A fixed time elastic control method and device for resisting deception attacks

Abstract

The invention discloses a fixed-time elastic control method and device for resisting deception attacks, belonging to the field of elastic control. The control method comprises the following steps: S1: establishing a mathematical model of deception attacks, and further designing a motor control system model subjected to deception attacks; S2: constructing a first virtual controller, a second virtual controller and a fixed time by using an intermediate error variable; S3: constructing a non-singular terminal sliding mode surface with fixed-time characteristics, and designing a corresponding parameter allocation rule; S4: designing a corresponding adaptive law and a fixed-time approaching sliding mode control law according to a system state, a non-singular terminal sliding mode surface and a super-helical algorithm; S5: controlling a motor system by using the designed equivalent and approaching sliding mode control laws; S6: establishing a Lyapunov function, and using the second method of the Lyapunov function to prove the stability of the control system; it can ensure that the motor system can still restore stable operation within a fixed time when subjected to a deception attack.

Description

Technical Field

[0001] The present invention relates to the field of elastic control, and more specifically, to a fixed-time elastic control method and device for resisting deception attacks. Background Art

[0002] Motor control systems are widely used in different important fields due to their fast response speed and high transmission efficiency, such as robotic systems, transportation systems, and industrial control systems. With the rapid development of science and technology and networked communications, traditional control systems have undergone major changes, making traditional motor control systems have the advantages of remote control, fast response, and high real-time performance.

[0003] However, while improving the network control of the system, the system is also more vulnerable to danger. For example, an important feature of the network control system is that all physical devices and control centers of the system are transmitted through network channels, which makes the system vulnerable to malicious network attacks, which will cause huge economic losses and even casualties. Therefore, ensuring the safety of the networked motor system is of great practical significance.

[0004] In the existing patents, certain improvements have been made to address the above-mentioned defects, such as:

[0005] Publication No. CN110531621B discloses a reliable control method for a networked system under hybrid attacks. The method aims at the control problem of a networked system in which both sensor and actuator channels are attacked by network. First, a control-oriented dynamic model of the system under hybrid attacks is established, and the attacks on the system are modeled. Further, an augmented system is constructed by designing auxiliary variables, and real-time estimation of the attacks is achieved by designing an augmented observer. Finally, a reliable controller is designed according to the output value of the attack observer to achieve elastic control of the system. However, the patent only considers a simple linear system, and the elastic control problem of motor control systems with complex characteristics has not been solved.

[0006] For another example, publication number CN108628329A discloses an anti-interference self-control method for a spacecraft whose measurement and control link is attacked by replay. This method aims at the attitude control problem of a spacecraft whose measurement and control link between the spacecraft and the ground system is attacked by replay and the spacecraft is disturbed by the environment. First, a mathematical model of the spacecraft whose measurement and control link is attacked is established, and an augmented system full-order observer is designed to observe the attitude control state and unknown interference of the system. Further, a feedback controller containing a watermark is designed to construct an anti-interference attitude control method for a spacecraft whose measurement and control link is attacked by replay. However, this patent only considers a simple second-order nonlinear system, and this method can only make the system converge gradually under network attacks, and cannot guarantee that the system will resume stable operation within a fixed time, resulting in excessive economic losses to the system.

[0007] Therefore, a new method is proposed to solve the problems that are not solved by the above two patents. Summary of the invention

[0008] 1. Technical issues to be solved

[0009] In view of the problems existing in the prior art, the purpose of the present invention is to provide a fixed-time elastic control device for resisting deception attacks, which can ensure that the motor system can still resume stable operation within a fixed time when it is attacked by deception.

[0010] 2. Technical solution

[0011] To solve the above problems, the present invention adopts the following technical solutions.

