Performance control method of limited nonlinear information physical system

Abstract

The invention discloses a performance control method of a limited nonlinear information physical system, which belongs to the technical field of intrusion tolerance control of information physical systems, and comprises the following steps of: establishing a control-oriented dynamic model of the limited nonlinear information physical system with external disturbance under spoofing attack; mathematical characterization is carried out on bounded multiplicative and additive spoofing attacks; a Lyapunov function based on a preset performance control method is constructed, and a system stability determination method based on a Nusb inequality is given; and coordinate change is introduced to meet full-state constraint, and a fixed time controller is designed by using a backstepping method, so that preset performance control of the limited nonlinear information physical system under spoofing attack and external disturbance is realized. The invention develops a fixed time intrusion tolerance controller based on a preset performance method, which can ensure the stable operation of a limited nonlinear information physical system under a spoofing attack with a small tracking error.

Description

Technical Field

[0001] The present invention relates to the technical field of intrusion-tolerant control for cyber-physical systems, and particularly to a performance control method for a constrained non-linear cyber-physical system. Background Art

[0002] In recent years, cyber-physical systems have been widely applied to critical infrastructures such as smart grids, connected vehicles, and industrial control systems. The deep integration of the cyber space and the physical space not only improves the system performance but also brings new challenges to the comprehensive security defense of cyber-physical systems due to the mutual influence of information security threats and engineering safety issues. In particular, malicious attackers can launch cyber attacks to invade information systems, causing serious non-contact damage to physical systems. Therefore, it is necessary to develop intrusion-tolerant control strategies to mitigate cyber attacks and enable the controlled system to achieve relatively satisfactory control performance.

[0003] Typical cyber attacks include spoofing attacks, denial-of-service attacks, and replay attacks. Among them, spoofing attacks can mislead the decision-making and control modules of cyber-physical systems by forging sensor or actuator data or control commands. For example, an attacker forges sensor data, causing the system to misjudge the physical environment state, resulting in incorrect control commands and further leading to equipment failures or system crashes. Therefore, the intrusion-tolerant control of cyber-physical systems with randomly jumping states under spoofing attacks is worthy of research.

[0004] Spoofing attacks can bring hazards such as system control failure, physical device damage, and damage to data integrity and confidentiality to cyber-physical systems, seriously affecting the overall security performance of cyber-physical systems. Existing design schemes for intrusion-tolerant controllers based on preset performance control usually require prior knowledge of the control direction of the system. In practical applications, however, the control direction cannot be known in advance, so the actual performance of existing intrusion-tolerant controller design schemes is not ideal. Summary of the Invention

[0005] The present invention provides a performance control method for a constrained non-linear cyber-physical system to solve the technical problem that the actual performance of existing intrusion-tolerant controller design schemes is not ideal.

[0006] To solve the above technical problem, the present invention provides the following technical solutions:

[0007] On the one hand, the present invention provides a performance control method for a constrained non-linear cyber-physical system, including:

[0008] Establishing a control-oriented dynamic model of a constrained non-linear cyber-physical system with external disturbances under spoofing attacks and mathematically characterizing bounded multiplicative and additive spoofing attacks;

[0009] Construct a Lyapunov function based on a preset performance control method and give a method for determining the system stability based on the Nussbaum inequality;

[0010] Introduce coordinate transformation to satisfy the full-state constraints and use the backstepping method to design a fixed-time controller to achieve the preset performance control of the constrained nonlinear cyber-physical system under deception attacks and external disturbances.

[0011] Furthermore, the expression of the dynamic model is:

[0012]

[0013] y = x1

[0014] where, represents the derivative of the i-th state with respect to time; represents the derivative of the n-th state with respect to time; x i+1 represents the (i + 1)-th state; n represents the highest order of the system; and are both unknown nonlinear functions; u represents the control input; x1 represents the first state; is the system state variable; x i represents the i-th state; T represents matrix transpose; R i represents the set of real numbers; y is the system output; d i (t) is the external disturbance; and are both unknown functions, which are defined as bounded;

[0015] The deception attack on the system control output is given by the following formula:

[0016] u = ζ(t)v + τ(t)

[0017] where, v is the actual control input; ζ(t) and τ(t) are the bounded multiplicative attack coefficient and additive attack coefficient respectively; ζ(t) is defined as bounded, that is: where, and are arbitrary positive constants.

