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Self-* Programming: Run-Time Parallel Control Search for Reflection Box. Olga Brukman and Shlomi Dolev Ben-Gurion University of the Negev Israel. Problem. Ideally Systems should anticipate every possible scenario Reality Engineers fail to create such systems despite the effort

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self programming run time parallel control search for reflection box

Self-* Programming: Run-Time Parallel Control Search for Reflection Box

Olga Brukman and Shlomi Dolev

Ben-Gurion University of the Negev

Israel

problem
Problem
  • Ideally
    • Systems should anticipate every possible scenario
  • Reality
    • Engineers fail to create such systems despite the effort
    • The number of possibilities of different interactions with dynamic environment is enormous
    • Relying on accumulated knowledge of human operator to deal with unexpected situations
example 1
Example 1
  • Airplane flying into ash cloud
    • Engines stopped
    • Pilots managed to fly the plane out of the cloud, waited till the engines cooled down, and were able to restart them
example 2
Example 2
  • Airplane crossing the speed of sound
    • Airplane control handles behave opposite to the expected behavior
    • Pilots increase the plane speed so it becomes higher than speed of sound, plane control is back to normal
our contribution automatic control search engine for dynamic environment
Our Contribution:Automatic Control Search Engine for Dynamic Environment
  • No assumptions on possible environment changes
  • Experimentation on replicas
  • Parallelization of experiments
  • Polynomial search time
    • Parallelization
    • Exposing system state
      • Observing system state (e.g., with Java reflection)
      • Setting system state to a certain state
system settings environment
System Settings: Environment
  • Environment is large, sophisticated, dynamic
    • Non deterministic infinite automaton
    • At every given time slot environment is
        • deterministic automaton
        • probabilistic automaton with a transition function Fi
  • Environment
    • Non-deterministic infinite automaton
  • Environment
    • DA/PA(F1)
  • Environment
    • DA/PA(F2)
  • Environment
    • DA/PA(F3)

t

t

system settings environment vs plant
System Settings: Environment vs. Plant

System

Environment

Environment

in’1…...., in’m

out’1,……,out’n

Plant

Control

in1,.., ink

Plant

out1, …,outl

Our program (control) interacts with some machinery in environment – plant

system settings environment and plant
System Settings: Environment and Plant

System

  • Environment is
    • Reentrant : no mutual replicas interference
    • History oblivious: deterministic repetition of behavior for the plants in the same initial state and with the same control

Environment

in’’1...., in’’m

in’1...., in’m

in’1….., in’m

out’1,……,out’n

out’’1,……,out’’n

out’1,……,out’n

Plant

Plant

Plant

Control1

Control1

Control2

slide9

System

Environment

in’1…...., in’m

out’1,……,out’n

Plant

|AP|=N ≤Nmax

Control

in1,.., ink

out1, …,outl

Recording

plant-environment

interaction

Control Search Engine

Observer

bhv={io1,…,ioj}

Goals=

Behaviors

Control

Generator

plant-environment

interaction

settings periodic control
Settings:PeriodicControl

bhv={io2, io3 , io4}, io2, io3 , io4

C={in1(in2, in3, in4)*}

+

Plant

automaton

=

P=3

in2

io2

in3

in1

io3

io1

in4

io4

algorithm i black box
Algorithm I: black-box
  • Complexity
    • Total number steps in experiments:
    • Longest experiment: O(PNmax)

C1

s

C2

x∙P

sstart

s

s

P(Nmax +1)

CM

scurr

s

sP_1

sP_2

sP_3

sP_N_max+1

scurr

P

0<i≤Nmax

P

algorithm iv reflection set box
Algorithm IV: reflection-set box

sN

s1

….

σΣ

σΣ

σ1

σ1

...

...

