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Intro To Graduate Research

by: Cassidy Casper

Intro To Graduate Research ECE 69500

Cassidy Casper
GPA 3.59

Jianghai Hu

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Jianghai Hu
Class Notes
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This 10 page Class Notes was uploaded by Cassidy Casper on Saturday September 19, 2015. The Class Notes belongs to ECE 69500 at Purdue University taught by Jianghai Hu in Fall. Since its upload, it has received 47 views. For similar materials see /class/207896/ece-69500-purdue-university in Electrical Engineering & Computer Science at Purdue University.

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Date Created: 09/19/15
AAE 6908 amp ECE 695A Hybrid Systems Theory and Applications Inseok Hwang Aeronautics and Astronautics Engineering Jianghai Hu Electrical and Computer Engineering Course Content Hybrid systems dynamical systems with interacting continuoustime and discretetime dynamics Their modeling analysis control and simulation Continuous and discrete system models Reachability analysis Stabilityanalysis Optimal control and differential games Estimation and identification Engineering applications Advancedtopics Course website l httpdynamoecnpurdueedujianghaiECE695A l Syllabus Lecture notes homework and solutions Software tools Literature on hybrid systems Related courses from other universities Course Organization See the handout sheet for detailed information Grading based on HW 15 and course project 85 Project proposal due Wed March 5 Project report due the final exam week 15 minute presentation Some ideas of project choices Investigation of a special class of hybrid systems Nontrivial application of hybrid systems on a practical problem in your own research area Literature review on a topics of HS not covered in the class Why Hybrid Systems Hybrid systems are everywhere Example Bouncing Ball When in the airygt0 Dynamics jj 79 11 1 9 2 l IL39 State equation 1 2 After collision y0 171 y 0 remains unchanged 2 lt 0 becomes in 2 gt O c E 0 1 is the coefficient of restitution Example Bouncing Ball cont jumping condition tranSition guard 10 2 lt 0 reset condition ca2 In the air time Infinite number of transitions in finite time Zeno hybrid systems Example Thermostat Room temperature x is controlled by switching a heater on and off 0 Goal regulate x at around 75 degree 0 Strategy Turn on the heater when X is below 70 degree Li 100 L39 x gt 100 Turn off the heater when X is above 80 degree d a a gt 0 Example Thermostat cont trivial reset I I L Heater off Heater 0 jjz gy i100 a continuousstate 75 110t E R 70 V discrete state 10 E Of70quot on Example Autopilot hbody hKVind h inertial 391 7quot body 39 in Xwind 9 X inertial Jr 7 7 7D 111 0 iwi L H0 irru Input thrust u1T pitch u29 lift L drag D Fiveflight modes Yz ght path angle q1 Speed Flight Path or angle of attack 39 Q23 Speecj qs Flight Path q4 Speed Altitude q5 Altitude See The Art onybrid Systems by J Lygeros C Tomlin Shankar Sastry for details Example Aircraft Conflict Resolution To avoid conflict each aircraft has several flying modes Protocolbased maneuvers for conflict resolution Identification and estimation from radar data Piper Dakota Example Supervisory Control Controller bank decide which controller to use Supervisor Controller 1 O O O Controllern System under control o Continuous variables u y and internal state of the system under control Discrete variables id of the controller chosen Example Portable Electronics Portable Digital Assistant PDA streaming Network Display mee az e from Internet Buffer 1 Buffer 2 Goal to save power consumption ofthe PDA Two data buffers inserted Control strategy Power off on network card if buffer 1 is full empty Power off decoder if buffer 1 is empty or if buffer 2 is full Hybrid system model Continuous variables amounts of data in the two buffers Discrete variables power states of the two buffers 4 possible values Design problem optimal buffer sizes that minimizes overall power Biological Systems B subtilis cell promotor Continuous state concentrations of proteins Proteins are transformed from RNAs protein RNA Rates of production are regulated by promotor via switches on the genetic network 1 4903 mature sublilin Hybrid Systems Overview In all these examples the systems under study have Continuous state governed by controlled differential equations Discrete state governed by some switching jumping strategies Continuous and discrete dynamics are coupled Evolution of the continuous state depends on the discrete state When and where the discrete state jumps may depend on the continuous state Hybrid Systems Overview Control Theory Compute Science Continuous dynamic Discrete dynamic systems ODE PDE Automata Hybnd SYStems Transition systems Stability Controllability Observability Decidability Complexity Aspects of Hybrid Systems Reachability Answers questions such as Starting from some initial position will the system state enter a forbidden part of the state space If it is possible to find a control so that the system state always remain inside the safe set no matterwhat the disturbances Aspects of Hybrid Systems Stability Answers questions such as Will the system state stay close to a certain point eventually Find the control law and switching strategy stabilizing the system Aspects of Hybrid Systems Optimality Answers questions such as Find the least costly way to get from point A to point B Refraction Aspects of Hybrid Systems Simulation mmmnrivlScW rm moduli m ymmcn cl n mu wing in a amvlannnai m1 WKIaquot Ptolemy a so ware tool developed by Prof Edward Lee at UC Berekely


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