Download presentation

Presentation is loading. Please wait.

Published byJunior Lang Modified about 1 year ago

1
Aditya Zutshi Sriram Sankaranarayanan Ashish Tiwari TIMED RELATIONAL ABSTRACTIONS FOR SAMPLED DATA CONTROL SYSTEMS

2
SAMPLED DATA CONTROL SYSTEMS

3
CONTROL SYSTEMS

4

5
SAMPLED CONTROL SYSTEMS Discrete Controller compute wait Ts actuatesense Plant: hybrid system Hybrid Plant M2 ODE2 M1 ODE1 M3 ODE3 Controller: software

6
System speed time SAMPLED CONTROL SYSTEMS Discrete Controller Physical Plant SA Desired Speed

7
System speed time SAMPLED CONTROL SYSTEMS Discrete Controller Physical Plant SA uphill!

8
PLANT – HYBRID AUTOMATON Down shift Up shift

9
RELATIONALIZATION Discrete System [Discrete Transition System] Physical System [Hybrid Automaton] Actuate (Ts) Sense (Ts) Abstract the plant dynamics using relations

10
RELATIONALIZATION Discrete System [Discrete Transition System] Physical System [Hybrid Automaton] Actuate (Ts) Sense (Ts)

11
RELATIONALIZATION Discrete System [Discrete Transition System] Actuate (Ts) Sense (Ts) ODE 1 ODE 2

12
RELATIONALIZATION Discrete System [Discrete Transition System] Actuate (Ts) Sense (Ts) R1R1 R2R2

13
RELATIONALIZATION Discrete System [Discrete Transition System] Physical System [Discrete Transition System] Actuate (Ts) Sense (Ts) Use existing tools to verify safety properties

14
TIMED RELATIONAL ABSTRACTIONS Plant state time Plant Dynamics

15
TIMED RELATIONAL ABSTRACTIONS Plant state time System Dynamics

16
TIMED RELATIONAL ABSTRACTIONS Plant state time Relational Abstraction R R R

17
TIMED RELATIONAL ABSTRACTIONS Relation R Captures states reachable in one sampling period Resulting abstraction is equivalent: when only controlled transitions are present sound: when autonomous transitions are present Plant state time R R R

18
CONTROLLED TRANSITIONS Relationalize

19
AUTONOMOUS TRANSITIONS

20
time m1 ODE1 Controlled Transitions m1 ODE1 m2 ODE2 Autonomous Transitions M1 ODE1 M2 ODE2 M5 ODE5 M3 ODE3 M4 ODE4 Dwell Time Restriction

21
AUTONOMOUS TRANSITIONS time m1 ODE1 Controlled Transitions m1 ODE1 m2 ODE2 Autonomous Transitions

22
The resulting abstraction is a quantified formula over exponentials. AUTONOMOUS TRANSITIONS Relationalize

23
Solution Using interval arithmetic rewrite the formula as a Interval linear inequalities Reformulate as a Linear Complementarity Problem Linearize the dynamics around the midpoint and iteratively find the bounds AUTONOMOUS TRANSITIONS

24
IMPLEMENTATION

25
Experiments: NAV and Heat benchmark set [Ivancic + Fehnker] Benchmarks formulated in the paper Results: Promising for systems with many controlled transitions + few autonomous transitions Precision loss as number of autonomous transition increases Our Approach: Is sound Provides proofs when the property is inductive Is exact for controlled transitions EXPERIMENTAL RESULTS

26

27
QUESTIONS?

28

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google