A network attack resilient constraint tracking control method for cyber-physical systems

Abstract

The application discloses a network attack resilience constraint tracking control method for a network physical system and belongs to the network security field; the algorithm is aimed at a network physical system with uncertainty and possible network attacks, verifies the resilience of the controlled system to network attack inputs and other deception or mixed threat attacks through an original controller design, proposes three game rules of a non-cooperative game and two Stackelberg competitions to select optimal control related parameters, and proves that the optimal selection is unique in the three rules. The network physical system has the ability to resist network attack inputs and other deception or mixed threat attacks by using the method.

Description

Technical Field

[0001] This invention relates to the field of network security technology, specifically to a method for elastic constraint tracking and control of network attacks on network physical systems. Background Technology

[0002] A Cyber-Physical System (CPS) is a mechanism for controlling or monitoring systems based on computer algorithms. The entire system is integrated with a network and is often referred to as the large-scale, geographically dispersed, complex, and heterogeneous Internet of Things (IoT). In recent years, the development and deployment of various types of Cyber-Physical Systems have grown exponentially, bringing tremendous impacts to all aspects of daily life, such as in power grids, transportation systems, healthcare equipment, and home appliances. Many such systems are deployed in critical infrastructure, life support facilities, or other locations extremely important to our daily lives.

[0003] The diversity of CPS applications deployed across networks in the Internet of Things (IoT) makes them vulnerable to cyber and physical attacks at different levels of systems, particularly in message transmission during smart manufacturing processes. This introduces security vulnerabilities into CPS applications, causing them to become uncontrollable and harm those who rely on them. Summary of the Invention

[0004] The purpose of this invention is to provide a network attack elastic constraint tracking and control method for network physical systems, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a network attack elastic constraint tracking and control method for network physical systems, step 1: establishing a network physical system model, considering that the network physical system is subjected to a set of network attacks with unknown priorities:

[0006]

[0007] In the formula: t∈R is time, q(t)∈R n It is a coordinate. It's speed. It is acceleration. It is an uncertain parameter. The unknown network attack input, δ(t)∈R, is an uncertain attack factor caused by deception and / or mixed threat attacks, τ(t)∈R. n It controls the input. The sets ∑ and Υ a It is compact, representing σ and v respectively. a The possible region to which it belongs. Furthermore, M(q, σ, t) is the inertia matrix. It is the Coriolis force / centrifugal force, and g(q, σ, t) is the gravitational force. This is the input matrix for a network attack. The matrix / vector is M(q, σ, t). , g(q, σ, t) and Having appropriate dimensions. Functions M(·), C(·), g(·), B a (·) indicates a continuous sequence;

[0008] The following constraints are proposed.

[0009]

[0010] in yes The i-th component, A li (·) and c l (·) are all C 1 , m≤n. These are the first-order forms of constraints. Each constraint may be complete or incomplete. Constraints can be represented in matrix form.

[0011]

[0012] where A=[A li ] m×n c = [c1 c2 … c m ] T

[0013] Step 2: Design an adaptive robust controller with elastic constraints:

[0014]

[0015] In the formula: Indicates the constraint following error by 0 represents the "nominal" part of M, the function It is continuous, P∈R m×m P > 0, κ > 0 is a scalar design parameter;

[0016]

[0017] In the formula: It is a scalar design parameter. It is a known function;

[0018] An adaptive robust controller with elastic constraints is:

[0019]

[0020] Considering a cyber-physical system, the controller enables the system to have the following performance characteristics:

[0021] (101) Uniform boundedness: For any r > 0, there exists a d(r) < ∞ such that if then for all t ≥ t0,

[0022] (102) Uniform ultimate boundedness: For any r > 0 and there exists a d > 0 such that for any when where

[0023] Step 3: Analyzing the elasticity in the constraint tracking performance:

[0024] Uniform boundedness guarantees that the constraint after the error β is limited within the region d(r) when t ≥ t0. Uniform ultimate boundedness performance guarantees that the error β is small enough, i.e., after a finite time the constraint is within the region Both d(r) and are related to R. For all σ ∈ ∑, v a ∈ Υ a , if there exists a region Q such that then the controlled system is elastic to the attack factor δ and cyber-attack input;

[0025] Step 4: Game-optimal selection of controller design parameters:

[0026] Three game rules of non-cooperative game and two Stackelberg competition are proposed to select the optimal control-related parameters;

[0027] Further, there are two interpretations of the constraint condition mentioned in Step 1. First, the constraint can be passive, that is, the environment or structure provides the constraint force to make the system comply with the constraint. Second, the constraint can be active, that is, the control input of the system provides the required force to meet the constraint.

