On the Robust Capability of Feedback Scheduling in ORB Middleware

1
On the Robust Capability of Feedback Scheduling
in ORB Middleware

• Bing Du
  David.C. Levy
• School of Electrical and Information
  Engineering University of Sydney

The University of Sydney
2
Outline of presentation

• Introduction.
• H8control scheduling Architecture.
• H8 robust controller and H8-NMPC controller.
• Overview of hORB Architecture
• Conclusion

3
Introduction

• Traditional scheduling are no longer promise the
  function and performance requirements of DRE
  systems.
• The common ORB middleware scheduling approaches
  cant provide real-time performance guarantees
  because they depend on accurate task execution
  times.

4
Introduction

• Many recent scheduling research approaches have
  applied feedback control theory, but little
  theoretical analysis has been provided about
  effects of the plant uncertainty and nonlinearity
  on the desired system performance.
• H8-nonlinear model predictive control scheduling
  (H8-NMPC) is provided an excellent theoretical
  framework for dealing with nonlinear stability
  and robustness issues by H8 theory.

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H8 control scheduling Architecture

• Task model
  
  U e / d r.
• Requested CPU utilization U ,release time r ,
  execution time e , deadline d
• The performance can be interpreted as a
  quality-of-service (QoS) measure. The system will
  control the rate of deadline misses by regulating
  the QoS of the task.

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H8 control scheduling Architecture

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H8 robust controller

• The physical process is a nonlinear model and can
  be treated in continuous time, with continuous
  signals, while the controller is a discrete time
  algorithm
• Tustin transform to transform continuous systems
  into discrete systems and back again
• S 2(z-1) / T(z1)

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Generalized nonlinear discrete-time H8 system
P is an LTI system f(q) is a static
nonlinearity and ? is a block structured, norm
bounded perturbation
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H8 robust controller

• Transfer function from w to e
• e Fl F u ( P ( s ), ? ), K ( s ) w G (
  s ) w
• satisfies a norm objective
• The problem is to design K(s) such that for all ?
  ? B?, K (s) stabilizes Fu(P(s), ?), and
• F u ( F l( P (s), K (s) ), ? ? 1.
• This is equivalent to K (s) satisfying
• µ Fl ( P ( s ) K ( s ) )lt1

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H8-NMPC controller

• Based on the derivation of a stationary
  Hamilton-Jacobi-Isaacs equation, which is the
  nonlinear analogous of the FHARE (fake H8
  algebraic Riccati equation), it is shown that the
  H8 NMPC control law is the solution of an
  associated infinite horizon H8 control problem,

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H8-NMPC controller

• a class of systems described by the following
  nonlinear set of differential equations
• (t) f ((t), u (t)), (0)
• where (t) and u (t) denotes the vector of
  states and inputs, respectively.

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H8-NMPC controller

• The finite horizon open-loop problem described
  above is mathematically formulated as follows
• find min J ((t), u () Tc, Tp)
• u ()
• with J ( x (t), u () Tc, Tp)
• where Tc and Tp denotes control horizon and
  prediction horizon, and u () denotes the
  internal input.

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Generalized and weighted performance block
diagram
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DK iteration

• The current approach to design a controller is
  known as DK iteration .
• Suppose that K(s) stabilizes P (s) and
• F(P (s) K(s)) ? 1
• This is an upper bound for the µ problem,
  implying that, 
• µF(P (s) K(s)) 1
• The µsynthesis problem can be replaced with
  the following approximation
• inf DF(P (s) K(s))D?¹
• D? Ð
• K(s) stabilizing

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Two tank system model to emulate a scheduling
system

• Design a controller that regulates the levels in
  tank2, h2.
• The task actuator controls the flow into the
  system. The tasks that adds the height of liquid
  tank 2 not higher than 100 cm can be admitted.
  QoS actuator can adjust the tank 2 liquid higher
  or lower so that the level keeps at 100 cm. The
  deadlines of accepted tasks can be achieved by
  EDF if the height of liquid tank 2 is below 100
  cm.

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Two tank system model of scheduling system
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Tracking simulation
perturbed system with 10 change. The inputs
are constrained to remain within 25-75
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Overview of hORB Architecture

• This framework is based on AMIDST 21 and
  deploys the advanced control theory mechanisms to
  provide deadline miss ratio and utilization
  guarantees and to adapt execution environment to
  variation in the resource availability.
• The H8-NMPC/connection threads on the server are
  connected with each client connection thread
  through a TCP connection called feedback lane.
• Each client receives the new QoS parameter for
  its remote method invocation requests from
  translator on the server through the feedback
  lane.

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hORB Architecture
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Conclusion

• Our mechanism give a systematically and
  theoretically platform to investigate how to deal
  with uncertainty and additive disturbance for
  real-time system and how to design a H8 control
  scheduling.
• The experimental results show that proposed
  scheduler improves the robust stable performance
  for uncertain real-time systems even when system
  parameters and workload vary.