Abstract
This paper investigates the simultaneous stabilization of a collection of battery-powered networked control systems (NCSs) with medium access constraint and communication energy limitation. Each time the channels can only accommodate a limited number of systems for communication and the successful packet arrival rate at the controller depends on the power used by the sensor. Then in order to satisfy the medium access constraint, reduce the communication energy cost and stabilize the collection of NCSs, one needs to decide when to schedule which plant to communicate by which channel and by which power level. Based on the average dwell time technique, sufficient conditions for the exponential mean square stability of a single plant are given at first. Then, based on the stability conditions, a period scheduling policy is proposed to assign the channel accessing sequence and power level such that all the plants are simultaneously stabilized. Finally, a new framework for channel assignment, power allocation and controller design is constructed, which can guarantee a desired decay rate for each system and a minimal energy consumption for the group of systems. The effectiveness of the methodology is demonstrated with numerical simulations.
Zusammenfassung
Dieser Beitrag untersucht die gleichzeitige Stabilisierung einer Anzahl batteriebetriebener vernetzter Steuerungssysteme (NCS) mit mittlerer Zugriffsbeschränkung und Kommunikationsenergiebegrenzung. Dabei können nur eine begrenzte Anzahl von Systemen miteinander kommunizieren und die erfolgreiche Paketankunftsrate am Controller hängt von der vom Sensor verbrauchten Leistung ab. Um die Medienzugriffsbeschränkung zu erfüllen, die Energiekosten für die Kommunikation zu reduzieren und die vernetzten Steuerungssysteme zu stabilisieren, muss entschieden werden, wann welches System mit welchen Kanal mit welcher Leistungsstufe innerhalb der vernetzten Steuerungssysteme mit den anderen Systemen kommunizieren kann. Dafür werden zuerst hinreichende Bedingungen für die exponentielle mittlere quadratische Stabilität auf der Basis der mittleren Verweilzeiten gegeben. Davon ausgehend wird eine Planungsstrategie vorgestellt, die es erlaubt, alle vernetzten Steuerungssysteme gleichzeitig zu stabilisieren. Anschließend wird eine Methodik für die Kanalzuweisung, die Leistungszuordnung und den Reglerentwurf beschrieben, die die Zugriffsbeschränkung für jedes Steuerungssystem und den minimalen Energieverbrauch alle miteinander vernetzten Steuerungssysteme garantiert. Die Leistungsfähigkeit der Vorgehensweise wird anhand von numerischen Simulationsuntersuchungen demonstriert.
Funding statement: This research was supported by Natural Science Foundation of China under Grant 61703072 and 61673084; the Fundamental Research fund for Central Universities under Grant 3132017128.
About the authors
Liyuan Wang was born in Dalian, China, in 1987. She received the B.S. degree in automation from Dalian Maritime University, in 2010 and the Ph.D. degree in control theory and control engineering from Dalian University of Technology in 2016. She is currently a lecturer of College of Mechanical and Electronic Engineering at Dalian Minzu University. Her research interests include networked control system and stochastic control.
Wei Yue was born in Shandong, China, on October 10, 1981. He received the B.S., M.E., and Ph.D. degrees in control theory and control engineering from Dalian Maritime University, Dalian, China, in 2006, 2008, and 2011, respectively. He is an Associate professor with the College of Marine Electrical Engineering, Dalian Maritime University. His research interests include intelligent vehicular platoon control, cluster cooperative planning, control and optimization.
Appendix A
Proof of Theorem 1.
Let
where
Then it holds from (10) that
When
Otherwise, when
Similarly, when
Combine (A3)–(A5) we know that
where
Then it follows from (A2) and (A6) that
where
If a quadratic form is considered in the piecewise Lyapunov-like function (A1), then
on the other hand
where
From (11) we know that
which means that
From (12) we know that
Then combine (A10)–(A12) we have
where
Appendix B
Proof of Lemma 1.
We proof this lemma by contradiction. Suppose that
Then we have
Let us construct a new set (
Then it is easy to know that
which means that conditions (5) and (6) in Problem 1 also hold for
Then the average communication energy consumption over each scheduling policy under
i. e.,
This completes the proof. □
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