Controller Redundancy Design for Cyber-Physical Systems

Continuous Systems 72 3.4.2 MSR of Interpolation Gain-Scheduling Controller with Delays 73 3.5 Stability Property of Switched Linear Systems from NetMSR and Reach Set Perspective 74 3.5.1 Reach Set of States with Delay 74 3.5.2 Switch Logic 75 3.5.3 Stability Analysis 75 3.6 Evaluations 77 3.6.1 Satellite Altitude Control Model 77 3.6.2 Simulation Configuration 77 3.6.3 NetMSR Evaluations 78 3.6.4 Reliability Evaluations 80 3.7 Conclusion and Future Work 82 Acknowledgments 82 3.A Appendix 83 3.A.1 Proof of Lemma 3.3 83 3.A.2 Proof of Lemma 3.4 84 References 85 Systems where the physical subsystem is tightly integrated with the cyber subsystem are usually referred as cyber-physical systems (CPS) [1-5]. CPS applications can be found in many areas, such as automated manufacturing, health care, civil infrastructure, avionics, aircraft, and vehicular communications [6]. Networked control systems (NCS) are considered to be a prominent subcategory of CPS, in which networks provide a means for communication among sensors, actuators, and controllers. As networking technology continues to increase in bandwidth capability and decrease in price, NCS will become more pervasive and have the potential to radically change the way the physical systems interact with each other and their environment. Communication networks have been used to exchange information among sensors, controllers, and actuators in digital control systems since the 1970s, originally motivated by the need of reducing costs for cabling, modularizing, and integrating system flexibly in the automobile industry. Today, many other applications of NCS can be easily found in diverse industries. For example, Avionics Full-Duplex Switched Ethernet (AFDX) is used in control systems of the Airbus A380 and Boeing B787 [7], and a new automotive network communications protocol, FlexRay was developed for vehicle control and is used in automobiles, such as the BMW 7 Series (F01), Audi A8, and Rolls-Royce Ghost [8]. Employing communications networks in control systems may considerably reduce integration complexity and make system architecture more scalable.