Table Of ContentStudies in Systems, Decision and Control 83
Huiping Li
Yang Shi
Robust Receding
Horizon Control
for Networked
and Distributed
Nonlinear Systems
Studies in Systems, Decision and Control
Volume 83
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Huiping Li Yang Shi
(cid:129)
Robust Receding Horizon
Control for Networked
and Distributed Nonlinear
Systems
123
HuipingLi Yang Shi
Schoolof Marine Science andTechnology Department ofMechanical Engineering
Northwestern Polytechnical University University of Victoria
Xi’an Victoria, BC
China Canada
ISSN 2198-4182 ISSN 2198-4190 (electronic)
Studies in Systems,DecisionandControl
ISBN978-3-319-48289-7 ISBN978-3-319-48290-3 (eBook)
DOI 10.1007/978-3-319-48290-3
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Preface
Theemergenceoflarge-scaleandnetworkedphysicalsystemssuchassmartgrids,
multi-robotsystems andtransportationsystems callsfornewtheory,methodology,
and frameworks for synthesizing and analyzing such systems from a control
engineering perspective. In such networked and large-scale systems, the grand
challenges for control include the network-induced communication constraints
(suchascommunicationdelays,anddatalosses),scalabilityissue,nonlinearity,and
uncertainty.
The receding horizon control (RHC) strategy is regaining popularity in recent
years, and it is particularly efficient and promising to handle communication con-
straints, provide satisfactory control performance, as well as deal with other issues
such as nonlinearity and disturbances. Specifically speaking, the RHC strategy is
abletoofferaheadinformationtocompensatefornetwork-inducedcommunication
constraints; it can achieve suboptimal performance for large-scale systems in a
distributed fashion; it is efficient in handling nonlinear control problem online and
iteratively. This book makes full use of these features of RHC and brings
RHC-based methodologies and frameworksfor the control of nonlinear networked
systems and large-scale systems.
The technical contents of the book contain eight self-contained chapters, which
maybedividedintofourparts.ThefirstpartisChap.1.Inthischapter,arelatively
comprehensive overview on the RHC for networked control systems (NCSs) and
distributedRHCforlarge-scaleagentsystemsisoffered,whichwouldgivereaders
aclearresearchbackground.ThesecondpartincludesChaps.2–4.Chapters2and3
provide novel approaches to solve the RHC-based control problem for nonlinear
NCSs with two-channel data losses and two-channel data loss and information
latency,respectively.Chapter4solvestheoutputfeedbackRHCproblemforNCSs
with measurement dropouts. The third part includes Chaps. 5–7, which focuses on
the distributed RHC problems for large-scale nonlinear systems. The methods on
dealing with external disturbances, transmission delays, and simultaneous occur-
renceofdelaysanddisturbancesarereportedinChaps.5–7.Finally,thefourthpart
contains Chap. 8, which provides a novel approach on the event-triggered RHC
problem for nonlinear systems, to save computational load and communication
v
vi Preface
resources. The event-triggered RHC is a very new topic and Chap. 8 provides a
basic but useful result.
For each control problem, this book not only provides practical solutions with
effective control algorithms and/or strategies, but also offers rigorous theoretical
analysis with provably correct design conditions. In addition, simulation examples
are provided in each chapter to show how to implement the developed algorithms
and/or strategies. This book would be useful for graduate students, control engi-
neers,anduniversityinstructors;howevertheyneedthebackgroundsonbasicRHC
before fully understanding this book. In particular, it is believed that the book
would be very helpful for those who are doing research in RHC for large-scale
systems and networked systems.
