全状态约束非线性系统自适应神经网络控制设计
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"基于神经网络控制的全状态约束非线性系统自适应学习设计"
这篇研究论文探讨了在全状态约束下的不确定非线性严格反馈系统的稳定控制问题。针对实际工程中常常遇到的状态约束问题，作者提出了一种自适应神经网络控制方法。其核心在于通过引入屏障Lyapunov函数（Barrier Lyapunov Function, BLF）来确保系统在运行过程中不会违反这些状态约束。
传统的控制策略在处理状态约束时可能会遇到挑战，而该论文提出的新颖的自适应反向传播设计巧妙地解决了这一问题。在反向传播过程中，BLF在每一步都被应用，从而确保了全状态约束始终得以满足。这种方法的一个显著特点是使用了最小学习参数，这有助于简化控制算法并提高其效率。
论文利用Lyapunov分析方法证明了闭合回路系统中的所有信号都是半全局一致最终有界的，这意味着系统不仅能够保持稳定，而且其输出可以有效地跟踪期望值。这样的设计对于确保系统的性能和鲁棒性至关重要，特别是在面对系统不确定性时。
通过神经网络控制，系统可以自适应地学习和调整其行为，以适应非线性和不确定性。这种自适应学习设计使得控制器能够在线估计未知模型参数，并根据实时数据动态调整控制策略，从而在满足约束条件下优化系统的性能。
这项工作为非线性系统的控制提供了一个创新的解决方案，它考虑了现实世界中常见的状态约束问题，并且通过引入BLF和自适应学习机制，提高了控制策略的可行性和有效性。这对于未来在机器人控制、航空航天、电力系统和其他需要精确控制且存在状态限制的领域有着广泛的应用前景。
1562 IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 27, NO. 7, JULY 2016
Neural Network Control-Based Adaptive Learning
Design for Nonlinear Systems With
Full-State Constraints
Yan-Jun Liu, Member, IEEE, Jing Li, Shaocheng Tong, Senior Member, IEEE,
and C. L. Philip Chen, Fellow, IEEE
Abstract—In order to stabilize a class of uncertain nonlinear
strict-feedback systems with full-state constraints, an adaptive
neural network control method is investigated in this paper.
The state constraints are frequently emerged in the real-life
plants and how to avoid the violation of state constraints is
an important task. By introducing a barrier Lyapunov func-
tion (BLF) to every step in a backstepping procedure, a novel
adaptive backstepping design is well developed to ensure that
the full-state constraints are not violated. At the same time,
one remarkable feature is that the minimal learning parameters
are employed in BLF backstepping design. By making use of
Lyapunov analysis, we can prove that all the signals in the
closed-loop system are semiglobal uniformly ultimately bounded
and the output is well driven to follow the desired output.
Finally, a simulation is given to verify the effectiveness of the
method.
Index Terms—Adaptive neural control, barrier Lyapunov
function (BLF), full-state constraints, neural networks (NNs),
nonlinear systems.
I. INTRODUCTION
B
ECAUSE the adaptive design technique is a powerful tool
for coping with uncertain systems, much improvement
has been advanced in recent two decades. The pioneer
approaches were developed in [1] for multifarious uncertain
nonlinear systems, e.g., the matching condition systems,
the strict-feedback systems, and the pure-feedback systems.
The different controllers have been framed using various
techniques, such as feedback linearization, inversion control,
backstepping design, fuzzy control, and so on [69]–[71], [83].
Whereafter, the adaptive control technique was one after
the other studied for different classes of nonlinear systems.
For example, an adaptive output feedback control was
addressed in [2] for a class of nonlinear discrete-time systems
with unknown control directions based on the discrete
Manuscript received April 26, 2015; revised November 5, 2015; accepted
November 8, 2015. Date of publication March 9, 2016; date of current version
June 15, 2016. This work was supported in part by the National Natural
Science Foundation of China under Grant 61374113, Grant 61473139, and
Grant 61572540 and in part by the Program for Liaoning Excellent Talents
in University under Grant LR2014016. (Corresponding author: Yan-Jun Liu.)
Y.-J. Liu, J. Li, and S. Tong are with the College of Science, Liaoning Uni-
versity of Technology, Jinzhou 121001, China (e-mail: liuyanjun@live.com;
15241624210@163.com; jztongsc@sohu.com).
C. L. P. Chen is with the Faculty of Science and Technology, University of
Macau, Macau 999078, China (e-mail: philipchen@umac.mo).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TNNLS.2015.2508926
Nussbaum gain. In [3], an adaptive tracking control was pro-
posed for nonlinear multi-input multioutput (MIMO) systems
with nonsymmetric input constraints, and the auxiliary system
was designed to solve the effect of input constraints. We men-
tion that the input (saturation) constraints have been exten-
sively studied in the literature and some advanced approaches
have been established. For example, a novel saturated linear
feedback was constructed in [72] for periodic systems with
input constraints. A new convex hull representation of
saturation constraints was established in [73] and [74], and an
efficient truncated predictor feedback approach was proposed
in [75] to solve the elliptical spacecraft rendezvous problem
with input constraints and delay. In recent years, the adaptive
control problem of output and state constraints has been an
active area. The adaptive control methods for nonlinear sys-
tems with constant [4] and time-varying [5] output constraints
were investigated by making use of barrier Lyapunov func-
tion (BLF). The nonlinear systems with partial state constraints
have been stabilized in [6]. The adaptive control of full-state-
constrained nonlinear systems was studied in [7] and [8].
Two practical applications were proposed for some real plants
with the output constraint [9] and the state constraints [10].
However, the considered systems in [1]–[10] are required to
be in the linear parametric forms. This requirement may be rig-
orous in the industrial plants. In order to account for unknown
dynamics without the linear parametric condition, the neural
networks (NNs) and the fuzzy logic systems have been incor-
porated into an adaptive control design owing to their excellent
approximation ability [11], [12]. Based on the adaptive fuzzy
or neural control technique, the stability problem for several
classes of nonlinear systems with unknown functions has been
addressed in [13]–[18], [56], [57], [60], and [61]. For nonlinear
systems with unknown functions and input nonlinearities,
several adaptive fuzzy or neural control methods were given
in [19]–[21], [63], [64], [67], [68], and [76]. A shortcoming
is that the systems must subject to the requirement of the
matching condition. To remove the matching condition,
based on the backstepping design method [1], the fuzzy
or neural control-based adaptive technique was presented
in [22]–[24], [58], [59], and [66] for nonlinear single
input single output (SISO) systems with unknown functions.
Subsequently, the control problem of nonlinear strict-feedback
large-scale systems was also studied in [25], [26], and [65].
Recently, the control problem of discrete-time systems
2162-237X © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Authorized licensed use limited to: SOUTH CHINA UNIVERSITY OF TECHNOLOGY. Downloaded on March 28,2020 at 12:27:18 UTC from IEEE Xplore. Restrictions apply.
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