Lecture 4.Applications

Summary

Tools such as HyTech, CheckMate, Uppaal, Kronos have been used in many contextstypically to verify safety of a control design or to get tight bounds on parameters (e.g. steam boiler, audio control)

This lecture shows where hybrid systems theory can fit in some application domains

Applications Outline

! Embedded Control Systems" Autonomous Mobile Robots" Biological Systems

Embedded Controller Development ProcessFor Automobile Transmissions

test on engine/vehicle

feature specification

code

production

Former Practice• describe control logic using

relay-ladder diagrams

• write assembly code for the control microprocessor

• drive the car around the test track

• fix bugs

• redesign

• hope for the best

Automotive Embedded Controller Design: State of the Practice

test on engine/vehicle

feature specification

code

production

executable spec.

code generation

simulation

hardware in the loop

executable spec.

Computer-Aided Control System Design

Executable Specifications Using MATLAB/Simulink/Stateflow

Transmission Control Logic

Opportunity to Apply Formal Verification Techniques

test on engine/vehicle

feature specification

code

production

executable spec.

code generation

simulation

hardware in the loop

executable spec.

Computer-Aided Control System Design

model checking

Objective:Verify feature behavior for the entire range of operating conditions.

Automotive Engine Control in Cut-off Mode

Application of CheckMate due to Krogh et al

Control law: Decide when to inject air/fuel for torque to minimize acceleration peaks during the cut-off operation.

Problem: Verify the event-driven implementation of a control law designed in continuous time.

Automotive Powertrain Model

Model from Magneti Marelli Engine Control Division

• Four-stroke, four cylinder engine

• Continuous-time powertrain model

• Hybrid model for cylinder cycles

x2

x1 v x2

x1

torque

start

simula

simula

C*x <= d

reach_zero

C*x <= d

reach_180

h000

h001

h010

h011

h100

h101

h110

h111

q

predictor

NOT

not2

NOT

not1

C*x <= d

h111

C*x <= d

h110

C*x <= d

h101

C*x <= d

h100

C*x <= d

h011

C*x <= d

h010

C*x <= d

h001

C*x <= d

h000

C*x <= d

finish_line

drivel ine

XORangle_trigger

angle (degrees)

q

angle

NOTNOT

u

M4

Mux M3

u

M2

MuxM1m

Demux

CheckMate Model

power traindynamics

Continuous Dynamics

x = Ax + Bu u = 0 (no air-fuel) or 10

x1 = engine block anglex2 = wheel revolution speed (radians)x3 = axle torsion angle (in radians)x4 = crankshaft revolution speed (rpm)x5 = crankshaft angle (degrees)

Controller Specification

Remain within acceleration

limits while tracking a sliding mode.

• Sliding mode control law derived in continuous time• Hybrid implementation due to discrete torque decisions

Cylinder Cycle

Phase_change

Phase_change

Phase_changePhase_change

Compression

Exhaust Intake

Combustion

Control decision to apply torque on the power stroke must be madebefore the intake stroke ⇒ three step lookahead.

x2

x1 v x2

x1

torque

start

simula

simula

C*x <= d

reach_zero

C*x <= d

reach_180

h000

h001

h010

h011

h100

h101

h110

h111

q

predictor

NOT

not2

NOT

not1

C*x <= d

h111

C*x <= d

h110

C*x <= d

h101

C*x <= d

h100

C*x <= d

h011

C*x <= d

h010

C*x <= d

h001

C*x <= d

h000

C*x <= d

finish_line

driveline

XORangle_trigger

angle (degrees)

q

angle

NOTNOT

u

M4

Mux M3

u

M2

MuxM1m

Demux

Crankshaft Angle Rate Logic

Cylinder state transitions occur every 180o. Crankshaft angle switches between 0o and 180o, angle rate switches between +rate and -rate.

Predictive Control Logic

The discrete state indicates the torquedecisions for the current and next twopower strokes (i.e., for three of thefour cylinders).

Transitions from each state dependon whether predicted state for thenext power stroke is closer to thesliding mode with or without torque.

The 9th state (not shown) is the “end simulation” state--reachable from any of the other 8 states.

Flowpipe for One Discrete Sequence

Applications Outline

# Embedded Control Systems! Autonomous Mobile Robots" Biological Systems

Programming Interacting Autonomous Robots

Many modesIndividual modes are well understood, but not their interaction.

