Global Output Feedback Control of Nonlinear Systems with Uncertain
Supply Rates
Xin Yu
1
, Tairen Sun
1
, Guohai Liu
1
1. School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China
E-mail: xyu@ujs.edu.cn; suntren@gmail.com; ghliu@ujs.edu.cn
Abstract: This paper considers the problem of global output feedback control for a class of nonlinear systems with
inverse dynamics. The main contribution of paper is that: For the inverse dynamics with uncertain ISS/iISS supply rates,
we construct a reduced-order observer-based output feedback controller, which drives the output of system to zero and
maintain other closed-loop signals bounded. Finally, a simulation example shows the effectiveness of the control scheme.
Key Words: Nonlinear systems, uncertain supply rates, reduced-order observer
1 INTRODUCTION
The notion of input-to-state stability (ISS) has been recog-
nized as a central concept in nonlinear control systems. [7]-
[10], [4] and the references therein investigated many kinds
of properties of ISS, and the controller design and stability
analysis for various classes of nonlinear systems with ISS
inverse dynamics. Subsequently, another important con-
cept, integral input-to-state stability (iISS), was firstly pre-
sented in [6], and several characterizations on iISS were
investigated in [1], in which iISS is proved to be strictly
weaker than ISS. Recently, [2]-[3] gave several Lyapunov-
based small-gain theorems covering iISS systems. Jiang
et al. in [5] firstly presented a unifying framework for the
robust global regulation via output feedback for nonlinear
systems with iISS inverse dynamics. Recently, [11] further
studied output feedback regulation for a class of nonlin-
ear systems with iISS inverse dynamics, in which the ob-
server gain is governed by a Riccati differential equation,
and Xu and Huang in [12] considered the output regulation
problem for output feedback systems with relative degree
one and iISS inverse dynamics. In [13], the authors con-
sidered reduced-order observer-based output feedback reg-
ulation for a class of nonlinear systems with iISS inverse
dynamics.
However, almost of the above papers only consider the
ISS/iISS inverse dynamics with known ISS/iISS supply
rates. When the inverse dynamics with uncertain ISS/iISS
supply rates, how to design a feedback controller for non-
linear systems seems to be an interesting work.
The main contribution of paper is that: For the inverse dy-
namics with uncertain ISS/iISS supply rates, and the sys-
tems being disturbed by L
2
noises, we construct a reduced-
This work was supported by the National Natural Science Foun-
dation of China (61304073, 61273154, 51077066, 61203054), Natural
Science Foundation of Jiangsu Province (BK20130533, BK20130536),
China Postdoctoral Science Foundation (2013M540421, 2013M541615),
Specialized Research Fund for the Doctoral Program of Higher Education
of China (20133227120012), Research Foundation for Advanced Talents
of Jiangsu University (13JDG012, 12JDG091).
order observer-based output feedback controller, which
drives the output of system to zero and maintain other
closed-loop signals bounded.
The remainder of paper is organized as follows. Section 2
is problem statements. Section 3 gives the design of output
feedback controller. Section 4 is the main results. A sim-
ulation example is given in Section 5. Section 6 concludes
the paper.
Notations: R
+
stands for the set of all nonnegative real
numbers, R
n
is the n-dimensional Euclidean space, |x| is
the usual Euclidean norm of a vector x. K denotes the set of
all functions γ : R
+
→ R
+
, which are continuous, strictly
increasing and γ(0)=0; K
∞
is the set of all functions
which are of class K and unbounded, KL denotes the set
of all functions β(s, t): R
+
× R
+
→ R
+
, which are of
class K for each fixed t, and decrease to zero as t →∞
for each fixed s. σ
1
(s)=O(σ
2
(s)) as s → 0+ means
that σ
1
(s) ≤ c
1
σ
2
(s) for some constant c
1
> 0 and all s
in a small neighborhood of zero, and σ
1
(s)=O(σ
2
(s))
as s →∞means that σ
1
(s) ≤ c
2
σ
2
(s) for some constant
c
2
> 0 and all large enough s. L
2
(R
+
; R) is the family of
all functions l : R
+
→ R such that
∞
0
l
2
(t)dt < ∞.
2 Problem Statements
In this paper, we consider a class of nonlinear systems with
the detailed form described as:
˙η = q(t, η, y),
˙x
i
= x
i+1
+ f
i
(t, ¯x
i
)+g
i
(t, η, y)+d
i
(t),
i =1, ···,n− 1,
˙x
n
= u + f
n
(t, ¯x
n
)+g
n
(t, η, y)+d
n
(t),
y = x
1
, (1)
where x =(x
1
, ···,x
n
) ∈ R
n
, u ∈ R, y ∈ R are the
state, the control input, and the measurable output, respec-
tively, η ∈ R
q
denotes the inverse dynamics, (x
2
, ···,x
n
)
and η are unmeasurable signals, ¯x
i
=(x
1
, ···,x
i
) ∈ R
i
,
i =1, ···,n. It is assumed that the modeled (or known)
98
978-1-4799-3708-0/14/$31.00
c
2014 IEEE
资源评论