[0028] Further, the second constraint method is adopted, and the constraint is differentiated with respect to t:

[0029]

[0030] Further, the second-order form of the constraint condition can be rewritten as:

[0031]

[0032] where l = 1, …, m;

[0033]

[0034] where b = [b1 b2... b m ] T ;

[0035] Further, before establishing the adaptive robust controller with elastic constraints in step 2, we first need to perform uncertainty decomposition and network attack input matrix decomposition;

[0036] Further explanation of uncertainty decomposition, we first make the following assumptions;

[0037] Assumption 1. For each (q, t) ∈ R n × R, σ ∈ ∑, M(q, σ, t) > 0, this assumption is valid in most applications; we now consider the uncertainty when designing the control τ. Let denote the "nominal" part, and the function is continuous.

[0038] Let

[0039] Then we can get

[0040] ΔD(q, σ, t) = D(q, t)E(q, σ, t)

[0041] Assumption 2: For each (q, t) ∈ R n × R, A(q, t) is full rank. This means that A(q, t)A T (q, t) is invertible.

[0042] Assumption 3: Based on assumption 2, for a given P ∈ R m×m , P > 0, let

[0043]

[0044] There is a constant ρ E > -1, which may be unknown, such that for all (q, t) ∈ R n × R,

[0045]

[0046] Here λ m (·) is the eigenvalue of the matrix.

[0047] Since the uncertainty bound ∑ is unknown, the constant ρ E is unknown. When there is no uncertainty, E = 0, W = 0, so we can choose ρ E ​=0. Therefore, through continuity, this assumption imposes the effects of uncertainty on M and Within a certain threshold of the possible deviation between them, this is unidirectional.

[0048] To further explain the decomposition of the network attack input matrix, we propose a decomposition method for the network attack input matrix B. a The decomposition, network attacks through B a This affects CPS. Assumption 2 guarantees (AD)(AD) T Under the premise of reversibility, let

[0049]

[0050] here

[0051]

[0052]

[0053] Theorem 1: According to Assumption 2, then for any uncertainty v

[0054]

[0055] Proof: We have

[0056]

[0057] This means that network attack input v passes through The input matrix will not affect system performance.

[0058] Furthermore, for cyber-physical systems with uncertainties and cyberattack inputs, a resilient and robust control method can be proposed, as presented below;

[0059] Assumption 4: There exist known or unknown... δ >0, such that for all t∈R, δ ≤δ(t)≤1;

[0060] Assumption 5: There exists a known or unknown constant vector. and a known function Makes all σ∈∑,v a ∈Υ a ,

[0061]

[0062] Here, the function Π(·) can be interpreted as the structure of an uncertain bound. The constant vector α may be related to the boundary sets ∑ and Υ. a related;

[0063] Let denote the constraint-following error Under the assumption 3, let

[0064]

[0065] where κ > 0 is a scalar design parameter. Under the assumption 5, let Let

[0066]

[0067] is a scalar design parameter.

[0068] Now, consider the control

[0069]

[0070] Here, the approximate constraint-following problem is considered. That is, β ≠ 0 (hence ). This can be due to modeling uncertainty. In addition, the system can not start on the constraint manifold at the beginning (i.e., β ≠ 0 when t = t0);

[0071] Let

[0072] Consider the system (1) under the assumptions 1-5, the control (12) makes the system have the following properties:

[0073] (1) Uniform boundedness: For any r > 0, there exists a d(r) < ∞ such that if then for all t ≥ t0,

[0074] (2) Uniform ultimate boundedness: For any r > 0 and there exists a d > 0 such that for any when where

[0075] Further, the proof of the uniform boundedness and the uniform ultimate boundedness is given as follows:

[0076] Let V = β T Pβ.(13)

[0077] First, by (13), we have

[0078]

[0079] By decomposing M -1 = D + ΔD and We have.