[0012] A fixed time elastic control method for resisting spoofing attacks, the method comprising the following steps:

[0013] S1: Establish a mathematical model of deception attack and further design a motor control system model that is subject to deception attack;

[0014] S2: construct the first virtual controller, the second virtual controller and the fixed time using the intermediate error variable;

[0015] S3: Construct a non-singular terminal sliding surface with fixed time characteristics and design the corresponding parameter allocation rule;

[0016] S4: Design the corresponding adaptive law and fixed-time approaching sliding mode control law according to the system state, non-singular terminal sliding mode surface and super-helical algorithm;

[0017] S5: Control the motor system using the designed equivalent and approaching sliding mode control laws;

[0018] S6: Establish the Lyapunov function, and given the corresponding Lyapunov function, use the second method of Lyapunov function to prove the stability of the control system.

[0019] A fixed time elastic control device for resisting spoofing attacks, the fixed time elastic control device is one embodiment of the fixed time elastic control method, comprising:

[0020] A system model building module, used to build a mathematical model of the motor control system subjected to a deception attack according to a control input dynamic value of the control system, a nonlinear dynamic value of the control system and a mathematical model of the deception attack;

[0021] An elastic controller establishment module is used to establish a fixed-time elastic controller according to a mathematical model of a motor control system, a state error, and a mathematical model of a deceptive public machine;

[0022] The control module is used for controlling the motor system using a flexible controller.

[0023] 3. Beneficial effects

[0024] Compared with the prior art, the advantages of the present invention are:

[0025] This scheme uses the mathematical model of the motor system and the deception attack to establish the mathematical model of the damaged motor system, and uses the power integral technology to design the first virtual control variable and the second virtual control variable to design the equivalent control law, and uses the power integral technology and the super spiral sliding mode technology to construct a fixed-time non-singular terminal sliding mode surface, and further designs the approach control law. Through the equivalent control law and the approach control law, a non-singular terminal sliding mode elastic controller is established to control the motor system under deception attack, so that the motor system has stronger security, and thus can ensure that the motor system can still ensure that the system can resume stable operation within a fixed time when it is attacked by deception. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flow chart of the fixed time elastic control method of the present invention;

[0027] Figure 2 A schematic diagram of an experimental platform for the fixed-time elastic control method of the present invention;

[0028] Figure 3 It is a curve diagram of the angular position, angular velocity and motor armature current variation of the networked motor system in the fixed time elastic control method of the present invention;

[0029] Figure 4 A curve diagram showing the variation of the non-singular terminal sliding mode surface of the networked motor system in the fixed-time elastic control method of the present invention;

[0030] Figure 5 A curve diagram showing a change in a time-varying control gain function of a networked motor system in a fixed-time elastic control method of the present invention;

[0031] Figure 6 It is a curve diagram of the unknown deception attack parameters and their upper limit estimation values ​​of the present invention. DETAILED DESCRIPTION

[0032] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention; it is obvious that the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments, and all other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making creative work are within the scope of protection of the present invention.

[0033] Embodiment 1:

[0034] A fixed time elastic control method for resisting spoofing attacks comprises the following steps:

[0035] S1: Establish a mathematical model of deception attack and further design a motor control system model that is subject to deception attack;

[0036] The mathematical model of the motor control system is established, and the formula for establishing the model is:

[0037]

[0038] Where q represents the angular position of the motor, represents the angular velocity of the motor, represents the angular acceleration of the motor, V0 represents the control input voltage, and I represents the armature current;

[0039] And, in formula (1):

[0040]

[0041] Among them, M0 represents the load mass of the motor system, m represents the mass of the connecting rod, L0 represents the length of the connecting rod, R0 represents the load radius, and K B represents the back electromotive force coefficient, G represents the gravity coefficient, M represents the armature reactance, J represents the moment of inertia, B0 represents the viscous friction coefficient, K τ represents the electromechanical coefficient;

[0042] Define the state variables:

[0043] x1=q

[0044]

[0045] x3=I

[0046] u=V0

[0047] Then, equation (1) is transformed into the state equation, which is:

[0048]

[0049] y=x1

[0050] in,

[0051] Considering the system is attacked by deception, the mathematical model is described as follows:

[0052]

[0053] in, represents the damaged control input, δ a Indicates that the unknown spoofing attack satisfies the condition δ a =b(t)g(x n ), b(t) represents the unknown time-varying parameter that satisfies the condition as well as represents an unknown bounded function;