[0018] Furthermore, the constructing a Lyapunov function based on a preset performance control method and giving a method for determining the system stability based on the Nussbaum inequality includes:

[0019] Set the preset performance function p i (t):

[0020]

[0021] where, p i0 , pi∞ and β i are both positive constants and satisfy p i0 > p i∞ ; e represents the natural constant, t represents time; n represents the highest order of the system;

[0022] The actual state error of the system when suffering from a deception attack is expressed as:

[0023] z i (t) = x i - x i,d , i = 1,..., n

[0024] where z i (t) represents the error of state x i ; x i represents the i-th state; x i,d represents the virtual controller of state x i ;

[0025] Design the Lyapunov function:

[0026]

[0027] where V i is the designed Lyapunov function; z i (t) represents the error of state x i ; p i (t) represents the preset performance function of state x i ;

[0028] If there exists a positive definite and unbounded Lyapunov function V that satisfies the following equation, then both V and χ are bounded;

[0029]

[0030] where, m0 and m1 are positive constants; g(γ) is a bounded function that is always positive or always negative; χ is a smooth function; N(χ) is a smooth Nussbaum-type function; t represents time; represents the adaptive parameter; dγ represents the integration variable;

[0031] If V is bounded and the actual state error satisfies |z i (t)| < p i (t), then there must exist a positive constant p i such that |z i (t)| is maintained at a distance of p i from the preset performance function p i ; that is, it satisfies:

[0032] |z i (t)| < pi (t)-p i <p i (t)

[0033] means the limit does not exist; thus the condition for system stability is that this limit exists; where, t0 represents any positive constant; z s (t) represents the state error; p s (t) represents the preset performance function.

[0034] Furthermore, introducing coordinate transformation to satisfy the full-state constraints and using the backstepping method to design a fixed-time controller includes:

[0035] Implementing coordinate transformation using the following formula:

[0036]

[0037] where, h i (t) represents the coordinate transformation function; z i (t) is the actual state error of the system; p i (t) is the preset performance function;

[0038] To achieve the preset control objective, design the following controller using the backstepping method:

[0039] x i+1,d =λ i N(χ i )h i (t), i = 1,..., n

[0040] v = x n+1,d

[0041] where, the preset control objective includes that all signals satisfy the preset constraint conditions and all signals within the closed-loop system are bounded; x i+1,d represents the virtual controller of state x i+1 ; h i (t) represents the coordinate transformation function; v represents the actual controller; x n+1,d represents the virtual controller of state x n+1 ; λ i is a constant variable; N(χ i ) is a Nussbaum-type function, χ i represents the adaptive parameter, which is a monotonically increasing smooth function, and its derivative with respect to time is:

[0042] Furthermore, after introducing coordinate transformation to satisfy the full-state constraints and using the backstepping method to design a fixed-time controller, the performance control method for the constrained nonlinear cyber-physical system further includes:

[0043] Prove the system stability condition to ensure the stable operation of the controlled system under deception attacks.

[0044] Furthermore, the proof of the system stability condition to ensure the stable operation of the controlled system under deception attacks includes:

[0045] Use the proof by contradiction to prove the system stability condition to ensure the stable operation of the controlled system under deception attacks.

[0046] Furthermore, the performance control method of the constrained nonlinear cyber-physical system further includes:

[0047] Use MATLAB to simulate the constrained nonlinear cyber-physical system under deception attacks and external disturbances, and verify the effectiveness of the performance control method of the constrained nonlinear cyber-physical system with an inverted pendulum as an example.

[0048] On the other hand, the present invention also provides an electronic device, which includes a processor and a memory; wherein, at least one instruction is stored in the memory, and the instruction is loaded and executed by the processor to implement the above method.

[0049] On another hand, the present invention also provides a computer-readable storage medium, in which at least one instruction is stored, and the instruction is loaded and executed by the processor to implement the above method.

[0050] The technical solution provided by the present invention innovatively realizes the coordinated control of attack suppression and performance constraint, and has three advantages compared with traditional methods: 1) The error boundary can be quantitatively set; 2) The full-state constraint can still be ensured under external disturbances and hybrid deception attacks; 3) All signals of the closed-loop system are bounded.

[0051] The beneficial effects brought by the technical solution provided by the present invention at least include:

[0052] The present invention proposes a new fixed-time intrusion-tolerant control strategy for a class of constrained uncertain nonlinear cyber-physical systems. The proposed strategy can effectively handle actuator attacks and external disturbances. Compared with traditional methods, the control strategy proposed by the present invention has lower complexity and can achieve the control objective without using a boundary function, improving the dynamic performance of the system. The control strategy proposed by the present invention can ensure that all tracking errors enter the preset constraint boundary within a fixed time, where the tracking accuracy is known in advance and can be reset by adjusting relevant design parameters, enhancing the intrusion tolerance of the system to actuator attacks. Description of the Drawings

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0054] Figure 1 is a schematic structural diagram of a cyber-physical system;

[0055] Figure 2 is a schematic execution flowchart of a performance control method for a constrained non-linear cyber-physical system provided by an embodiment of the present invention;

