CN107544472A - A kind of optimal switching false data method for implanting - Google Patents

A kind of optimal switching false data method for implanting Download PDF

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CN107544472A
CN107544472A CN201710935494.6A CN201710935494A CN107544472A CN 107544472 A CN107544472 A CN 107544472A CN 201710935494 A CN201710935494 A CN 201710935494A CN 107544472 A CN107544472 A CN 107544472A
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孙健
伍光宇
陈杰
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Beijing Institute of Technology BIT
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Abstract

本发明提供一种最优切换假数据注入方法,具体过程为:注入矩阵设计:向有限个子系统注入虚假数据的情形下,考虑所有可能的子系统注入组合,对不同的注入组合设计不同的注入矩阵;最优切换策略:在线计算注入矩阵的切换时刻,在切换时刻选取不同的注入矩阵,通过切换使二次性能指标时刻达到最大;最优假数据注入:通过所有子系统的状态信息构造最优的虚假数据,向相应的子系统注入最优的虚假数据。本发明提高了假数据注入方法的灵活性和有效性,可用于测试工业控制系统对于假数据注入的防御效果。

The present invention provides an optimal switching false data injection method, the specific process is: injection matrix design: in the case of injecting false data into a limited number of subsystems, consider all possible subsystem injection combinations, and design different injection combinations for different injection combinations matrix; optimal switching strategy: calculate the switching time of the injection matrix online, select different injection matrices at the switching time, and maximize the secondary performance index time through switching; optimal false data injection: construct the most The optimal false data is injected into the corresponding subsystem. The invention improves the flexibility and effectiveness of the false data injection method, and can be used to test the defense effect of the industrial control system for the false data injection.

Description

一种最优切换假数据注入方法An Optimal Handoff False Data Injection Method

技术领域technical field

本发明涉及工业控制系统、信息物理融合系统的安全性,针对工业控制系统、信息物理融合系统设计了一种最优切换假数据注入方法。The invention relates to the security of an industrial control system and a cyber-physical fusion system, and designs an optimal switching false data injection method for the industrial control system and the cyber-physical fusion system.

背景技术Background technique

工业控制系统广泛应用于电力、冶金、石化、铁路和航空等领域,并且与国家关键基础设施紧密相连。工业控制系统一旦发生重大的安全事件可能对依赖于它的物理系统的可靠、安全操作产生重大影响,不仅造成经济损失、威胁生命财产安全,而且还可能对国家安全造成威胁。工业控制系统已经是国家安全战略的重要组成部分,工业控制系统一旦受到恶意攻击,造成的损失将无法估计。Industrial control systems are widely used in fields such as electric power, metallurgy, petrochemical, railway and aviation, and are closely connected with national critical infrastructure. Once a major security incident occurs in an industrial control system, it may have a major impact on the reliable and safe operation of the physical system that depends on it, not only causing economic losses, threatening the safety of life and property, but also threatening national security. The industrial control system is already an important part of the national security strategy. Once the industrial control system is maliciously attacked, the losses caused will be incalculable.

传统的工业控制系统通常以厂区为单位,是相对孤立的、与外界通信较少。但随着互联网技术的普及与发展,特别是物联网技术的兴起,在企业综合自动化需求指引下,工业控制系统也向着网络化方向发展。现代工业制系统不再是信息孤岛,成为一种典型的信息物理融合系统。近年以来,针对工业控制系统的安全问题的案例报道屡见不鲜。如2010年的“震网”病毒入侵伊朗布什尔核电站,对西门子公司的数据采集与监控系统进行攻击,迫使伊朗的核计划一再推迟。欧美等国家已经把工控安全列为国家战略。近年来,工业控制系统安全也受到了我国行政管理部门和科研管理部门的高度重视,并纳入了相关的研究计划。The traditional industrial control system is usually based on the factory area, which is relatively isolated and has less communication with the outside world. However, with the popularization and development of Internet technology, especially the rise of Internet of Things technology, under the guidance of the comprehensive automation needs of enterprises, industrial control systems are also developing towards networking. The modern industrial system is no longer an isolated island of information, but has become a typical information-physical fusion system. In recent years, case reports on security issues of industrial control systems are common. For example, in 2010, the "Stuxnet" virus invaded Iran's Bushehr nuclear power plant and attacked Siemens' data collection and monitoring system, forcing Iran's nuclear program to be postponed repeatedly. Countries such as Europe and the United States have listed industrial control security as a national strategy. In recent years, the safety of industrial control systems has also been highly valued by the administrative and scientific research management departments of our country, and has been incorporated into relevant research plans.