[0054] Mathematical model of integrated motor control system and deception attack, the mathematical model of the motor control system under deception attack is described as:

[0055]

[0056] y=x1

[0057] in, is a composite uncertainty term including deception attacks;

[0058] S2: construct the first virtual controller, the second virtual controller and the fixed time using the intermediate error variable;

[0059] The error variable model and virtual control variables of the system are constructed using the following formula:

[0060]

[0061] in, express is the first dummy control variable, is the first virtual control variable, ξ1 is the first error variable, ξ2 is the second error variable, and ξ3 is the third error variable;

[0062] The nonlinear time-varying gain β1(x1) and The following conditions must be met:

[0063]

[0064] And, in formula (52):

[0065]

[0066]

[0067] Among them, the design parameters γ1, γ2, a, μ are all greater than 0, and a, μ satisfy the condition μ ≥ a ≥ max {r i}, i = 1, 2, 3; an equivalent controller is constructed by using the error variable model and the virtual control variable, and the construction formula is:

[0068]

[0069] in, is the intermediate variable, i=1,2,3;

[0070] Time-varying gain function Satisfy the following formula:

[0071]

[0072] And, in formula (61), the calculation formula of the design variable is:

[0073]

[0074]

[0075] And, in formula (612):

[0076]

[0077] S3: Construct a non-singular terminal sliding surface with fixed time characteristics and design the corresponding parameter allocation rule;

[0078] The non-singular terminal sliding surface is established using the formula:

[0079]

[0080] in, is the intermediate variable, i=1,2,3;

[0081]

[0082] The distribution rule of sliding surface parameters is r i+1 =r i +τ, whose design parameters satisfy r i >0,τ<0,i=1,2,3,design parameters a,μ are both greater than 0,satisfy the condition μ≥a≥max{r i}.

[0083] S4: Design the corresponding adaptive law and fixed-time approaching sliding mode control law according to the system state, non-singular terminal sliding mode surface and super-helical algorithm;

[0084] Through the system state variables, sliding surface and mathematical model of unknown deception attack, the adaptive law is constructed, and the formula for its construction is:

[0085]

[0086] Among them, a and w1 are designed positive constants, and the initial value of the adaptive law

[0087] The approaching controller is constructed by adaptive law and sliding surface, and the formula for its construction is:

[0088]

[0089] Among them, ò, l1, l2, k1, k2 are design parameters. is the upper bound of the time-varying unknown parameter b, It is an unknown upper bound An estimated value of

[0090] And, in formula (9):

[0091]

[0092] S5: Control the motor system using the designed equivalent and approaching sliding mode control laws;

[0093] The non-singular terminal sliding mode elastic controller is established through the equivalent control law and the approaching control law. The formula for establishing it is:

[0094]

[0095] Among them, u eq (t) represents the equivalent control law, u r (t) represents the reaching control law,

[0096] S6: Establish the Lyapunov function, and given the corresponding Lyapunov function, use the second method of Lyapunov function to prove the stability of the control system, including the following steps:

[0097] A1: Select the Lyapunov function:

[0098]

[0099] The derivative of V1(x1) with respect to time and the related derivation formula of the first virtual controller are obtained as follows:

[0100]

[0101] A2: Select the positive definite Lyapunov function, which is:

[0102]

[0103] against Taking the derivative with respect to time, we get the following formula:

[0104]

[0105] According to the relevant derivation formula of the second virtual controller, the following formula is obtained:

[0106]

[0107] A3: Select the positive definite Lyapunov function, which is:

[0108]

[0109] against Taking the derivative with respect to time, we get the following formula:

[0110]

[0111] And, in formula (17):

[0112]

[0113] And, in formula (172):

[0114]

[0115] Among them, in formula (173) and formula (1721) According to the relevant derivation formula of the equivalent control law, we get:

[0116]

[0117] Taking the derivative of the non-singular terminal sliding surface s(t) with respect to time, we get:

[0118]

[0119] use get:

[0120]

[0121] in as well as

[0122] A3: Select the positive definite Lyapunov function, which is:

