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摘要: 对于远程复杂的操控系统，信息物理融合系统（Cyber-physical system，CPS）主要依靠无线网络实现从传感器到控制器，从控制器到执行器间的信息传输，由于其依靠网络传输数据的特性使其控制系统极易遭到安全威胁.本文从物理系统入手，意图保护CPS系统中物理实体的正常运行不受由于恶意攻击造成网络空间入侵带来的干扰.以受到数据包时序攻击的信息物理融合系统为研究对象，将其安全性研究抽象为一个博弈过程，基于非合作博弈的两人零和博弈模型，设计了可变延迟情况下鲁棒输出反馈的极大极小控制器.并且采用参数化的软约束二次型目标函数，在控制器设计时引入干扰衰减因子γ，通过对γ的取值使得二次型目标函数取极小值，从而保证了最差情况下的稳定控制，在满足γ的约束条件下，本文通过粒子群搜索算法得出γ的值.另外，本文还对所设计的极大极小控制器，与线性二次型高斯（Linear quadratic Gaussian，LQG）控制对比分析，用双水箱系统进行了仿真验证，发现在受攻击情况下本文所设计的控制器最终能够实现稳定控制，而LQG却不能.Abstract: As a remote control system, the cyber-physical system (CPS) relies mainly on wireless networks to realize the transmission of information from sensors to controllers and from controllers to actuators. Because of this characteristic, the control system of CPS is vulnerable to security threats. Starting with physical devices, the aim of this paper is to protect normal operation of physical entities in CPS system from the interference of network intrusion caused by malicious attacks. Taking the cyber-physical systems suffered packets scheduling attacks into consideration, its secure control was abstracted as a process of two person zero sum game. Based on two person zero sum model of non-cooperative game, the paper designed a min-max controller with a robust output-feedback under time-varying delays. In this paper, a parameterized soft constraint quadratic objective function was adopted. Also, interference attenuation factor γ was introduced in the controller design and the minimum value of the quadratic objective function was determined by the value of γ which guaranteed the stability control under the worst case. Within the constraint of γ, we get the value of γ through particle swarm search algorithm. In addition, the min-max controller is analyzed and compared with the linear quadratic Gaussian (LQG) control, and the simulation was conducted on a two tanks system. The result showed that the min-max controller can stabilize the attacked system, but LQG cannot.1) 本文责任编委 许斌
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图 1 无线传感器网络控制系统模型
(虚线表示无线网络, 实线表示有线网络)
Fig. 1 Model of wireless sensor network control system
(The dashed line shows the wireless network, and the solid line shows the wired network.)
图 5 可变延迟下的数据传输示意图
Fig. 5 A schematic diagram of data transmission under variable delay
表 1 水箱参数
Table 1 Water tank equipment parameters
名称 参数大小 设备质量 6.6 kg 模型尺寸$(H\times W\times L)$ 30.5 cm$\times$ 30.5 cm$\times$ 91.5 cm 泵流量常数 3.3 cm$^3$/(V$\cdot$s) 压力传感器灵敏度 6.1 cm/V 水箱高度 30 cm 水箱内部直径 4.45 cm 流出孔直径 0.48 cm 
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