Transcript Framework and Modeling of H∞ Nonlinear Model Predictive

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
Outline of presentation





Introduction.
H∞control scheduling Architecture.
H∞ robust controller and H∞-NMPC
controller.
Overview of hORB Architecture
Conclusion
Introduction


Traditional scheduling are no longer promise the
function and performance requirements of DRE
systems.
The common ORB middleware scheduling
approaches can’t provide real-time performance
guarantees because they depend on accurate task
execution times.
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.
H∞-nonlinear model predictive control scheduling
(H∞-NMPC) is provided an excellent theoretical
framework for dealing with nonlinear stability and
robustness issues by H∞ theory.
H∞ 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-ofservice (QoS) measure. The system will control the rate
of deadline misses by regulating the QoS of the task.
H∞ control scheduling Architecture
(z)
DMR
(z)
+
-
DMR(z)
+
ref
K(z)
A(z)
Q(z)
P(z)
+
Model switch
+
+
(z)
H∞ 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(z+1)
Generalized nonlinear discrete-time H∞ system
F(q)
m
z

v
n
P
e
w
y
u
sampler
K
Hold
P is an LTI system; f(q) is a static nonlinearity; and Δ is a
block structured, norm bounded perturbation
H∞ robust controller
Transfer function from w to e
e = Fℓ [ F u ( P ( s ), Δ ), K ( s )] w = G ( s ) w
satisfies a norm objective
 The problem is to design K(s) such that for all Δ  BΔ,
K (s) stabilizes Fu(P(s), Δ), and
|| F u ( F ℓ( P (s), K (s) ), Δ ||  ≤ 1.
This is equivalent to K (s) satisfying
μ [ Fℓ ( P ( s ) ; K ( s ) )]<1

H∞-NMPC controller

Based on the derivation of a stationary
Hamilton-Jacobi-Isaacs equation, which is the
nonlinear analogous of the FHARE (fake H∞
algebraic Riccati equation), it is shown that the
H∞ NMPC control law is the solution of an
associated
infinite horizon
control
xH∞
x
x
0
problem,
H∞-NMPC controller

a class of systems described by the following
nonlinear set of differential equations:
x (t) = f ((t), u (t)), x (0) = x0
where x(t) and u (t) denotes the vector of states and
inputs, respectively.
H∞-NMPC controller

The finite horizon open-loop problem described
above is mathematically formulated as follows:
find min J ((t), ū (∙); Tc, Tp)
ū (∙)
t Tp
with J ( x (t), ū (∙); Tc, Tp) =  F ( x ( ), u ( )) d
t
where Tc and Tp denotes control horizon and
prediction horizon, and ū (∙) denotes the internal input.
Generalized and weighted performance block diagram

(z)
W2
DMRref(z)
+
K(0)
-
W3
DMR(z)
W1
S1
+
+
+ +
P(z)
W4
(z)
+
K(z)
W5
+
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,
μ[F(P (s); K(s))] ≤ 1
The μsynthesis problem can be replaced with the following
approximation
inf || DF(P (s); K(s))D‾¹ ||
DЄ Đ
K(s) stabilizing
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.
Two tank system model of scheduling system
Tank 1
QoS Actuator
Task Actuator
Pump
Tank 2
Tracking simulation
H
PI
75
14
13
Level 2(cm)
Pump (%)
50
12
11
25
500
1000 Time (S)
500
1000
perturbed system with +10% change. The inputs are constrained to
remain within 25-75%
Time (S)
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 H∞-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.
hORB Architecture
APPLICATION
Comparator
DMR ref
controller
miss Rate
monitor
sensor
probe
input
QoS monitor
sensor
translator
actuator
MIDDLEWARE PLATFORM
probe
probe
COMPUTING & COMMUNICATION RESOURCES
output
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 H∞ 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.