事件驱动的非线性折扣最优电力系统调节

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"这篇研究论文探讨了事件驱动的非线性折扣最优控制在电力系统应用中的问题。通过使用神经网络近似架构，在事件驱动的自适应批评框架下处理非线性折扣最优调节。" 正文：在电力系统和其他复杂工程领域中，优化控制策略是确保系统高效、稳定运行的关键。论文"Event-Driven Nonlinear Discounted Optimal Regulation Involving a Power System Application"深入研究了一种基于事件驱动的非线性折扣最优控制方法。这种方法利用神经网络作为近似工具，以解决实时优化问题。传统的控制策略通常依赖于预先设定的稳定控制政策，但该论文提出了一种改进的学习算法，使得在无需初始稳定控制策略的情况下，也能通过训练神经网络得出事件驱动的折扣最优控制律。这一创新点减少了对预设控制策略的依赖，增加了系统的灵活性。论文中，闭合回路系统被建模为脉冲模型，这允许将稳定性问题转化为脉冲系统分析。作者采用了Lyapunov稳定性理论来解决相关稳定性问题，确保在事件触发时系统的行为可控且稳定。这样的方法有助于减少计算开销，同时保持系统性能。为了验证所提出的控制设计方法的有效性，论文进行了包括电力系统在内的模拟研究。电力系统是一个典型的非线性动态系统，其稳定性和效率对于现代社会至关重要。通过仿真，研究证明了该方法能有效应用于电力系统的优化控制，提高其运行效率和稳定性。这篇由Ding Wang, Haibo He, Xiangnan Zhong, 和 Derong Liu合作的IEEE Transactions on Industrial Electronics论文，为事件驱动的非线性控制理论提供了一个新的视角，尤其是在电力系统应用中的实用性。通过结合神经网络和自适应学习规则，该研究为未来智能电网和自动化控制系统的优化设计提供了有价值的参考。

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 10, OCTOBER 2017 8177

Event-Driven Nonlinear Discounted Optimal

Regulation Involving a Power System Application

Ding Wang, Member, IEEE, Haibo He, Senior Member, IEEE, Xiangnan Zhong, Student Member, IEEE,

and Derong Liu, Fellow, IEEE

Abstract—By employing neural network approximation

architecture, the nonlinear discounted optimal regulation

is handled under event-driven adaptive critic framework.

The main idea lies in adopting an improved learning algo-

rithm, so that the event-driven discounted optimal control

law can be derived via training a neural network. The stabil-

ity guarantee and simulation illustration are also included.

It is highlighted that the initial stabilizing control policy is

not required during the implementation process with the

combined learning rule. Moreover, the closed-loop system

is formulated as an impulsive model. Then, the related sta-

bility issue is addressed by using the Lyapunov approach.

The simulation studies, including an application to a power

system, are also conducted to verify the effectiveness of

the present design method.

Index Terms—Adaptive/approximate dynamic program-

ming, approximation, discount factor, event-driven control,

neural networks, optimal regulation, power system.

I. INTRODUCTION

HERE exists a severe difﬁculty called the “curse of dimen-

sionality” when solving the Hamilton–Jacobi–Bellman

equation during nonlinear optimal regulation design. Hence,

a series of iterative methods have been developed to tackle

the optimal control problems. Among them, neural networks

have served as an important function approximation archi-

tecture to perform the iterative calculation. In fact, neural

Manuscript received December 19, 2016; revised February 12, 2017

and March 18, 2017; accepted April 4, 2017. Date of publication April 27,

2017; date of c urrent version September 11, 2017. This work was sup-

ported in part by the National Natural Science Foundation of China under

Grant U1501251, Grant 61533017, Grant 61233001, Grant 51529701,

and Grant 61520106009, in part by the Beijing Natural Science Foun-

dation under Grant 4162065, in part by the U.S. National Science Foun-

dation under Grant ECCS 1053717, and in part by the Early Career

Development Award of SKLMCCS. (Corresponding author: Haibo He.)

D. Wang is with The State Key Laboratory of Management and Con-

trol for Complex Systems, Institute of Automation, Chinese Academy of

Sciences, Beijing 100190, China, and also with the School of Computer

and Control Engineering, University of Chinese Academy of S ciences,

Beijing 100049, China. This research was conducted when D. Wang

was a Visiting Scholar at the Department of Electrical, Computer, and

Biomedical Engineering, University of Rhode Island, Kingston, RI 02881

USA (e-mail: ding.wang@ia.ac.cn).

H. He and X. Zhong are with the Department of Electrical, Computer

and Biomedical Engineering, University of Rhode Island, Kingston, RI

02881 USA (e-mail: he@ele.uri.edu; xzhong@ele.uri.edu).

D. Liu is with the School of Automation, Guangdong University of

Technology, Guangzhou 510006, China (e-mail: derongliu@foxmail.

com).

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/TIE.2017.2698377

networks are widely adopted to perform learning and ap-

proximation abilities for practical feedback stabilization prob-

lems [1]–[5], especially for optimal control design [5]. Re-

cently, a signiﬁcant breakthrough has been made in adaptive

boundary control design and stability analysis for inﬁnite di-

mensional systems with constraints [2], [3]. Based on neural

networks, adaptive/approximate dynamic programming [6], [7]

is regarded as a key technique to design optimal controllers

adaptively and forward-in-time. In the last decade, extensive

developments of adaptive/approximate dynamic programming

have been achieved in aspect of optimal control for discrete-time

systems [8]–[12] and continuous-time systems [13]–[17]. For

example, Modares and Lewis [14] studied the linear quadratic

tracking control with discounted cost function of partially un-

known continuous-time systems based on the reinforcement

learning technique. One also has observed the extensions of

regulation design to various intelligent control strategies for

complex systems, such as decentralized control [18], consen-

sus control [19], H

∞

control [20], and tracking control [21].

However, the aforementioned results are mainly obtained based

on time-driven design, which would inevitably cause frequent

adjustments of the actuator state and might result in serious en-

ergy consumption. Thus, conducting time/event transformation

to achieve event-driven design has become a new avenue for the

feedback control community.

With the rapid development of network-based systems, more

and more control loops are closed through some communication

media. The increasing interest in saving the computational load

of networked control systems results in an extensive attention

with respect to the event-triggering mechanism. Under the gen-

eral framework of event-driven approaches, the actuators are

updated only when certain conditions are violated to guarantee

both stability performance and control efﬁciency of the target

plants. Recently, the event-driven adaptive critic control has pro-

vided a new channel to implement nonlinear intelligent optimal

stabilization [22]–[26]. For example, Sahoo et al. [22] presented

a novel approximation-based event-triggered control scheme

of multi-input multioutput unknown nonlinear continuous-time

systems in afﬁne form. Vamvoudakis et al. [23] proposed an

event-driven tracking control algorithm for nonlinear systems

with an inﬁnite horizon discounted cost function. Under the

new framework, the designed controller is only updated when

an event is triggered, thereby reducing the computational burden

of two processes including neural network learning and adaptive

optimal control.

See http://www.ieee.org/publications

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