[0080]

[0081] From equation (8), By equation (9) and

[0082]

[0083] Based on equation (10)

[0084]

[0085] By And performing matrix cancellation, we have

[0086]

[0087] By ΔD = DE, using Rayleigh principle, we have

[0088]

[0089] By ΔD = DE,

[0090]

[0091] By similar algebraic manipulation as pi, we can prove

[0092]

[0093] In addition

[0094]

[0095] Combining equation (21) and equation (22),

[0096]

[0097] Therefore, using equation (16), equation (19) and equation (23), we have

[0098]

[0099] If

[0100]

[0101] If

[0102]

[0103] Thus we can conclude that for all

[0104]

[0105] where After invoking the standard parameters,

[0106]

[0107]

[0108] where γ1= λ min (P), γ2= λ max (P), and, for any Uniform ultimate boundedness also follows from

[0109]

[0110]

[0111] Further, the elasticity of the constraint tracking performance in Step 3 is divided into two cases, the first case is without DOS (denial of service) attack and network attack input, and the second case is with DOS and network attack input;

[0112] Further, if there is no DoS (denial of service) attack, then δ(t)≡1. If there is no network attack input, then v a (t)≡0. In this special case, we reduce the value of R because it only needs to consider the bound of σ, not the bound of v a , which in turn reduces the value of η (denoted as η reduced below). Then R simplifies to

[0113]

[0114] The reduction of R in turn reduces d(r) (for r>R) and d . That is, both the uniformly bounded region and the uniformly ultimately bounded region will be reduced, which means the enhancement of the constraint after performance. In addition, if η reduced and ρ E are known, then a suitable R reduced can be chosen by choosing a suitable κ, which is a contrast to the design parameters;

[0115] Further, when the cyber-physical system is subjected to DoS attack and other network attacks, the obtained R is as shown in (29), where δ ≤1, The impact of the attack needs to be explained. This means a worsening of the performance constraints because R in (29) is greater than R reduced On the other hand, it is worth noting that R in (29) is always present in any δ > 0 and any finite This is related to the bounds on σ and v a ; this means that the controlled CPS is resilient to DoS attacks and cyber attack inputs;

[0116] Further, in step 4 the non-cooperative game is a zero-sum game and Stackelberg is a strategic game;

[0117] Further, the optimal control parameter selection with non-cooperative game, assume that there are two players 1 and 2, player 1 is κ, player 2 is δ, player 1 represents the interests of the system, and player 2 represents the interests of the network attacker; let

[0118]

[0119] The first term is related to the size of the uniformly bounded and uniformly ultimately bounded region, which is obtained by replacing δ R in (29) with δ. The second term is related to the control cost, ω > 0 is a weight factor,

[0120] The cost of player 1 is

[0121] J1(κ, δ) = J(κ, δ) (34)

[0122] The cost of player 2 is

[0123] J2(κ, δ) = -J(κ, δ).(35)

[0124] Each player intends to make his own decision to minimize his own cost;

[0125] Obviously, J1(κ, δ) + J2(κ, δ) = 0, which means that this is a two-person zero-sum game.

[0126] Definition 2: Let the allowed decision regions of players 1 and 2 be represented as D1 = (0, ∞) and D2 = [ δ , 1] respectively;

[0127] Consider a decision pair (κ * , δ * ) ∈ D1 × D2. For all κ ∈ D1 and δ ∈ D2,

[0128] J1(κ * , δ * ) ≤ J1(κ, δ* ), J2(κ * , δ * ) ≤ J2(κ * , δ) (36)

[0129] Definition 3: A decision pair (κ * , δ * ) ∈ D1 x D2 is a saddle point if for all κ ∈ D1 and δ ∈ D2,

[0130] J(κ * , δ) ≤ J(κ * , δ * ) ≤ J(κ, δ * ) (37)

[0131] Lemma 1: Consider a two-person zero-sum game. A saddle point is always a Nash equilibrium and vice versa;

[0132] Proof:

[0133] Suppose (κ * , δ * ) ∈ D1 x D2 is a saddle point:

[0134] J(κ * , δ) ≤ J(κ * , δ * ) ≤ J(κ, δ * ) (38)

[0135] Since J = J1, we have:

[0136] J(κ * , δ * ) ≤ J(κ, δ * ) or J1(κ * , δ * ) ≤ J1(κ, δ * ).

