Hypersonic velocity rocket vehicle sampling safety control method under mixed attack

Abstract

The invention relates to the technical field of control, in particular to a hypersonic velocity rocket vehicle sampling safety control method under hybrid attacks, which comprises the following steps: constructing a model of a hypersonic velocity rocket vehicle control system; based on the model, designing a hypersonic rocket vehicle sampling safety controller under hybrid attacks, the hybrid attacks including DoS attacks and spoofing attacks; and solving the hypersonic velocity rocket vehicle sampling safety controller by using a Lyapunov functional to obtain a controller gain, and substituting the controller gain into the hypersonic velocity rocket vehicle control system to complete control. According to the invention, stable control of the hypersonic rocket vehicle is realized on the premise of considering DoS attack and spoofing attack, and the method has the characteristics of high control efficiency, easy realization and strong anti-interference capability.

Description

Technical Field

[0001] The present invention relates to the field of control technology, and in particular to a method for controlling the sampling safety of a hypersonic rocket vehicle under hybrid attack. Background Art

[0002] Hypersonic rocket vehicles feature high flight speeds, strong maneuverability, and complex aerodynamic characteristics. Their control systems must sample and process large amounts of flight data in a short period of time and make precise control decisions based on real-time conditions. This places extremely high demands on the sampling and control systems, requiring them to ensure both the accuracy and real-time nature of the sampled data, as well as rapid response and robust anti-interference capabilities. Denial-of-Service (DoS) attacks and spoofing attacks are two common attacks that can affect sampling signals. The former directly blocks signal transmission, paralyzing the system or congesting the signal channel; the latter tamper with data and signals to send false information to the target system, causing it to make erroneous decisions. Therefore, to ensure system stability, it is essential to implement cruise control and safe surface temperature control for the hypersonic rocket vehicle. Therefore, the present invention proposes a method for safe sampling control of a hypersonic rocket vehicle under hybrid attacks. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for controlling the sampling safety of a hypersonic rocket vehicle under hybrid attacks, which realizes the stable control of the hypersonic rocket vehicle under the premise of considering DoS attacks and deception attacks, and has the characteristics of high control efficiency, easy implementation and strong anti-interference ability.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack comprises:

[0006] Build a model of the hypersonic rocket vehicle control system;

[0007] Based on the model, a sampling safety controller for a hypersonic rocket vehicle under hybrid attacks is designed, wherein the hybrid attacks include DoS attacks and deception attacks;

[0008] The Lyapunov functional is used to solve the hypersonic rocket vehicle sampling safety controller, obtain the controller gain, and substitute it into the hypersonic rocket vehicle control system to complete the control.

[0009] Optionally, constructing the model of the hypersonic rocket vehicle control system includes: constructing a mathematical model of cruise control and surface temperature control of the hypersonic rocket vehicle, expressed as:

[0010]

[0011] in, is the derivative of x(t) with respect to t, x(t) is the velocity error, and t is the time; for The derivative with respect to t, is the temperature error, z is the spatial position; A1, G1, B1, Υ, Θ, A2, G2, B2 are the setting coefficients; u1(t) is the controller input speed error, and u2(z, t) is the controller input temperature error.

[0012] Optionally, designing a hypersonic rocket vehicle sampling safety controller under hybrid attack based on the model includes:

[0013] The sampling working time parameters are set, and a hybrid attack is carried out using DoS attack and deception attack to build a hypersonic rocket vehicle sampling security controller.

[0014] Optionally, the DoS attack satisfies the following conditions:

[0015] Prob{β0(t k )=1}=E{β0(t k )}=β0,Prob{β0(t k )=0}=1-β0;

[0016] Prob{β1(t k )=1}=E{β1(t k )}=β1,Prob{β1(t k )=0}=1-β1;

[0017] Among them, β0(t k ) and β1(t k ) is a random variable, t k is the kth sampling moment, E{} is the expectation of the corresponding function, and β0 is β0(t k ) takes the value of 1, β1 is β1(t k ) is the probability of taking the value of 1.

[0018] Optionally, the spoofing attack satisfies the following conditions:

[0019] ||v1(t k )||2≤||H1x(t k )||2;

[0020]

[0021] Among them, v1(t k ) is a malicious attack signal targeting speed, v2(z, t k ) is a malicious attack signal targeting temperature, H1 is the upper bound of speed attack, and H2 is the upper bound of temperature attack; x(tk ) is the velocity error at the kth sampling moment, is the temperature error at the kth sampling moment.

[0022] Optionally, the hypersonic rocket vehicle sampling safety controller is:

[0023]

[0024] Where k and w are controller gains; u1(t) is the controller input speed error, u2(z, t) is the controller input temperature error, t is time, z is spatial position, t k+1 is the k+1th sampling time.