工业控制系统的通信网络易受到黑客的入侵。入侵者通过突破工业防火墙,接入现场总线访问通讯网络,通过对通讯报文的窃听、阻塞、延时、篡改、注入、重放等手段。对网络上传输的传感数据、控制程序代码进行阻断或恶意修改。当攻击者隐蔽的接入控制器后,执行设计好的恶意程序,使执行器误动作来恶化被控对象的性能。研究工业控制系统的假数据注入方法,可以做到“知已知彼”、为更好的做好安全防御奠定良好的基础。研究假数据注入方法需要从系统理论的角度分析注入者的意图和策略。Yilin Mo等在文献(Falsedata injection attacks against state estimation in wireless sensor networks,in Proc.49th IEEE Conf.Decision and Control(CDC),2010,pp.5967-5972.)分析了如何将假数据注入部分传感器中,来改变稳态卡尔曼滤波器的估计值,并避免故障检测器报警。将假数据注入问题描述为一个含约束的优化问题,并得到其可达区域的上下界。Annarita Giani等在文献(Smart Grid Data Integrity Attacks.IEEE Transaction onSmart Grid.2013:4(3),pp.1244-1253.)中指出由于地理上的限制,同时向大量的功率测量仪注入虚假数据是不可能的。并提出了一种在向两个功率测量仪和向任意的功率测量仪注入两种情形下的所有不可检测的注入方法。Jinping Hao等在文献(Sparse MaliciousFalse Data Injection Attacks and Defense Mechanisms in Smart Grids.IEEETransactions on Industrial Informatics,2015:11(5),pp.1198-1209.)讨论了在可修改任意测量值和仅修改特定的状态变量两种情形下,如何向智能电网的广域测控系统中注入稀疏假数据。提出了一种搜索算法来寻找对假数据注入免疫的测量值集合来保护系统。Guangyu Wu等在文献(Optimal Data Integrity Attack on Actuators in Cyber-Physical Systems,American Control Conference(ACC),2016,pp.1160-1164.)分析了如何向控制系统的执行器注入虚假数据,使二次误差指标达到最优,并给出了最优性条件和问题的特解。Anibal Sanjab等在文献(Data Injection Attacks on Smart Grids WithMultiple Adversaries:A Game-Theoreti Perspective.IEEE Transactions on SmartGrid,2016:7(4),pp 2038-2048.)中引入了存在多个攻击者和一个防守者的Stackelberg博弈模型,防守者在决定保护哪些测量值前可预测攻击者的行为,并提出了一种分布式学习算法来寻找平衡点。Communication networks of industrial control systems are vulnerable to hackers. The intruder breaks through the industrial firewall, accesses the field bus to access the communication network, and uses methods such as eavesdropping, blocking, delaying, tampering, injecting, and replaying the communication messages. Block or maliciously modify the sensor data and control program codes transmitted on the network. When the attacker accesses the controller covertly, he executes the designed malicious program, making the executor malfunction and deteriorating the performance of the controlled object. Studying the false data injection method of the industrial control system can achieve "knowing what you know" and laying a good foundation for better security defense. Studying fake data injection methods requires analyzing the intention and strategy of the injector from the perspective of system theory. Yilin Mo et al. analyzed how to inject false data into some sensors in the literature (Falsedata injection attacks against state estimation in wireless sensor networks, in Proc.49th IEEE Conf. Decision and Control (CDC), 2010, pp.5967-5972.) , to change the estimate of the steady-state Kalman filter and avoid fault detector alarms. The fake data injection problem is described as a constrained optimization problem, and the upper and lower bounds of its reachable region are obtained. Annarita Giani et al. pointed out in the literature (Smart Grid Data Integrity Attacks.IEEE Transaction on Smart Grid.2013:4(3),pp.1244-1253.) that due to geographical restrictions, injecting false data into a large number of power measuring instruments at the same time is impossible. And a method for all undetectable injections under two situations of injecting into two power meters and injecting into an arbitrary power meter is proposed. In the literature (Sparse Malicious False Data Injection Attacks and Defense Mechanisms in Smart Grids. IEEETransactions on Industrial Informatics, 2015:11(5), pp.1198-1209.), Jinping Hao et al. How to inject sparse fake data into the wide-area measurement and control system of smart grid under the two situations of state variables. A search algorithm is proposed to find a set of measurements that are immune to fake data injection to protect the system. In the literature (Optimal Data Integrity Attack on Actuators in Cyber-Physical Systems, American Control Conference (ACC), 2016, pp.1160-1164.), Guangyu Wu et al. analyzed how to inject false data into the actuators of the control system, so that the secondary The error index is optimal, and the optimality condition and the special solution of the problem are given. Anibal Sanjab et al. introduced the existence of multiple attackers and a defense The defender's Stackelberg game model, the defender can predict the behavior of the attacker before deciding which measurements to protect, and a distributed learning algorithm is proposed to find the balance point.