[0123]

[0124] in and a>0. represents the estimation error, where is the upper bound of b The estimated value satisfies

[0125] V s Taking the derivative of (s(t),υ(t)) with respect to time, we get:

[0126]

[0127] in,

[0128] According to the related derivation formulas of the approaching control law and the adaptive law, we get:

[0129]

[0130] in, The time constant of the sliding mode approaching stage is

[0131]

[0132] From formula (23), we can further obtain:

[0133]

[0134] From equation (24), we can conclude that the sliding surface s(t) and its variable υ(t) are bounded before the sliding approach stage, and we can conclude that when When |u r (t)+δ a | is bounded;

[0135] Assuming the above bound is M, then using the equivalent control law, we can get Satisfy the following formula:

[0136]

[0137] A5: Construct a composite Lyapunov function:

[0138]

[0139] in, Since τ<0, we can get From the above derivation, we can conclude that:

[0140]

[0141] in, because Conclusion From the above derivation, we can conclude that:

[0142]

[0143] in, against Taking the derivative with respect to time, we get:

[0144]

[0145] in,

[0146] set up When

[0147]

[0148] From the above derivation, we can conclude that:

[0149]

[0150] Therefore, it can be obtained that the state of the motor system can be In, converges to the set Inside;

[0151] A6: According to A5, all states of the closed-loop system are bounded in fixed time. In the approaching sliding surface, if t→T r When , s(t)→0 and υ(t)→0;

[0152] If the system state variable reaches the sliding surface, that is, t>T r When s(t)=0 and υ(t)→0, then u r (t)+δ a =0, then if t>T r hour, Satisfies the following formula:

[0153]

[0154] From the above formula, if t>T f =T r +T s The motor system is fixed-time stable when

[0155]

[0156] Therefore, this embodiment provides a flexible controller constructed for any motor control system that satisfies formula (1) and the deception attack model of formula (3). By determining the nonlinear dynamic formula of the motor system, the deception attack parameters or functions, the method provided by this embodiment can be used to obtain the flexible controller of the motor control system under the deception attack. The effectiveness of the method provided by this embodiment is demonstrated by a specific system model below.

[0157] The relevant parameters of the verification system are as follows: M0 = 0.434 kg, m = 0.506 kg, L0 = 0.305 m, R0 = 0.023 m, K B =0.90N·m / A, G=9.8m / s 2 , R=0.5Ω, M=0.025H, J=1.625kg·m 2 , B0=0.01625N·m·s / rad, K τ =0.90N·m / A.

[0158] The spoofing attack is:

[0159] The initial angular position, angular velocity and current of the motor system are: q = -0.5, I = -6,

[0160]

[0161] like Figure 3 As shown, it is a curve diagram of the change of the angular position, angular velocity and current of the motor system. It can be seen from the figure that when the system is attacked by deception, the stable performance of the system can still be guaranteed within a fixed time. Figure 4 It is a curve diagram of the non-singular terminal sliding surface variables. It can be seen that the estimated surface goes from the approaching stage to the sliding stage within a fixed time. Figure 5 is the curve diagram of the time-varying gain function value, Figure 6 To spoof unknown parameter values, there is Figure 5 and Figure 6 It can be seen that the resilient controller of the motor system can generate time-varying gain function values ​​and estimated values ​​of unknown parameters to resist spoofing attacks.

[0162] Embodiment 2:

[0163] This embodiment is a fixed time elastic control device for resisting spoofing attacks. The fixed time elastic control device is one implementation of the fixed time elastic control method, including:

[0164] A system model building module, used to build a mathematical model of the motor control system subjected to a deception attack according to a control input dynamic value of the control system, a nonlinear dynamic value of the control system and a mathematical model of the deception attack;

[0165] An elastic controller establishment module is used to establish a fixed-time elastic controller according to a mathematical model of a motor control system, a state error, and a mathematical model of a deceptive public machine;

[0166] The control module is used for controlling the motor system using a flexible controller.