[0025] Optionally, the Lyapunov functional is:

[0026]

[0027] Where V(t) is the Lyapunov functional, V i (t) is the Lyapunov functional component, t k is the kth sampling time, t k+1 is the k+1th sampling time.

[0028] The beneficial effects of the present invention are:

[0029] The present invention proposes a sampling safety control method for a hypersonic rocket vehicle under mixed attacks. This method achieves stable control of the hypersonic rocket vehicle while taking into account DoS attacks and deception attacks. The method has the characteristics of high control efficiency, ease of implementation, and strong anti-interference ability. A suitable Lyapunov functional is constructed to ensure the exponential stability of the hypersonic rocket vehicle control system and achieve the desired steady-state value. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0031] Figure 1 This is a flow chart of a method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack according to an embodiment of the present invention;

[0032] Figure 2 Schematic diagram of x(t) when there is no control effect in the simulation results of an embodiment of the present invention;

[0033] Figure 3When there is no control effect in the simulation results of the embodiment of the present invention Schematic diagram of;

[0034] Figure 4 Schematic diagram of x(t) after sampling safety control is applied in the simulation results of an embodiment of the present invention;

[0035] Figure 5 The simulation results of the embodiment of the present invention are subjected to sampling safety control. Schematic diagram of;

[0036] Figure 6 Schematic diagram of the control signal u1(t) in the simulation results of an embodiment of the present invention;

[0037] Figure 7 Schematic diagram of the second norm of the control signal u2(z, t) in the simulation results of an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0039] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] The notation used in this paper is standard and is introduced here before continuing. If the dimension of a matrix is ​​not explicitly stated, it is assumed to be compatible with algebraic operations. ||.|| represents the Euclidean norm of a vector. Both represent n-dimensional Euclidean space, represents a set of n×m real matrices. diag represents a diagonal matrix. For a symmetric matrix *Refers to terms caused by symmetry.

[0041] like Figure 1 As shown, this embodiment provides a method for controlling the safety of sampling by a hypersonic rocket vehicle under a hybrid attack, including:

[0042] Build a model of the hypersonic rocket vehicle control system;

[0043] Based on the model, a sampling safety controller for a hypersonic rocket vehicle under hybrid attacks is designed, wherein the hybrid attacks include DoS attacks and deception attacks;

[0044] The Lyapunov functional is used to solve the hypersonic rocket vehicle sampling safety controller, obtain the controller gain, and substitute it into the hypersonic rocket vehicle control system to complete the control.

[0045] Specifically, this embodiment achieves stable control of a hypersonic rocket vehicle while taking into account DoS and spoofing attacks, featuring high control efficiency, ease of implementation, and strong anti-interference capabilities. A suitable Lyapunov functional is constructed to ensure exponential stability of the hypersonic rocket vehicle control system and achieve the desired steady-state value. The specific steps include:

[0046] S1, construct the model of the hypersonic rocket vehicle control system, including the mathematical model of the hypersonic rocket vehicle's cruise control and surface temperature control;

[0047] S2, considers DoS attacks and spoofing attacks;

[0048] S3, design a safety controller for sampling hypersonic rocket vehicles under hybrid attack;

[0049] S4, construct a suitable Lyapunov function, use Lyapunov stability theory to obtain the exponential stability conditions of the hypersonic rocket vehicle control system, and make the system reach the desired steady-state value.

[0050] In this embodiment, a model of a hypersonic rocket vehicle control system is constructed, including a mathematical model of cruise control and surface temperature control of the hypersonic rocket vehicle, specifically including the following contents:

[0051]

[0052] The boundary conditions are as follows:

[0053]

[0054] and initial conditions:

[0055]

[0056] in, represents the mass of the hypersonic rocket vehicle, ω(t) represents the displacement of the hypersonic rocket vehicle, and represents the velocity and acceleration of the hypersonic rocket vehicle, represents the aerodynamic drag coefficient, represents the viscous friction coefficient, represents the material density of the hypersonic rocket vehicle, represents the material specific heat of the hypersonic rocket vehicle, T(l, t) represents the surface temperature of the hypersonic rocket vehicle, which depends on the time t and the spatial position l of the rocket vehicle body surface, and the subscript t represents the partial derivative with respect to t. represents the second-order partial derivative of T(l, t) with respect to the spatial position l, represents the thermal conductivity of the hypersonic rocket vehicle, represents the circumference of the hypersonic rocket vehicle, represents the convective heat transfer coefficient of the hypersonic rocket vehicle, represents the cross-sectional area of ​​the hypersonic rocket vehicle, ε represents the material emissivity of the hypersonic rocket vehicle, represents the Bolzmann constant, T1 represents the temperature of the material around the surface of the hypersonic rocket vehicle, T2 represents the temperature of the material perpendicular to the surface of the hypersonic rocket vehicle, represents the dynamic viscosity, are known parameters, represents the controller input, L represents the length of the hypersonic rocket vehicle, and denote the first-order partial derivatives of T(l, t) with respect to the spatial position l at l = 0 and l = L, respectively; ω0 and T0(l) denote the initial values ​​of the hypersonic rocket vehicle system;