Software designModes designed bottom-upProtocols top-down

Modular design to ensure reusability

Tasks: Formation control, cooperative control

Software Design MethodologyCHARON Code

(High level language)

Java Code

CHARON to Java TranslatorCHARON to Java Translator

Control Code GeneratorControl Code Generator

Java Libraries

Human InterfaceHuman Interface

Simulator Code GeneratorSimulator Code Generator

Drivers

Vision-Based Control: Mode Switching

Motion Controller

Reactive Vision Based Controllers

Frame Grabber Actuators

AvoidObstacle

CollisionRecovery

EdgeDetector

CollisionDetector

Color BlobFinder

Robot PositionEstimator

TargetDetector

Range Mapper

Wall-Following

Control

Controllers for Maintaining Formation

X

Y

d

(x2,y2,θ2)

(x1,y1,θ1)l12

v1, ω1

ψ12

v2, ω2

X

Y

d

(x2,y2,θ2)

(x1,y1,θ1)l12

v1, ω1

(x3,y3,θ3)

l23v2, ω2

v3, ω3

• Estimate of relative position, orientation, linear and angular velocities required! )]ˆsin()ˆ(cossin[1

)ˆcos(ˆ)ˆ(sincos

jiiiijijijijijj

j

jiiiijijijijijj

vblsd

vblsv

θ−θ+ω+γ+γ=ω

θ−θ+ω+γ−γ=

Multirobot Coordination

R1

R2

R3

R1

R2R3

Rules for Mode Switching

R2

R1

R3

l12

l13

l23

l12l23

r1 r2

r1

r2

l13

AutonomousNavigation

l-ψψψψ13

l-ψψψψ23

l12 l- l

l13 = l23

l13 = l23 + l12

l13 = l23 - l12

l12 =l13 + l23

R

r2

r1

Sensor constraints

Leader Follower and Obstacle Avoidance

Leader is teleoperated Leader is autonomous

Obs

R1

R2 l12

lO2R2 R1

(l12,,ψ12 )

Mode Switching and Maintain Formation

Applications Outline

# Embedded Control Systems# Autonomous Mobile Robots! Biological Systems

Cellular Networks

"Networks of interacting biomolecules carry out many essential functions in living cells (gene regulation, protein production)

"Both positive and negative feedback loops"Design principles poorly understood "Large amounts of data is becoming available"Beyond Human Genome: Behavioral models of

cellular networks"Modeling becoming increasingly relevant as an

aid to narrow the space of experiments

Regulatory Networks

cell-to-cellsignaling

START STOPgene

transcriptiontranslation

regulation

nascentprotein

chemicalreaction

+

-

negative

positive

gene expression

Hybrid Modeling of Biological Systems

START STOPluxR gene

transcriptiontranslation

regulation

proteinLuxR

chemicalreaction

-+

negative

positive

Ai

Ai

CRP

Traditionally, biological systems are modeled using smooth functions.

Xmκ

Xmν

X

),,X( XmXm νκΦ

10.5

2swX1

swX

transporttransformdecaysynthesisdt

]x[d ±±−=

luxRkHluxR

)b)),,AiLuxR(1(

),,CRP([Tdt

)luxR(d

GRNA

AiLuxRAiLuxR

CRPCRPc

−−

+−−

=

−− νκΦ

νκΦ

LuxRkCorLuxRAir

HLuxRluxRT

dt)LuxR(d

Gdb

spl

Ai/LuxRAi/LuxR−+−

−−=

Hybrid ModelingAt low concentrations, a continuous approximation model might not be appropriate. Instead, a stochastic model should be used.

stochastic modellow conc

continuous modelhigh conc

In some cases, the biological description of a system is itself hybrid.

Essentiallyhybrid systemDiscrete jump

(mRNA)

Nonlinear dynamics(proteins involved in chemical reactions)

Linear dynamics(proteins not involvedin chemical reactions)

moderegulatoryprotein/complex

Luminescence / Quorum Sensingin Vibrio Fischeri

Luminescence Regulation

CRP

luxICDABEGluxR

Ai

LuxA

LuxB

luciferase

LuxI

Substrate

LuxR

lux box

CRP binding siteLuxR Ai

OL OR

-

+-

+ cAMP

Reachability

)Co(x 8

)Ai(x7

)L I(

switching surface

lum dynamics

nonlum dynamics

sw88 xx =

10bAxx +=&

sw88 xx ≥

lum

00bAxx +=&

sw88 xx ≤

non-lum

sw88 xx =

Under what conditionscan the bacterium switch on the light?

sw8x

0ibAxx +=&

=

8

7

4

xxx

x

+=

00

)bc(TTHb

iclRNA

0i

1c,0c 10 ==

Simulation Results

external Ai(input)

concentrationsfor various

entities

luminesence(output)

switchhistory

switchhistory

Summary

$ Hybrid systems are necessary to model some biological regulatory networks.

$ The simulation results of the luminescence control in Vibriofischeri are in accordance with phenomena observed in experiments.

$ Modeling concepts such as hierarchy, concurrency, reuse, are relevant for modular specifications

$ Exploiting the structure of real biological systems will be essential to meet the challenge posed by the enormous complexity of biological regulatory networks.

Conclusions

" A rich variety of domains match hybrid systems paradigm

" Traditional benefits: safety verification, design of hybrid controllers

" Formal models can be beneficial in more ways: modeling, understanding, programming, simulation

" Emerging potential for integration with software engineering design tools