[0137] Since J = -J2, we also have

[0138] J(κ * , δ) ≤ J(κ * , δ * ) or -J2(κ * , δ) ≤ -J2(κ * , δ * ).

[0139] The latter result is, dropping the negative sign and reversing the inequality,

[0140] J2(κ * , δ) ≥ J2(κ * , δ * )

[0141] Thus, the saddle point is always a Nash equilibrium; the converse can be proved in the same way.

[0142] This lemma shows that the Nash equilibrium can be solved by analyzing the single cost J (by finding its minima and maxima) rather than analyzing J1 and J2 separately.

[0143] Now we solve the Nash equilibrium, we use Lemma 1 to analyze J individually; taking the derivative, we have

[0144]

[0145]

[0146] where

[0147]

[0148] Thus

[0149]

[0150] For all κ ∈ D1, δ ∈ D2, thus, by equation (42),

[0151] δ * = δ .(43)

[0152] By we get

[0153]

[0154] This means:

[0155]

[0156] Since δ = δ δ , we solve for κ * :

[0157]

[0158] We note that when κ = κ * , δ = δ *

[0159]

[0160] Thus, (κ * , δ * ) is indeed a Nash equilibrium.

[0161] Further, using Stackelberg competition to select optimal control parameters,​

[0162] The "optimal" solution is based on the "rules" of the game.

[0163] "Best" in one game does not mean best in another game. Thus, to make a comparison, we consider another game: Stackelberg competition.

[0164] Stackelberg competition is a strategic game in which a leader moves first, and then followers move sequentially. The leader must know in advance that the followers observe his actions. By understanding the leader's actions, the followers react with corresponding rational actions.

[0165] We consider two possible choices for the leader and the follower

[0166] (1) Player 1 is the leader and player 2 is the follower: For any given action K of player 1, the follower (player 2) decides to choose the corresponding action d to minimize J2 (or maximize J). That is, based on (33), for a given K, player 2 always chooses

[0167] d = arg min J2 (K, d) (39) δ

[0168] Knowing this is what player 2 will do, player 1 chooses K to minimize

[0169]

[0170] This means, by the same analysis as (39)-(46),

[0171]

[0172] Stackelberg strategies (47) and (49) are the same as Nash equilibria (43) and (46).

[0173] (2) Player 2 is the leader and player 1 is the follower: For any given action d of player 2 (the leader), player 1 (the follower) decides to choose the corresponding action K to minimize J1. That is, according to (33), for a given d, player 1 always chooses K to minimize

[0174]

[0175] This means, by the same analysis as (39)-(46), K = arg min J1 (K, d) (45)

[0176]

[0177] ​Knowing this is the way of the player 1, the player 2 chooses delta to minimize J(kappa, delta), which means delta = 0 δ

[0178] According to this selection, the player 1 chooses, by The solution of kappa

[0179]

[0180] This Stackelberg strategy (52) and (53) is the same as the previous (47) and (49), and also the same as the Nash equilibrium (43) and (46);

[0181] The game theory framework requires that, after analyzing the three game rules (i.e., one non-cooperative game rule and two Stackelberg competition rules), there is a unique "optimal" choice of the control design parameter kappa.

[0182] Compared with the prior art, the beneficial effects of the present application are:

[0183] 1、The present application is aimed at a networked physical system with uncertainty and possible network attack, and verifies the resilience of the controlled system to network attack input and other deception or hybrid threat attacks through an innovative controller design; three game rules of a non-cooperative game and two Stackelberg competitions are proposed to select the optimal control involved parameter, and it is proved that the optimal choice is unique among the three rules. The networked physical system has the ability to resist network attack input and other deception or hybrid threat attacks by using the method of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0184] Figure 1 is a flowchart of the present application;

[0185] Figure 2 is a translation / tilt device diagram installed on a UA V of the present application;

[0186] Figure 3 is a configuration diagram of the translation / tilt device network control system of the present application;

[0187] Figure 4 is a trajectory diagram of theta 1 and theta 2 of the translation / tilt device in the present application;