[0057] The required stable speed and temperature meet the following requirements: and is the steady-state input of the controller. The control objective is to make the speed and temperature of the hypersonic rocket vehicle reach the desired steady-state ω d =20 and T d =40, in order to simplify the representation of the original system, a dimensionless transformation is introduced: After dimensionless transformation, the original system is transformed into the following form:

[0058]

[0059] The speed error is defined as The temperature error is And define the coefficient Assume the controller input error The original system is transformed into the following:

[0060]

[0061] Subject to boundary and initial conditions:

[0062]

[0063]

[0064] in, is the derivative of x(t) with respect to t, for The derivative with respect to t, and They are The derivative with respect to z at z = 0 and z = 1 is, for The second derivative with respect to z is defined as and

[0065] The final hypersonic rocket vehicle control system model can be represented by the following model:

[0066]

[0067] Among them, A1=α2, G1=0, Υ=β1, Θ=0, G2=β5, and and t∈[0,∞) represent spatial position and time respectively.

[0068] The steps of introducing the sampling control mechanism in this embodiment include:

[0069] Divide the total time interval into a series of disjoint time intervals Where 0=t0<t1<t2…<t2<t k+1 …satisfy t k , t k+1 are the two sampling moments before and after, h k is the sampling period, and the working interval h is defined k =s k -t k , set two positive scalars h1 and h2 so that the working range satisfies

[0070] The hypersonic rocket vehicle control system is attacked using a DoS attack. A DoS attack is a network attack method in which the attacker uses various means to disable the target computer or network from providing normal services, thereby preventing legitimate users from accessing normal service resources.

[0071] Setting 1: Define the random variable β0(t k ) and β1(t k ), which takes values ​​between 0 and 1 and satisfies the following conditions:

[0072] Prob{β0(t k )=1}=E{β0(tk )}=β0,Prob{β0(t k )=0}=1-β0 (9);

[0073] Prob{β1(t k )=1}=E{β1(t k )}=β1,Prob{β1(t k )=0}=1-β1 (10);

[0074] When its value is 1, it means that no DoS attack occurs; when its value is 0, it means that a DoS attack occurs.

[0075] Consider a deception attack. A deception attack completely replaces the original data with a malicious attack signal or appends a signal to the original data, thereby destroying data transmission. The malicious attack signal can be modeled as v1(t k ) and v2(z, t k ), the attack signal is related to the originally sent data and meets the following settings.

[0076] Assumption 2: The deception attack is bounded, that is, the attack signal has the following bounded conditions:

[0077] ||v1(t k )||2≤||H1x(t k )||2 (11);

[0078]

[0079] Among them, H1 and H2 are artificially given parameters used to describe the strength of the upper bound of the attack.

[0080] The final hybrid attack hypersonic rocket vehicle sampling safety control method is as follows:

[0081]

[0082] Where k and w are controller gains. Substituting the controller into formula (13) yields:

[0083]

[0084] In step S4 of this embodiment, the stability is proved by using the Lyapunov theorem, and the Lyapunov functional used is as follows:

[0085]

[0086] Where V1(t)=x(t)p1x(t);

[0087]

[0088] And, among them Given a matrix p1>0, p2>0, p3>0, and there is When t∈[t k , t k+1 ], considering p1>0, p2>0 and formula (15), we can get V(t)>0, t∈[t k , t k+1 ].

[0089] Taking the derivative of V(t) and taking the expectation, we can get:

[0090]

[0091] Given a scalar α>0, the column vector If the following linear matrix inequality holds:

[0092] Γ i >0,i=1,2 (17);

[0093] N i >0,i=1,2 (18);

[0094] Ξ1+h k Ξ2≤0 (19);

[0095] Ξ3-h k Ξ4≤0 (20);

[0096] in,

[0097] The specific matrix elements are as follows:

[0098]

[0099]

[0100] Then the hypersonic rocket vehicle control system is exponentially stable, where formulas (17) and (18) make V(t)>0, t∈[t k , t k+1 ].

[0101] According to formulas (19) and (20), we can get:

[0102]

[0103] Furthermore, integrating both sides of the inequality yields:

[0104]

[0105] Obviously, V(t) is in the interval [t k , t k+1 ] is continuous, so we can get:

[0106]

[0107] Therefore, it can be deduced from the above formula that the hypersonic rocket vehicle control system is exponentially stable.