σ2

σ2

Ap

  • Off line search of the constructed plant automaton
    • Try all controls of form from every state
  • Complexity
    • Total number of steps in experiments:
    • Longest experiment: O(1)
probabilistic environment
Probabilistic Environment
  • Plant is unaware of the entire state of the environment
    • Environment can be considered to be probabilistic automaton
    • Plant transition function is probabilistic
  • Control search algorithm executes all the time
    • Due to probabilistic transition function of plant automaton
  • Monitoring
    • Recognize changes in the plant probabilistic transition function
probabilistic plant automaton
Probabilistic Plant Automaton
  • 0≤pr(s, s’, σ, io) ≤ 1
  • prmin– minimal probability

σ1, io1,1, pr1,1

sj

si

σ1, io1,2 ,pr1,2

σm, iom,1 ,prm,1

σm, iom,2 ,prm,2

computing probabilistic plant automata graph ppag
Computing Probabilistic Plant Automata Graph (PPAG)

σ

sj?

si

io?

SF times

PPAG[si,sj,σ,io]=pr

  • SF=1/prmin: number of experiments required to discover the edges with the smallest probability
preprocessing behavior suffix probability bsp table
Preprocessing: Behavior Suffix Probability (BSP) Table
  • For every state s and j=1,…,|bhv|:
    • BSP[si ,j] = [prmax, σ]
      • prmax is the maximal probability to obtain suffix (bhv,j) starting from plant in state si ;

σis the first entry in this control

  • BSP computed from PPAG

pr1

prmax

si

σ

pr2

pr3

j

preprocessing behavior suffix probability bsp table cont
Preprocessing: Behavior Suffix Probability (BSP) Table Cont.
  • Base step: for every si compute BSP[si,1]
    • For every si find input σ that produces bhv[k] with the highest probability : max{PPAG[si, *, σ,bhv[k]]}

pr1

σ1 (io1)

σ(bhv[k])

prmax

si

σ2 (io2)

pr2

σ3(io3)

pr3

1

preprocessing behavior suffix probability bsp table cont1
Preprocessing: Behavior Suffix Probability (BSP) Table Cont.
  • Assume we computed all entries BSP[si ,j] for every si and j≤m
  • BSP[si , (m+1)]?
    • Let σbe the one that yields the largest value of
      • Σs_j (PPAG[si,sj,σ,bhv[k-m-1]]∙BSP[s,m].pr)
    • BSP[si, m+1]=[Σs_j (PPAG[si,s, σ,bhv[k-m-1]]∙BSP[s,m].pr), σ]

s,s’,s’’,…

pr1= Σs_j (PPAG[si,sj,σ1,bhv[k-m-1]].pr∙BSP[sj,m].pr)

σ1 (bhv[k-m-1])

s,s’,s’’,..

σ(bhv[k-m-1])

prmax=Σs_j (PPAG[si,sj, σ,bhv[k-m-1]]∙BSP[sj ,m].pr)

si

σ2 (bhv[k-m-1])

s,s’,s’’,..

pr2= Σs_j (PPAG[si,sj,σ2,bhv[k-m-1]].pr∙BSP[sj,m].pr)

σ3 (bhv[k-m-1])

s,s’,s’’,…

pr3= Σs_j (PPAG[si,sj,σ3,bhv[k-m-1]].pr∙BSP[sj,m].pr)

1

algorithm v reflection set box
Algorithm V: reflection-set box

sstart=max{BSP[s,|bhv|].pr}

BSP[sstart,k].σ

BSP[snext,k-1]>BSP[sstart,k]

snext

pr=0.4

sstart

pr=0.6

snext

BSP[snext,k-1]<BSP[sstart,k]

algorithm vi reflection box
Algorithm VI: reflection box

sbest=max{BSP[s,k].pr}

BSP[sstart,k].σ

BSP[snext,k-1]>BSP[sstart,k]

snext

pr=0.7

sbest

sstart

pr=0.3

snext

BSP[snext,k-1]<BSP[sstart,k]

s’best=max{BSP[s,k].pr}

conclusions
Conclusions
  • Framework for automatic control search
  • Control, plant, environment
    • Deterministic plant
    • Probabilistic plant
  • Polynomial time
    • Parallelization
    • Exposing plant state