在大规模的工业控制系统中,传感器、执行器节点往往分布在较广阔的地域内,同时入侵者的能量往往有限,不可能对所有的传感器或执行器节点同时注入假数据。因此,如何最优的选择注入假数据的次序是一个需要考虑的问题。In large-scale industrial control systems, sensor and actuator nodes are often distributed in a wider area, and the energy of intruders is often limited, so it is impossible to inject false data to all sensor or actuator nodes at the same time. Therefore, how to optimally select the order of injecting fake data is a problem that needs to be considered.

发明内容Contents of the invention

本发明的目的是针对包含多个子系统的大规模物理信息系统,提供一种最优切换假数据注入方法,该方法可任意选择每次注入的子系统数目,提供注入矩阵的设计方法和切换原则,以及假数据的设计规则,该方法为防御方法的设计提供测试手段。The purpose of the present invention is to provide a method of optimal switching false data injection for a large-scale physical information system including multiple subsystems, which can arbitrarily select the number of subsystems injected each time, and provide a design method and switching principle of the injection matrix , and the design rules of fake data, this method provides testing means for the design of defense methods.

本发明解决其技术问题的技术方案是:The technical scheme that the present invention solves its technical problem is:

一种最优切换假数据注入方法,具体过程为:A method for injecting optimal switching false data, the specific process is:

注入矩阵设计:向有限个子系统注入虚假数据的情形下,考虑所有可能的子系统注入组合,对不同的注入组合设计不同的注入矩阵;Injection matrix design: In the case of injecting false data into a limited number of subsystems, consider all possible injection combinations of subsystems, and design different injection matrices for different injection combinations;

最优切换策略:在线计算注入矩阵的切换时刻,在切换时刻选取不同的注入矩阵,通过切换使二次性能指标时刻达到最大;Optimal switching strategy: Calculate the switching time of the injection matrix online, select a different injection matrix at the switching time, and maximize the secondary performance index time through switching;

最优假数据注入:通过所有子系统的状态信息构造最优的虚假数据,向相应的子系统注入最优的虚假数据。Optimal false data injection: Construct optimal false data through state information of all subsystems, and inject optimal false data into corresponding subsystems.

进一步地,本发明所述二次性能评价指标为:Further, the secondary performance evaluation index of the present invention is:

其中,为有限时间区间,权矩阵S、Q为n×n的半正定权矩阵,权矩阵R为m×m的正定权矩阵,xc为n个假数据注入系统的状态,ua为注入的m维假数据向量。in, is a finite time interval, the weight matrix S and Q are n×n semi-positive definite weight matrices, the weight matrix R is a m×m positive definite weight matrix, x c is the state of n fake data injected into the system, and u a is the injected m dimensional dummy data vector.