[0056] Figure 3 is a control schematic diagram of an inverted pendulum system;

[0057] Figure 4 is a schematic diagram of the simulation result of the output tracking error provided by an embodiment of the present invention;

[0058] Figure 5 is a schematic diagram of the simulation result of the state tracking error provided by an embodiment of the present invention;

[0059] Figure 6 is a schematic diagram of the control input and control signal provided by an embodiment of the present invention;

[0060] Figure 7 is a schematic diagram of the system output, state, and adaptive parameters provided by an embodiment of the present invention;

[0061] Figure 8 is a system block diagram of an electronic device provided by an embodiment of the present invention. Specific Embodiments

[0062] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will further describe the embodiments of the present invention in detail with reference to the drawings.

[0063] First of all, it should be noted that in the embodiments of the present invention, words such as "exemplarily" and "for example" are used to represent examples, illustrations, or explanations. Any embodiment or design solution described as "exemplary" in the present invention should not be interpreted as being more preferred or having more advantages than other embodiments or design solutions. Exactly, the use of the word "exemplarily" is intended to present concepts in a specific manner. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one of the two can be selected.

[0064] First Embodiment

[0065] This embodiment provides a preset performance control method for a constrained nonlinear cyber-physical system with external disturbances under deception attacks. The aim is to provide a novel intrusion-tolerant control scheme based on preset performance control for the constrained nonlinear cyber-physical system under deception attacks, aiming to ensure the stable operation of the constrained nonlinear cyber-physical system under deception attacks with a small tracking error. This method can be applied to cyber-physical systems such as Figure 1 as shown; the execution process of this method is as shown in Figure 2 and includes the following steps:

[0066] S1. Establish a control-oriented dynamic model of a constrained nonlinear cyber-physical system with external disturbances under deception attacks, and mathematically characterize bounded multiplicative and additive deception attacks;

[0067] Specifically, in this embodiment, the dynamic model is:

[0068]

[0069] where, represents the derivative of the \(i\)-th state with respect to time; represents the derivative of the \(n\)-th state with respect to time; \(x\) i+1 represents the \((i + 1)\)-th state; \(n\) represents the highest order of the system; and are both unknown nonlinear functions; \(u\) represents the control input; \(x_1\) represents the first state; is the system state variable; \(x\) i represents the \(i\)-th state; \(T\) represents matrix transpose; \(R\) i represents the set of real numbers; \(y\) is the system output, \(d\) i (\(t\)) is the external disturbance, and are both unknown functions, which are defined as bounded.

[0070] The deception attack on the system control output is given by the following formula:

[0071] \(u=\zeta(t)v+\tau(t)\) (2)

[0072] where, \(v\) represents the actual control input, and \(\zeta(t)\) and \(\tau(t)\) are the bounded multiplicative attack coefficient and additive attack coefficient respectively. In the present invention, \(\zeta(t)\) is no longer a small constant, but is defined as bounded. That is

[0073]

[0074] where, and are any positive constants.

[0075] S2. Construct a Lyapunov function based on a preset performance control method and give a method for determining the system stability based on the Nussbaum inequality;

[0076] Specifically, in this embodiment, the implementation process of the above S2 is as follows:

[0077] Set a preset performance function p i (t):

[0078]

[0079] where p i0 , p i∞ and β i are all positive constants and satisfy p i0 > p i∞ ; e represents the natural constant, t represents time; n represents the highest order of the system.

[0080] The actual state error of the system when suffering from a deception attack is:

[0081] z i (t) = x i - x i,d , i = 1,..., n. (5)

[0082] where z i (t) represents the error of state x i ; x i represents the i-th state; x i,d represents the virtual controller of state x i ;

[0083] Design a Lyapunov function:

[0084]

[0085] where V i is the designed Lyapunov function; z i (t) represents the error of state x i ; p i (t) represents the preset performance function of state x i ;

[0086] A continuous even function N(χ) is considered if it satisfies the following conditions:

[0087]

[0088] where s represents an arbitrary constant; dχ represents the integration variable;

[0089] Such a function is called a Nussbaum-type function.

[0090] If there exists a positive definite and unbounded Lyapunov function V that satisfies the following inequality:

[0091]

[0092] where m0 and m1 are positive constants, g(γ) is a bounded function that is always positive or always negative, χ is a smooth function, and N(χ) is a smooth Nussbaum-type function. Then, both V and χ are bounded. t represents time; represents the adaptive parameter; dγ represents the integration variable;

[0093] If V in Equation (8) is bounded and the actual state error satisfies |z i (t)| < p i (t), then there must exist a positive constant p i such that |z i (t)| is maintained at a distance of p i from the preset performance function p i . That is, it satisfies:

[0094] |z i (t)| < p i (t) - p i < p i (t) (9)

[0095] means that the limit does not exist. Therefore, the condition for system stability is that this limit exists. Where, t0 represents any positive constant; z s (t) represents the state error; p s (t) represents the preset performance function.