Xi’an, China Huiping Li
Victoria, Canada Yang Shi
October 2015
Acknowledgments
Although this book is an accumulation and fruit of 6-year research in the area of
receding horizon control for networked large-scale systems, we are indebted to
many colleagues and friends. We thank Prof. Wu-sheng Lu at the University of
Victoria, BC, Canada, for his discussions and instructions in the theory of convex
optimization, and Prof. Wei Ren and Dr. Daniela Constantinescu for providing
suggestions in multi-agent systems. In addition, we wish to express thanks to
Dr. Jian Wu for providing help in area of linear algebra, to Dr. Ji Huang for his
comments on networked control systems, to Dr. Xiaotao Liu for the useful sug-
gestions and discussions on receding horizon control. We also wish to thank
Dr. Hui Zhang, Mr. Mingxi Liu, Mr. Bingxian Mu, Mr. Chao Shen, and
Mr.YuanyeChengfortheirsupportduringtheresearchperiodattheUniversityof
Victoria.
We also would like to thank the reviewers for reviewing this book and Oliver
Jackson and Nisha S. Keeran at Springer for providing assistance to get this
manuscript published.
Finally,wewouldliketothankthefinancialsupportfromtheChinaScholarship
Council(CSC),theNaturalSciencesandEngineeringResearchCouncilofCanada
and the Canada Foundation of Innovation, the University of Victoria, National
Natural Science Foundation of China (NSFC) under Grant 61473225, 61502395,
and 61473116, Northwestern Polytechnical University.
Xi’an, China Huiping Li
Victoria, Canada Yang Shi
vii
Contents
1 Introduction and Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Control Systems with Communication Networks (NCSs). . . . . . . 1
1.2 Introduction to Receding Horizon Control (RHC). . . . . . . . . . . . 4
1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 RHC-based Control of NCSs. . . . . . . . . . . . . . . . . . . . . 6
1.3.2 Distributed RHC of Large-Scale Systems . . . . . . . . . . . . 8
1.4 Motivation of the Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Outline of This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Note and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 RHC of Networked Nonlinear Systems with Two-Channel
Packet Dropouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Preliminary Results and Modeling . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Regional ISpS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Network Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.3 Buffer Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Predictive Networked Controller Design . . . . . . . . . . . . . . . . . . 25
2.3.1 Constrained Optimization Problem. . . . . . . . . . . . . . . . . 25
2.3.2 Control Packet Generation . . . . . . . . . . . . . . . . . . . . . . 26
2.3.3 Packet Transmission and Compensation
Strategy Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.4 Explicit Control Law and Closed-Loop Model. . . . . . . . . 28
2.4 Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Note and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
ix
x Contents
3 Min-Max RHC of Nonlinear NCSs with Delays
and Packet Dropouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Problem Formulation and Preliminaries. . . . . . . . . . . . . . . . . . . 42
3.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 Networked Controller Design. . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Control System Structure . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Min-Max RHC-Based Control Packet Design . . . . . . . . . 47
3.3.3 Compensation Strategy. . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4 Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.5 Simulation Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6 Note and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4 Output Feedback RHC of NCSs with Intermittent
Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Observer Design and Estimation Error Analysis. . . . . . . . . . . . . 68
4.3.1 Observer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3.2 Bounds of Estimation Error. . . . . . . . . . . . . . . . . . . . . . 69
4.4 Robust Output Feedback RHC Design . . . . . . . . . . . . . . . . . . . 70
4.4.1 Nominal State Feedback RHC. . . . . . . . . . . . . . . . . . . . 70
4.4.2 Constraints Tightening . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4.3 Robust Output Feedback RHC Algorithm. . . . . . . . . . . . 75
4.5 Feasibility and Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . 75
4.5.1 Feasibility Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.5.2 Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.6 Simulations and Comparison Studies . . . . . . . . . . . . . . . . . . . . 79
4.6.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.6.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.7 Note and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5 Robust Distributed RHC of Constrained Nonlinear Systems. . . . . . 89
5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . 89
5.1.2 Main Contents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.1.3 Organization and Notations. . . . . . . . . . . . . . . . . . . . . . 91
5.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3 Robust Distributed RHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3.1 Setup of Robust Distributed RHC . . . . . . . . . . . . . . . . . 94
5.3.2 Robust Distributed RHC Algorithm . . . . . . . . . . . . . . . . 97