进一步地,本发明所述注入矩阵设计:设注入矩阵的形式为i=1,…,N,为m维行向量,j=1,…,n,n为假数据注入系统的个数,r为同一时间段内有能力同时注入虚假数据的子系统的个数;任意设定注入矩阵中r个非零行向量。Further, the injection matrix design of the present invention: Let the form of the injection matrix be i=1,...,N, is an m-dimensional row vector, j=1,...,n, n is the number of false data injection systems, and r is the number of subsystems capable of injecting false data at the same time within the same period of time; r non-zero row vectors in the injection matrix are arbitrarily set.

进一步地,本发明最优切换策略:通过极大值原理求解最优切换时刻使二次性能指标达到最大,获得注入矩阵的在线切换条件为Furthermore, the optimal switching strategy of the present invention: solve the optimal switching time through the maximum value principle to maximize the secondary performance index, and obtain the online switching condition of the injection matrix as

其中,为有限时间范围,xc(t0)、xc(tf)分别表示在t0和tf时刻n个假数据注入系统的状态,λ(tf)表示tf时刻协态变量。in, is a finite time range, x c (t 0 ), x c (t f ) represent the state of n fake data injected into the system at time t 0 and t f respectively, and λ(t f ) represents the co-state variable at time t f .

进一步地,本发明最优虚假数据注入为:Further, the optimal false data injection of the present invention is:

其中,ua为最优虚假数据,即注入的m维假数据向量,xc为假数据注入系统的状态,Pi为代数里卡提方程的解;Among them, u a is the optimal false data, that is, the injected m-dimensional false data vector, x c is the state of the false data injected into the system, and P i is the solution of the algebraic Riccati equation;

其中,A为n×n的系统矩阵。Among them, A is an n×n system matrix.

有益效果Beneficial effect

第一,本发明最优假数据构造为状态反馈形式,便于实现,同时本发明切换策略可在线实时计算,便于得到全局最优解。First, the optimal false data of the present invention is constructed in the form of state feedback, which is easy to implement, and the switching strategy of the present invention can be calculated online in real time, which is convenient for obtaining the global optimal solution.

第二,本发明通过篡改包含控制、传感等信息的传输数据,改变控制系统的动态性能,适用于测试工业控制系统、信息物理融合系统对于假数据注入的防御效果,为防御方法的设计提供测试手段。Second, the present invention changes the dynamic performance of the control system by tampering with the transmission data containing information such as control and sensing, and is suitable for testing the defense effect of industrial control systems and cyber-physical fusion systems on false data injection, providing a basis for the design of defense methods. means of testing.

附图说明Description of drawings

图1为本发明最优切换假数据注入方法的流程图;Fig. 1 is the flow chart of optimal switching false data injection method of the present invention;

图2是一个包含3个子系统的物理信息系统和攻击者的结构图;Figure 2 is a structural diagram of a physical information system and an attacker including 3 subsystems;

图3是三种注入组合的切换时间图;Figure 3 is a switching time diagram of three injection combinations;

图4是向系统注入假数据后的状态轨迹图。Figure 4 is a state trajectory diagram after injecting fake data into the system.

具体实施方式detailed description

下面详细描述本发明的实施例,所述实施例的示例在附图中示出。下面通过参考附图描述的实施例是示例性的,仅用于解释本发明,而不能理解为对本发明的限制。Embodiments of the invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

假定一个健康系统的模型为:Suppose a model of a healthy system is:

假数据注入系统的模型为:The model of fake data injection system is:

其中,xc为n维列向量,分别表示n个假数据注入系统的状态,ua为注入的m维假数据向量。假定{A,Ba}是可控的。在有限时间内,定义二次性能评价指标为:Among them, x c is an n-dimensional column vector, which respectively represent the states of n fake data injected into the system, and u a is an injected m-dimensional fake data vector. Suppose {A,B a } is controllable. for a limited time Inside, define the secondary performance evaluation index as:

其中,A为n×n的系统矩阵,Ba为m×m的注入矩阵,其结构代表了注入方向。权矩阵S、Q为n×n的半正定权矩阵,权矩阵R为m×m的正定权矩阵。Among them, A is an n×n system matrix, B a is an m×m injection matrix, and its structure represents the injection direction. The weight matrices S and Q are positive semi-definite weight matrices of n×n, and the weight matrix R is positive definite weight matrix of m×m.