[0167] The above is only a preferred specific implementation of the present invention; however, the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solution and its improved conception within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A fixed time elastic control method for resisting spoofing attacks, characterized in that: The following steps are included: S1: Establish a mathematical model of deception attack and design a motor control system model that is subject to deception attack; In S1, a mathematical model of the motor control system is established, and the formula for establishing the model is: Where q represents the angular position of the motor, represents the angular velocity of the motor, represents the angular acceleration of the motor, V0 represents the control input voltage, and I represents the armature current; And, in formula (1): Among them, M0 represents the load mass of the motor system, m represents the mass of the connecting rod, L0 represents the length of the connecting rod, R0 represents the load radius, and K B represents the back electromotive force coefficient, G represents the gravity coefficient, M represents the armature reactance, J represents the moment of inertia, B0 represents the viscous friction coefficient, K τ represents the electromechanical coefficient; Define the state variables: x1=q x3=I u=V0 Then, equation (1) is transformed into the state equation, which is: in, Considering the system is attacked by deception, the mathematical model is described as follows: in, represents the damaged control input, δ a Indicates that the unknown spoofing attack meets the conditions b(t) represents the unknown time-varying parameter that satisfies the condition as well as represents an unknown bounded function; Mathematical model of integrated motor control system and deception attack, the mathematical model of the motor control system under deception attack is described as: in, is a composite uncertainty term including deception attacks; S2: construct the first virtual controller, the second virtual controller and the fixed time using the intermediate error variable; In S2, the error variable model and virtual control variables of the system are constructed, and the formula used is: in, express is the first dummy control variable, is the first virtual control variable, ξ1 is the first error variable, ξ2 is the second error variable, and ξ3 is the third error variable; the nonlinear time-varying gain β1(x1) and The following conditions must be met: And, in formula (52): Among them, the design parameters γ1, γ2, a, μ are all greater than 0, and a, μ satisfy the condition μ ≥ a ≥ max {r i }, i = 1, 2, 3; an equivalent controller is constructed by using the error variable model and the virtual control variable, and the construction formula is: in, is the intermediate variable, i=1,2,3; Time-varying gain function Satisfy the following formula: And, in formula (61), the calculation formula of the design variable is: And, in formula (612): S3: Construct a non-singular terminal sliding surface with fixed time characteristics and design the corresponding parameter allocation rule; In S3, a non-singular terminal sliding surface is established, and the formula used is: in, is the intermediate variable, i=1,2,3; The distribution rule of sliding surface parameters is r i+1 =r i +τ, whose design parameters satisfy r i >0,τ<0,i=1,2,3,design parameters a,μ are both greater than 0,satisfy the condition μ≥a≥max{r i }; S4: Design the corresponding adaptive law and fixed-time approaching sliding mode control law according to the system state, non-singular terminal sliding mode surface and super-helical algorithm; In S4, an adaptive law is constructed through the system state variables, the sliding surface, and the mathematical model of the unknown deception attack. The formula for the construction is: Among them, a and w1 are designed positive constants, and the initial value of the adaptive law The approaching controller is constructed by adaptive law and sliding surface, and the formula for its construction is: Among them, ò, l1, l2, k1, k2 are design parameters. is the upper bound of the time-varying unknown parameter b, It is an unknown upper bound An estimated value of And, in formula (9): S5: Use the designed equivalent and approaching sliding mode control laws to control the motor system; In S5, a non-singular terminal sliding mode elastic controller is established through an equivalent control law and a reaching control law, and the established formula is: Among them, u eq (t) represents the equivalent control law, u r (t) represents the reaching control law, 2. A fixed time elastic control device for resisting spoofing attacks, characterized in that: The fixed time elastic control method according to claim 1 is characterized by comprising: A system model building module, used to build a mathematical model of the motor control system subjected to a deception attack according to a control input dynamic value of the control system, a nonlinear dynamic value of the control system and a mathematical model of the deception attack; An elastic controller establishment module is used to establish a fixed-time elastic controller according to a mathematical model of a motor control system, a state error, and a mathematical model of a deceptive public machine; The control module is used for controlling the motor system using a flexible controller.

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