[0188] Figure 5 is a tracking error diagram of theta 1 and theta 2 of the translation / tilt device in the present application;

[0189] Figure 6 is a diagram of the relationship between J and kappa, delta of the translation / tilt device in the present application. DETAILED DESCRIPTION

[0190] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0191] Please refer to Figures 1-6 A network attack resilient constraint tracking control method for networked physical systems, a pan / tilt device is installed under a firefighting unmanned aerial vehicle to drive a water spraying device. A firefighting unmanned aerial vehicle (UAV) has a water spraying device installed under the UAV to drive the water spraying device, as shown in Figure 1 The unmanned aerial vehicle with the water spraying device is often applied to firefighting work in high-rise buildings. The pan / tilt device has two degrees of freedom to meet the trajectory tracking requirement of the water spraying nozzle. The pan / tilt device has two degrees of freedom to meet the trajectory tracking requirement of the water spraying nozzle. The pan motor and the tilt motor drive the device to rotate in the horizontal and vertical directions. The water spraying nozzle can guide water to spray in the required direction.

[0192] The pan / tilt device and the control system are configured as shown in Figure 2 The pan / tilt device is driven by two motors. The two motors are driven by a remote controller. The angle position and speed information are collected by encoders. The communication between the pan / tilt device and the remote operation control station is wireless. The remote controller receives and monitors the motion state information and sends commands through the wireless network. The pan / tilt device and the control system can be regarded as a networked physical system. The remote network control will induce some side effects such as communication delay and packet loss under DoS and other network attacks. Such results may cause system performance degradation or even instability.

[0193] The pan / tilt device is modeled as follows:

[0194] The mechanical system can be represented by the method commonly used in robot technology by regarding the mechanical system as a two-degree-of-freedom mechanical arm. The link coordinate system is established as shown in Figure 1

[0195] As mentioned earlier, the gimbal of the pan / tilt system has two rotary joints, the pan joint and the tilt joint. The combined motion part with the pan motor is called the yaw motion part, and the part with the tilt motor is called the pitch motion part. Hereinafter, the part with the tilt motor is referred to as the pitch motion part.

[0196] Considering Figure 1 the pan / tilt device system under network attack in ​

[0197]

[0198] where

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206] gi = 0, g2= m2gs2y 2c - m2gc2x 2c

[0207] where si = sin θi, s2= sin θ2, ci = cos θi, c2= cos θ2. θi is the rotation angle of the i-th joint, mi, m2are the masses of the yaw and pitch mechanisms, respectively, (x 1c , y 1c , z 1c ) is the center of mass of the yaw mechanism, (x 2c , y 2c , z 2c ) is the center of mass of the pitch mechanism, I 1xx , I 1yy , I 1zz is the principal moment of inertia of the yaw mechanism, I 2xx , I 2yy , I 2zz is the principal moment of inertia of the pitch mechanism, g is the acceleration of gravity.

[0208] The constraint conditions to be followed are:

[0209] We consider the moving trajectory of the water jet nozzle endpoint as a constraint condition to be followed. As an illustrative example, we choose the target nozzle endpoint moving trajectory of the translational / tilt system to be a circle.

[0210] Suppose the desired trajectory constraints of θi are

[0211]

[0212] Taking the first order derivative of (55) with respect to time, the constraint equation can be written in the form of (3), which gives

[0213]

[0214] Simulation analysis

[0215] Consider a pan / tilt system (54) in the presence of uncertainty, DoS attacks and other cyber attacks. Assume that the mass is an uncertain parameter. Δm 1，2 (t) can be a time-varying unknown variation of m 1，2 with unknown possible bounds.

[0216] Assumptions 1-5 can be verified. Here Let κ = 0.7, δ = 0.7, Assume the initial condition is inconsistent: 01(0) = 0.1, This means that the translation / tilt does not start from the constraint manifold at t = t0.

[0217] To satisfy the desired trajectory (55), i.e., the ideal circle, even in the presence of uncertainty, Dos attacks and cyber attacks, we use control (12) to operate the system. Figure 3 For the tracking result, Figure 4 For the tracking error, the tracking error converges rapidly to zero and remains within a very small region. Therefore, this method has good tracking control effect on systems with uncertainty and anti-cyber attack capability.