本发明一种最优切换假数据注入方法,如图1所示,具体过程为:A kind of optimal switching false data injection method of the present invention, as shown in Figure 1, specific process is:

(1)注入矩阵设计:(1) Injection matrix design:

假定注入者可在线监听所有子系统的状态信息,但由于注入者能量有限,或由于子系统分布区域较广,注入者无法在同一时间段内向所有子系统注入虚假数据,仅有能力同时向r个子系统注入。那么注入矩阵共有种形式可供选择,且每个注入矩阵有r个非零行。不同的子系统的注入组合将带来不同的注入效果,为了达到最优的效果,注入者应在不同的时刻向不同的子系统注入虚假数据,以最大化二次性能评价指标。It is assumed that the injector can monitor the state information of all subsystems online, but due to the limited energy of the injector or the wide distribution of subsystems, the injector cannot inject false data into all subsystems at the same time, and only has the ability to simultaneously inject r Subsystem injection. Then the injected matrix has There are several forms to choose from, and each injection matrix has r non-zero rows. The injection combination of different subsystems will bring different injection effects. In order to achieve the optimal effect, the injector should inject false data into different subsystems at different times to maximize the secondary performance evaluation index.

定义注入矩阵:i=1,…,N,为m维行向量,j=1,…,n。注入者可任意设计注入矩阵的非零行向量的值来确定不同的注入矩阵。Define the injection matrix: i=1,...,N, is an m-dimensional row vector, j=1,...,n. The injector can arbitrarily design the values of the non-zero row vectors of the injection matrix to determine different injection matrices.

(2)最优切换策略:(2) Optimal switching strategy:

通过极大值原理求解最优切换注入问题,得到协态方程:The optimal switching injection problem is solved by the maximum value principle, and the costate equation is obtained:

状态方程:Equation of state:

及边界条件:and boundary conditions:

λ(tf)=Sxc(tf)λ(t f )=Sx c (t f )

注入矩阵的在线切换条件为:The online switching condition of injection matrix is:

已知xc(t0)、xc(tf)和λ(tf),求解两点边值问题即可得到协态变量初值λ(t0)和切换时刻。Given x c (t 0 ), x c (t f ) and λ(t f ), the initial value of the costate variable λ(t 0 ) and the switching time can be obtained by solving the two-point boundary value problem.

本发明通过求解代数里卡提方程得到无限时间性能评价指标下的最优状态反馈,通过计算协态变量的分量和来确定不同注入矩阵间的最优切换次序。The invention obtains the optimal state feedback under the infinite time performance evaluation index by solving the algebraic Riccati equation, and determines the optimal switching sequence between different injection matrices by calculating the component sum of co-state variables.

(3)最优假数据注入:(3) Optimal fake data injection:

向相应的子系统中注入最优假数据:Inject optimal fake data into the corresponding subsystem:

当tf→∞,协态变量λ(t)=Pixc(t),Pi为代数里卡提方程的解,满足:When t f →∞, the co-state variable λ(t)=P i x c (t), and P i is the solution of the algebraic Riccati equation, which satisfies:

采用合适的Q、R和Bi的组合,使里卡提方程有解,最优假数据变为:Using a suitable combination of Q, R and Bi , the Riccati equation has a solution, and the optimal false data becomes:

ua构造为状态反馈的形式。u a is constructed as a form of state feedback.

对此过程进行离散化实现,设采样周期为T。Discretize this process, and set the sampling period as T.

Step 1:初始化i(0)和xc(0)Step 1: Initialize i(0) and x c (0)

λ(0)=Pi(0)xc(0)λ(0)=P i(0) x c (0)

Step 2:循环计算:Step 2: Loop calculation:

λ(k)=Pi(k)xc(k)λ(k)=P i(k) x c (k)

下面参照附图,对本发明中的实施进行详细的说明。The implementation of the present invention will be described in detail below with reference to the accompanying drawings.

