Download presentation

Presentation is loading. Please wait.

Published byGuy Dickman Modified over 3 years ago

1
Dr. Vered Gafni 1 Modeling Real-Time Systems

2
Dr. Vered Gafni 2 Behavioral Model (Signature, Time) Signature: v 1 :D 1, v 2 :D 2,…,v n :D n S = (D 1 … D n ) (states’ space) Time: (T, , 0) Behavior: : T S Discrete, Continuous

3
Dr. Vered Gafni 3 Signature: E - a finite set of events (env. & reactions) Time domain: T={ (R + ) | (t 0 t 1 t 2 …): (a)t 0 =0, t i t i+1, i=0,1,… (b) t R +. i. t t i } Timed trace over (E,T) is an -sequence: T = ( 0,t 0 ) ( 1,t 1 ) ( 2,t 2 ) … where: i 2 E, (t 0 t 1 t 2 …) T Controller Behavioral Model: Timed Traces Controller – a set of timed traces over E and T. finite variability, non-Zenon t0t0 t1t1 t2t2 00 11 22 Event – Instantaneous occurrence

4
Dr. Vered Gafni 4 Environment events Model : {P 1, P 2,…P N } where P i : {R + D i }, i=1..N Event – Boolean relation on P i becomes true/false. E.g., = def tr( p j K) then occur( ) = {t | p j (t) K becomes true}. Environment & Controller Events non-Zenon Controller events Model – a set of (parallel) tasks (transition systems) over a set of variables Event –Assignment of a certain variable (write memory location). TempHigh = def tr( Temp 30 )

5
Process properties: TrainLocation : {0..100}Km GatePosition : (0-90) SemaphoreState : {pass, stop} Process events: Tin = def tr(TrainLocation=x I ) Tout = def tr(TrainLocation=x O ) Close! = def tr(GatePosition=0°) Open! = def tr(GatePosition=90°) Example: Railroad Crossing Controller actions: close = def GatePort:=1 open = def GatePort:=0 pass = def LightsPort:=1 stop = def LightsPort:=0 xIxI xOxO 5 E={ T in, T out, close, close!, open, open!, stop, pass }

6
Dr. Vered Gafni 6 General reactive software: controller comprises a set of (concurrent) tasks. reactive behavior of a task concerns: initiation, synchronization, termination. About Controller Computations & Events Computations: Asynchronous – take observable duration (initiation

7
Dr. Vered Gafni 7 Synchronous/Asynchronous Computations Formally, synchronous computation = executed in zero time, In practice, it is sufficient that the computation terminates before next environment event. Sequence of sync. computations is a sync. In practice, only finite sequences that respect “next event” rule. Finally, only the synchronous trace is of interest.

8
Dr. Vered Gafni 8 System behavior: –Time step – time advances + an event set. –Reaction step – time freezes but new event set. A trace always starts with: ( , 0) A reaction step may follow only trace elements: ( , t) Super step – a sequence of reaction-steps (triggered actions) that follow a time step until stabilization ( = ). Thus, a trace looks like: … ( ,2.0) ({p,q},3.1) ({r},3.1) ( ,3.1) ({q,r},3.8) … Synchronous trace time step reaction step time step super step

9
Dr. Vered Gafni 9 Activation by occurrence of events (may occur simultaneously) t`tt`` {E 2 }{E 1 }{E 1, E 2, E 3 } In practice, observations are taken w.r.t. to a finite precision clock, hence Discrete time (modeled by N), Nearby events may get same time record, still order is preserved. … ({p,q},53) ({r},53) ({u,w},62) … So far: Event Driven Traces

10
Dr. Vered Gafni 10 Global clock activation signature includes periodic event ‘tick’. Events during (t i-1,t i ] considered at t i (order/repetition are lost). titi t i-1 t i+1 t i+2 E2E2 E3E3 E1E1 {E 1, E 2, E 3 } Time model N, but time-tag coincidences with index, hence represented by un-timed traces: 0 1 2 … where i 2 E + ‘tick’ duration, Note: k may consist of the event ‘tick’ solely. Clock Driven Execution Model

11
Dr. Vered Gafni 11 Asynchronous Computation in Clock Driven Model

12
In practice …. 12 Clock driven synchronous model, hence traces are untimed (time given by index) Clock + Event driven synchronous model, but external events are tagged with last RTC

13
Dr. Vered Gafni 13 Hybrid Systems: continuous properties If 'pass' is accepted within 1 sec. then the speed remains steady till it exits the crossing. If 'pass' has not been accepted within 1 second then the train starts slowing down at a rate of 5m/s until 'pass' signal is accepted or otherwise until its speed zeroes. When the expected pass signal is accepted, the train accelerates again to 20m/s.

14
Dr. Vered Gafni 14 Hybrid Systems: Time model & Variables Time model: T=[0, ) - non-negative continuous (physical) time Variables Piecewise continuous (pwc) Continuous range Discrete range Events Non Zeno

15
Dr. Vered Gafni 15 Hybrid models V = V d V c (disjoint sets), S=D V (states, D unified domain) E – set of events, =2 E flow={ | : R D Vc } s.t.: = (t) is defined on interval [0,t ] or [0,t ), where t >0. = (t,v) is differentiable on (0,t ) and lim t t (t,v) D Vc trace: w 1 w 2 … s.t.: k either: w k =((s k-1,t),,(s k,t)) -- , s k-1,s k S, t R or: w k =((s k-1,t), ,(s k, t’)) -- s k-1,s k S, t,t’ R , flow s.t.: s d k-1 =s d k, t’ t t

Similar presentations

OK

SATEL Semi Automatic TEsting Language University of Geneva Levi Lúcio VALID Meeting - Besançon 10/3/06.

SATEL Semi Automatic TEsting Language University of Geneva Levi Lúcio VALID Meeting - Besançon 10/3/06.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download ppt on pulse code modulation Ppt on sports awards in india Ppt on disk formatting in windows Ppt on international tourism in india Convert doc file to ppt online form Ppt on overview of financial services in india Ppt on mauryan art Ppt on revolt of 1857 india Ppt on good leadership Sample ppt on personality test