Design of Optimal Tracking Controller for Nonlinear Discrete System
with Input Delay Using Information Fusion Estimation Method
WANG Zhi-sheng and WANG Dao-bo
College of Automation, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China.
Abstract: Based on the theory of information fusion estimation, information fusion optimal tracking control algorithms of
nonlinear discrete system with input delay are proposed. All information with respect to control strategy, including ideal
control strategy, expected object trajectory, and system dynamical equation are regarded as measuring information of
control strategy. Therefore, the question of optimal control can be transferred into one of information fusion estimation,
and the algorithms of optimal tracking control of time-delayed nonlinear discrete-system are given in detail. In the end,
the mathematical simulation results show the validity of the algorithms presented in this paper.
Key words: time-delayed system; nonlinear control; information fusion control; nonlinear estimation
1 Introduction
Time delays are inherent in many physical and technological systems, such as turbojet engine, microwave
oscillator, nuclear reactor and long transmission lines. The presence of input delays, if not considered in a
controller design, may cause instability or serious deterioration in the performance of the resulting control
systems
[1]
.
In this paper, based on the theory of information fusion estimation
[2]
, we present a new method to designate
optimal tracking control for a class of nonlinear discrete system with input delay. The main idea of this method
is that all information about control strategy, including ideal control strategy, expected object trajectory, and
system dynamics information, is regarded as measuring information of control strategy. Therefore, the question
of optimal control can be transferred into one of information fusion estimation, and the algorithms of optimal
tracking control are given in detail. Finally, a numerical example is provided to illustrate the proposed method,
and the mathematical simulation results show its validity.
2 Information Fusion Estimation Theory
The Equation (1) can be expressed as the uniform linear information fusion model.
vHxy += (1)
where, is datum; is the estimated;
1×
∈
m
Ry
1×
∈
n
Rx
nm
R
×
is information transferring matrix; and is the
measuring error,and
v
0][
vE , . Pv =]var[
Obviously, information is made up of both datum and Information Weight (IW). Here,
1−
is called IW
of
with respect to itself, and
T 1−
is named as IW of
with respect to
. When
T 1−
is reversible, the
variance of the estimation from
x
ˆ
is the inverse of
T 1−
. Frequently, the IW of information about itself
and its variance are reciprocal value mutually.
Theorem 1
[2]
: Suppose can be used to express all information aboutNivxHy
iii
~1, =+=
, and ,
, are mutually irrelevant. If is non-singular, then is the optimal
fusion estimation of
0][ =
i
vE
ii
Pv =]var[
N
yyy ,,,
21
L
∑
=
−
N
i
ii
T
i
HPH
1
1
x
ˆ
,
1−
is IW of . And
x
ˆ
∑
=
−
−
=
N
i
ii
T
i
HPHP
1
1
1
(2)
(3)
∑
=
−
−
=
N
i
ii
T
i
yPHxP
1
1
1
ˆ
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