图2是注入者对三个子系统互联的物理信息系统注入虚假数据的结构图。注入者将虚假数据注入到子系统的动态方程中,每次仅向两子系统注入,系统参数选取如下:Figure 2 is a structural diagram of an injector injecting false data into a physical information system interconnected with three subsystems. The injector injects false data into the dynamic equations of the subsystems, and injects only two subsystems each time. The system parameters are selected as follows:

初始条件:x0=[2,2,2]T,λ(0)=P1x0=[0.7,0.65,0.65]T。注入矩阵设计为如下形式:Initial conditions: x 0 =[2,2,2] T , λ(0)=P 1 x 0 =[0.7,0.65,0.65] T . The injection matrix is designed as follows:

三个注入矩阵对应的代数里卡提方程的解为:The solutions to the algebraic Riccati equations corresponding to the three injected matrices are:

图3是三种注入组合的切换时间图。Figure 3 is a switching time diagram of three injection combinations.

图4是向系统注入假数据后的状态轨迹图。Figure 4 is a state trajectory diagram after injecting fake data into the system.

从图中可以看出,被注入子系统轨迹严重偏离健康系统的轨迹,但最终仍趋于稳态。最优切换时间和注入矩阵的选取均在线获得,由此得到的最优次序对应的性能评价指标优于其他切换次序。It can be seen from the figure that the trajectory of the injected subsystem deviates severely from that of the healthy system, but eventually tends to a steady state. The optimal switching time and the selection of the injection matrix are obtained online, and the performance evaluation index corresponding to the optimal sequence is better than other switching sequences.

以上所述的仅为本发明的较佳实施例而已,本发明不仅仅局限于上述实施例,凡在本发明的精神和原则之内所做的局部改动、等同替换、改进等均应包含在本发明的保护范围之内。What has been described above is only a preferred embodiment of the present invention, and the present invention is not limited to the above-mentioned embodiment, and all local changes, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in within the protection scope of the present invention.

Claims (5)