[0218] Now we discuss the optimal selection of the control design parameter κ. Through the above discussion and analysis, we obtain that in the three game theory optimal selections of non-cooperative game and two Stackelberg competitive games, the optimal control design parameter κ is unique regardless of which method is used.

[0219] Again consider (54), still the above uncertain parameters and cyber attacks, we choose ρ E = 2, ω = 3. From (33), the relationship of cost J with κ, δ is shown as Figure 5

[0220] From Figure 5 we can clearly see the saddle point or Nash equilibrium. Therefore, for a given δ, there is an optimal κ * that minimizes J at the saddle point.

[0221] Assume that due to DoS attacks, δ = 0.3, through (46), we obtain κ​* = 0.3347, which is an optimal design parameter. For an intuitive observation of the contrast effect, κ = 1 is chosen as a contrast. Figure 6 Simulation results for the tracking errors of θ1and θ2.

[0222] The simulation results show that for θ1and θ2, the tracking errors using κ * = 0.3347 are indeed smaller than κ = 1.

[0223] While the embodiments of the application have been illustrated and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the spirit and scope of the application, which is defined by the appended claims and their equivalents.

Claims

1. A method for resilient constraint tracking and control of network attacks in cyber-physical systems, characterized in that: The steps include: Step 1: Establishing a cyber-physical system model, considering that the cyber-physical system is subjected to a set of network attacks with unknown priorities: wherein: is time, is coordinate, is velocity, is acceleration, is an uncertain parameter, is an unknown cyber attack input, is an uncertain attack factor due to spoofing and / or mixed threat attacks, is a control input, set and are compact, representing and possibly the region to which they belong, in addition, is an inertia matrix, is a Coriolis / centrifugal force, is a gravitational force, is a cyber attack input matrix, matrix / vector and have appropriate dimensions, functions , , , are continuous; The following constraints are proposed: where is the first component of and is , which are first-order forms of constraints, each constraint can be holonomic or non-holonomic, the constraint conditions are expressed in matrix form: wherein ; Step 2: Designing an adaptive robust controller with elastic constraints: where: represents the constraint following error , with 0 represents the "nominal" part of the function is continuous, , is a scalar design parameter;​ wherein: is a scalar design parameter, is a known function; The adaptive robust controller with elastic constraints is: Considering the cyber-physical system, the controller makes the system have the following performance: (101) Uniform boundedness: for any , there exists a such that if , then for all , ; (102) Uniform final boundedness: for any and there exists a such that for any when where ; Step 3: Analysis of the elasticity in constraint tracking performance: When uniform boundedness guarantees that the error after the constraint is limited in the region uniform ultimate boundedness performance guarantees that the error is small enough, i.e., in a finite time after the attack in the region and are related to , for all , if there exists a region such that , then the controlled system is resilient to attack factors and cyber-attack inputs; Step 4: Game optimal selection of controller design parameters: Three game rules of non-cooperative game and two Stackelberg competition are proposed to select the optimal control involving parameters and . 2.The network attack resilient constraint tracking control method for cyber-physical systems according to claim 1, wherein: There are two ways to interpret the constraints mentioned in Step 1, first, the constraints may be passive, that is, the environment or structure provides the constraint force to make the system comply with the constraints; second, the constraints may be very active, that is, the control input of the system provides the required force to meet the constraints. 3.The network attack resilient constraint tracking control method for cyber-physical systems according to claim 2, wherein: The constraint interpretation method adopts a second constraint method, and the constraint is applied to derivation: The second-order form of the constraint condition can be rewritten as: wherein ; wherein . 4.The network attack resilient constraint tracking control method for cyber-physical systems of claim 1, wherein: Before establishing the adaptive robust controller with elastic constraints in Step 2, uncertainty decomposition and network attack input matrix decomposition are first needed. 5.The network attack resilient constraint tracking control method for cyber-physical systems of claim 1, wherein: In Step 3, the analysis of the elasticity in constraint tracking performance is divided into two cases, the first is without DOS attack and network attack input, and the second is with both DOS and network attack input. 6.The network attack resilient constraint tracking control method for cyber-physical systems of claim 1, wherein: In Step 4, non-cooperative game is a zero-sum game, and Stackelberg is a strategic game.

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