[0108] Furthermore, the gain of the sampling safety controller is solved according to the above derivation, as follows:

[0109] definition: Λ=diag{n1, n1, n1, n2, n2, n2, n2},

[0110] Among them, r1~r5 are given scalars. Obviously, by multiplying the formula (17) by Λ i , Formula (18) is multiplied by Formula (19) is multiplied by Formula (20) is multiplied by The following inequality can be obtained:

[0111]

[0112] in,

[0113] The specific matrix elements are as follows:

[0114]

[0115]

[0116] The controller gain is thus obtained as:

[0117]

[0118] The effectiveness of the hypersonic rocket vehicle sampling safety control method under mixed attack proposed in this embodiment is verified and illustrated through simulation experiments, as follows:

[0119] The specific parameters of the hypersonic rocket vehicle are: L=1m, ε=0.965, T1=100K, T2=40K.

[0120] Select α=0.6,r1=30,r2=20,r3=45,r4=30,r5=10,DoS attack parameters β0=0.9,β1=0.95,spoofing attack H1=0.1,H1=0.2,v1(t k )=tanh(H1x(t k )), Sampling period h k =h1=h2=0.2s, using the LMI toolbox of MATLAB to solve formulas (24)-(27), we can obtain: k=-2.3699, w=-2.5013.

[0121] Set the initial condition x0 = -1.5, The control time is 15s. The simulation results can be obtained by substituting various parameters into the hypersonic rocket vehicle control system and applying the sampling safety controller of the above controller gain to the system. Figure 2 and Figure 3 Represent x(t) and images, Figure 4 and Figure 5 Represents x(t) and images, Figure 6 and Figure 7 are the images of the two norms of the control signals u1(t) and u2(z, t), respectively. It can be seen that x(t) and It quickly approaches 0, which means that the speed and temperature of the hypersonic rocket vehicle quickly reach the control target under control.

[0122] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack, characterized in that: include: Build a model of the hypersonic rocket vehicle control system; Based on the model, a sampling safety controller for a hypersonic rocket vehicle under hybrid attacks is designed, wherein the hybrid attacks include DoS attacks and deception attacks; The Lyapunov functional is used to solve the hypersonic rocket vehicle sampling safety controller, obtain the controller gain, and substitute it into the hypersonic rocket vehicle control system to complete the control.

2. The method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack according to claim 1 is characterized in that: Constructing the model of the hypersonic rocket vehicle control system includes: constructing a mathematical model of cruise control and surface temperature control of the hypersonic rocket vehicle, which is expressed as: in, is the derivative of x(t) with respect to t, x(t) is the velocity error, and t is the time; for The derivative with respect to t, is the temperature error, z is the spatial position; A1, G1, B1, Υ, Θ, A2, G2, B2 are the setting coefficients; u1(t) is the controller input speed error, and u2(z, t) is the controller input temperature error.

3. The method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack according to claim 1 is characterized in that: Based on the model, the design of a sampling safety controller for a hypersonic rocket vehicle under mixed attack includes: The sampling working time parameters are set, and a hybrid attack is carried out using DoS attack and deception attack to build a hypersonic rocket vehicle sampling security controller.

4. The method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack according to claim 3 is characterized in that: The DoS attack satisfies the following conditions: Prob{β0(t k )=1}=E{β0(t k )}=β0,Prob{β0(t k )=0}=1-β0; Prob{β1(t k )=1}=E{β1(t k )}=β1,Prob{β1(t k )=0}=1-β1; Among them, β0(t k ) and β1(t k ) is a random variable, t k is the kth sampling moment, E{} is the expectation of the corresponding function, and β0 is β0(t k ) takes the value of 1, β is β1(t k ) is the probability of taking the value of 1.

5. The method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack according to claim 4 is characterized in that: The deception attack satisfies the following conditions: ||v1(t k )||2≤||H1x(t k )||2; Among them, v1(t k ) is a malicious attack signal targeting speed, v2(z, t k ) is a malicious attack signal targeting temperature, H1 is the upper bound of speed attack, and H2 is the upper bound of temperature attack; x(t k ) is the velocity error at the kth sampling moment, is the temperature error at the kth sampling moment.

6. The method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack according to claim 5 is characterized in that: The hypersonic rocket vehicle sampling safety controller is: u1(t)=kβ0(t k )x(t k )+v1(t k ), Where k and w are controller gains; u1(t) is the controller input speed error, u2(z, t) is the controller input temperature error, t is time, z is spatial position, t k+1 is the k+1th sampling time.

7. The method for controlling the sampling safety of a hypersonic rocket vehicle under a hybrid attack according to claim 1 is characterized in that: The Lyapunov functional is: Where V(t) is the Lyapunov functional, V i (t) is the Lyapunov functional component, t k is the kth sampling time, t k+1 is the k+1th sampling time.

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