1.一种最优切换假数据注入方法,其特征在于,具体过程为:1. A method for optimally switching false data injection, characterized in that the specific process is: 注入矩阵设计:向有限个子系统注入虚假数据的情形下,考虑所有可能的子系统注入组合,对不同的注入组合设计不同的注入矩阵;Injection matrix design: In the case of injecting false data into a limited number of subsystems, consider all possible injection combinations of subsystems, and design different injection matrices for different injection combinations; 最优切换策略:在线计算注入矩阵的切换时刻,在切换时刻选取不同的注入矩阵,通过切换使二次性能指标时刻达到最大;Optimal switching strategy: Calculate the switching time of the injection matrix online, select a different injection matrix at the switching time, and maximize the secondary performance index time through switching; 最优假数据注入:通过所有子系统的状态信息构造最优的虚假数据,向相应的子系统注入最优的虚假数据。Optimal false data injection: Construct optimal false data through state information of all subsystems, and inject optimal false data into corresponding subsystems. 2.根据权利要求1所述最优切换假数据注入方法,其特征在于,所述二次性能评价指标为:2. according to the described optimal switching false data injection method of claim 1, it is characterized in that, described secondary performance evaluation index is: <mrow> <mi>max</mi> <mi> </mi> <mi>J</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mi>x</mi> <mi>c</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>Sx</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msubsup> <mo>&amp;Integral;</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <msub> <mi>t</mi> <mi>f</mi> </msub> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mi>c</mi> <mi>T</mi> </msubsup> <msub> <mi>Qx</mi> <mi>c</mi> </msub> <mo>-</mo> <msubsup> <mi>u</mi> <mi>a</mi> <mi>T</mi> </msubsup> <msub> <mi>Ru</mi> <mi>a</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow> <mrow><mi>max</mi><mi></mi><mi>J</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msubsup><mi>x</mi><mi>c</mi><mi>T</mi></msubsup><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><msub><mi>Sx</mi><mi>c</mi></msub><mrow><mo>(</mo><msub><mi>t</mi><mi>f</mi></msub><mo>)</mo></mrow><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msubsup><mo>&amp;Integral;</mo><msub><mi>t</mi><mn>0</mn></msub><msub><mi>t</mi><mi>f</mi></msub></msubsup><mrow><mo>(</mo><msubsup><mi>x</mi><mi>c</mi><mi>T</mi></msubsup><msub><mi>Qx</mi><mi>c</mi></msub><mo>-</mo><msubsup><mi>u</mi><mi>a</mi><mi>T</mi></msubsup><msub><mi>Ru</mi><mi>a</mi></msub><mo>)</mo></mrow><mi>d</mi><mi>t</mi></mrow> 其中,为有限时间区间,权矩阵S、Q为n×n的半正定权矩阵,权矩阵R为m×m的正定权矩阵,xc为n个假数据注入系统的状态,ua为注入的m维假数据向量。in, is a finite time interval, the weight matrix S and Q are n×n semi-positive definite weight matrices, the weight matrix R is a m×m positive definite weight matrix, x c is the state of n fake data injected into the system, and u a is the injected m dimensional dummy data vector. 3.根据权利要求2所述最优切换假数据注入方法,其特征在于,所述注入矩阵设计:设注入矩阵的形式为i=1,…,N,为m维行向量,j=1,…,n,n为假数据注入系统的个数,r为同一时间段内有能力同时注入虚假数据的子系统的个数;任意设定注入矩阵中r个非零行向量。3. according to the described optimum switching false data injection method of claim 2, it is characterized in that, described injection matrix design: let the form of injection matrix be i=1,...,N, is an m-dimensional row vector, j=1,...,n, n is the number of false data injection systems, and r is the number of subsystems capable of injecting false data at the same time within the same period of time; r non-zero row vectors in the injection matrix are arbitrarily set. 4.根据权利要求3所述最优切换假数据注入方法,其特征在于,最优切换策略:通过极大值原理求解最优切换时刻使二次性能指标达到最大,获得注入矩阵的在线切换条件为4. according to claim 3 described optimal switching false data injection method, it is characterized in that, optimal switching strategy: solve optimal switching moment by maximum value principle and make secondary performance index reach maximum, obtain the online switching condition of injection matrix for <mrow> <mi>i</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>arg</mi> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mi>N</mi> </mrow> </munder> <mi>&amp;lambda;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>B</mi> <mi>i</mi> </msub> <msup> <mi>R</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>B</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>&amp;lambda;</mi> <msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> </mrow> <mrow><mi>i</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>arg</mi><munder><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>...</mo><mi>N</mi></mrow></munder><mi>&amp;lambda;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msub><mi>B</mi><mi>i</mi></msub><msup><mi>R</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msubsup><mi>B</mi><mi>i</mi><mi>T</mi></msubsup><mi>&amp;lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup></mrow> 其中,为有限时间范围,xc(t0)、xc(tf)分别表示在t0和tf时刻n个假数据注入系统的状态,λ(tf)表示tf时刻协态变量。in, is a finite time range, x c (t 0 ), x c (t f ) represent the state of n fake data injected into the system at time t 0 and t f respectively, and λ(t f ) represents the co-state variable at time t f . 5.根据权利要求4所述最优切换假数据注入方法,其特征在于,最优虚假数据注入为:5. according to the described optimal switching false data injection method of claim 4, it is characterized in that, optimal false data injection is: <mrow> <msub> <mi>u</mi> <mi>a</mi> </msub> <mo>=</mo> <msup> <mi>R</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>B</mi> <mi>i</mi> <mi>T</mi> </msubsup> <msub> <mi>P</mi> <mi>i</mi> </msub> <msub> <mi>x</mi> <mi>c</mi> </msub> </mrow> <mrow><msub><mi>u</mi><mi>a</mi></msub><mo>=</mo><msup><mi>R</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msubsup><mi>B</mi><mi>i</mi><mi>T</mi></msubsup><msub><mi>P</mi><mi>i</mi></msub><msub><mi>x</mi><mi>c</mi></msub></mrow> 其中,ua为最优虚假数据,即注入的m维假数据向量,xc为假数据注入系统的状态,Pi为代数里卡提方程的解;Among them, u a is the optimal false data, that is, the injected m-dimensional false data vector, x c is the state of the false data injected into the system, and P i is the solution of the algebraic Riccati equation; <mrow> <msup> <mi>A</mi> <mi>T</mi> </msup> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>P</mi> <mi>i</mi> </msub> <msup> <mi>A</mi> <mi>T</mi> </msup> <mo>+</mo> <msub> <mi>P</mi> <mi>i</mi> </msub> <msub> <mi>B</mi> <mi>i</mi> </msub> <msup> <mi>R</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>B</mi> <mi>i</mi> <mi>T</mi> </msubsup> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>+</mo> <mi>Q</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow><msup><mi>A</mi><mi>T</mi></msup><msub><mi>P</mi><mi>i</mi></msub><mo>+</mo><msub><mi>P</mi><mi>i</mi></msub><msup><mi>A</mi><mi>T</mi></msup><mo>+</mo><msub><mi>P</mi><mi>i</mi></msub><msub><mi>B</mi><mi>i</mi></msub><msup><mi>R</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msubsup><mi>B</mi><mi>i</mi><mi>T</mi></msubsup><msub><mi>P</mi><mi>i</mi></msub><mo>+</mo><mi>Q</mi><mo>=</mo><mn>0</mn></mrow> 其中,A为n×n的系统矩阵。Among them, A is an n×n system matrix.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113325705A (en) * 2021-04-30 2021-08-31 同济大学 Slamming-slamming control method of linear switching system
CN119376380A (en) * 2024-12-27 2025-01-28 万维检验认证集团有限公司 A vehicle safety performance testing and certification method and system

