 05. June 2015 1 / 28 Overview Overview
More informationProbabilistic Model Checking and Strategy Synthesis for Robot Navigation
Probabilistic Model Checking and Strategy Synthesis for Robot Navigation Dave Parker University of Birmingham (joint work with Bruno Lacerda, Nick Hawes) AIMS CDT, Oxford, May 2015 Overview Probabilistic
More informationSynthesizing Switching Logic for Safety and Dwell-Time Requirements
Synthesizing Switching Logic for Safety and Dwell-Time Requirements Susmit Jha UC Berkeley jha@eecs.berkeley.edu Sumit Gulwani Microsoft Research sumitg@microsoft.com Sanjit A. Seshia UC Berkeley sseshia@eecs.berkeley.edu
More informationSwitching Regime Estimation
Switching Regime Estimation Series de Tiempo BIrkbeck March 2013 Martin Sola (FE) Markov Switching models 01/13 1 / 52 The economy (the time series) often behaves very different in periods such as booms
More informationClass 11 Non-Parametric Models of a Service System; GI/GI/1, GI/GI/n: Exact & Approximate Analysis.
Service Engineering Class 11 Non-Parametric Models of a Service System; GI/GI/1, GI/GI/n: Exact & Approximate Analysis. G/G/1 Queue: Virtual Waiting Time (Unfinished Work). GI/GI/1: Lindley s Equations
More informationThe Transition Probability Function P ij (t)
The Transition Probability Function P ij (t) Consider a continuous time Markov chain {X(t), t 0}. We are interested in the probability that in t time units the process will be in state j, given that it
More informationReachability Analysis for Hybrid Dynamic Systems*
Reachability nalysis for Hybrid Dynamic Systems* Olaf Stursberg Faculty of Electrical Engineering and Information Technology Technische Universität München * Thanks to: Matthias lthoff, Edmund M. Clarke,
More informationCSE 311 Lecture 23: Finite State Machines. Emina Torlak and Kevin Zatloukal
CSE 3 Lecture 3: Finite State Machines Emina Torlak and Kevin Zatloukal Topics Finite state machines (FSMs) Definition and examples. Finite state machines with output Definition and examples. Finite state
More informationQueueing Theory I Summary! Little s Law! Queueing System Notation! Stationary Analysis of Elementary Queueing Systems " M/M/1 " M/M/m " M/M/1/K "
Queueing Theory I Summary Little s Law Queueing System Notation Stationary Analysis of Elementary Queueing Systems " M/M/1 " M/M/m " M/M/1/K " Little s Law a(t): the process that counts the number of arrivals
More informationA Novel Integral-Based Event Triggering Control for Linear Time-Invariant Systems
53rd IEEE Conference on Decision and Control December 15-17, 2014. Los Angeles, California, USA A Novel Integral-Based Event Triggering Control for Linear Time-Invariant Systems Seyed Hossein Mousavi 1,
More information