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102761122A (en) * 2012-07-06 2012-10-31 华北电力大学 Defense method of false data injection attack of power state estimation system
WO2012154664A2 (en) * 2011-05-06 2012-11-15 University Of North Carolina At Chapel Hill Methods, systems, and computer readable media for detecting injected machine code
CN104573510A (en) * 2015-02-06 2015-04-29 西南科技大学 Smart grid malicious data injection attack and detection method
CN105791280A (en) * 2016-02-29 2016-07-20 西安交通大学 A Method Against Data Integrity Attacks in Power System DC State Estimation
CN107016236A (en) * 2017-03-23 2017-08-04 新疆电力建设调试所 Power network false data detection method for injection attack based on non-linear measurement equation

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2012154664A2 (en) * 2011-05-06 2012-11-15 University Of North Carolina At Chapel Hill Methods, systems, and computer readable media for detecting injected machine code
CN102761122A (en) * 2012-07-06 2012-10-31 华北电力大学 Defense method of false data injection attack of power state estimation system
CN104573510A (en) * 2015-02-06 2015-04-29 西南科技大学 Smart grid malicious data injection attack and detection method
CN105791280A (en) * 2016-02-29 2016-07-20 西安交通大学 A Method Against Data Integrity Attacks in Power System DC State Estimation
CN107016236A (en) * 2017-03-23 2017-08-04 新疆电力建设调试所 Power network false data detection method for injection attack based on non-linear measurement equation

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
GUANGYU WU ET AL: "Optimal Switching Integrity Attacks in Cyber-Physical System", 《2017 32ND YOUTH ACADEMIC ANNUAL CONFERENCE OF CHINESE ASSOCIATION OF AUTOMATION(YAC)》 *
李春玲: "基于线性二次型最优控制的光伏并网发电系统的研究", 《中国博士学位论文全文数据库(电子期刊)工程科技II辑》 *
现代工程数学手册编委会: "《现代工程数学手册》", 30 June 1990, 华南理工大学出版社 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113325705A (en) * 2021-04-30 2021-08-31 同济大学 Slamming-slamming control method of linear switching system
CN113325705B (en) * 2021-04-30 2022-09-30 同济大学 A bang-bang control method for a linear switching system
CN119376380A (en) * 2024-12-27 2025-01-28 万维检验认证集团有限公司 A vehicle safety performance testing and certification method and system

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