[0096] S3. Introduce a coordinate transformation to satisfy the full-state constraint, and use the backstepping method to design a fixed-time controller to achieve the preset performance control of the constrained cyber-physical system under deception attacks and external disturbances;

[0097] Specifically, in this embodiment, the implementation process of the above S3 is as follows:

[0098] To solve the problem of the unknown sign of the function ψ i (x i ), the present invention proposes a new type of coordinate transformation method:

[0099]

[0100] where h i (t) represents the coordinate transformation function; z i (t) is the actual state error of the system, p i(t) is a preset performance function. The control objectives of the present invention mainly include two points: 1) all signals satisfy the preset constraint conditions; 2) all signals within the closed-loop system are bounded. To achieve the control objectives, a backstepping method is used to design the following controller:

[0101]

[0102] Among them, x i+1,d represents the virtual controller of state x i+1 ; h i (t) represents the coordinate transformation function; v represents the actual controller; x n+1,d represents the virtual controller of state x n+1 ; λ i is a constant variable, N(χ i ) is a Nussbaum-type function, χ i represents the adaptive parameter, which is a monotonically increasing smooth function, and its derivative is:

[0103]

[0104] The Nussbaum-type function adopted by the present invention is:

[0105]

[0106] The Nussbaum function is not limited to this special form, and any function satisfying requirement (7) can be used for proof.

[0107] Through the above solution, for the problem that the existing intrusion-tolerant controller design scheme based on preset performance control usually requires prior knowledge of the control direction of the system, while in practical applications, the control direction cannot be known in advance, the Nussbaum inequality adopted in this embodiment plays a key role in solving this technical problem.

[0108] S4. Use the proof by contradiction to prove the system stability condition and ensure the stable operation of the controlled system under spoofing attacks;

[0109] Specifically, in this embodiment, the implementation process of the above S4 is as follows:

[0110] To prove that (9) holds, the present invention uses the proof by contradiction. Assume that there exists a time t j representing the time when |z i (t)| is greater than p i (t) for the first time, and t s is defined as the smallest t j , that is:

[0111]

[0112] means that the limit exists. From 0 to ts Within the time range, as long as a conclusion contradictory to the hypothesis is found, the hypothesis can be proven false. Through the backstepping method, it can be obtained that:

[0113]

[0114] where, V i represents the Lyapunov function of state x i ; V i (0) represents the initial value of V i ; F i represents where represents the derivative of the preset performance function; λ i represents any positive constant; the parameter G ix (t) satisfies the conditions of inequality (8). From (9), there exists a positive constant p i such that |z i (t)| < p i (t) - p i < p i (t). This means that the limit does not exist. This contradicts the assumed conclusion. Therefore:

[0115]

[0116] Control objective 1 is achieved. From inequality (8), both V and χ are bounded, and it can be deduced that control objective 2 is achieved.

[0117] In summary, for a class of constrained uncertain cyber-physical systems, this embodiment proposes a new fixed-time intrusion-tolerant control strategy. The proposed strategy can effectively handle actuator attacks and external disturbances. Compared with traditional methods, the control strategy proposed in this embodiment has a lower complexity and can achieve the control objective without using a boundary function, improving the dynamic performance of the system. The control strategy proposed in this embodiment can ensure that all tracking errors enter the preset constraint boundary within a fixed time, where the tracking accuracy is known in advance and can be reset by adjusting relevant design parameters, enhancing the intrusion-tolerant ability of the system against actuator attacks.

[0118] Next, to verify the effectiveness of this scheme, MATLAB is used to simulate the constrained nonlinear cyber-physical system under spoofing attacks and external disturbances, and the effectiveness of the proposed control method is verified using an inverted pendulum as an example. Specifically, this embodiment uses the second-order pendulum model shown as Figure 3 for simulation:

[0119]

[0120] where:

[0121]

[0122] Among them, x1 represents the angle of the second-order pendulum, and x2 represents the angular velocity. The gravitational acceleration g = 9.8 m / s 2 , m = 0.1 kg and m c = 1 kg represent the weight of the cart and the weight of the pendulum rod in the second-order pendulum respectively. The general length of the pendulum rod l = 0.5 m, d(t) = 0.1*rand represents the disturbance, and the spoofing attack occurs at t = 10 s:

[0123]

[0124] Component failures also exist simultaneously:

[0125]

[0126] The initial state of the system is x1(0) = 0 and x2(0) = 0, and the preset performance function of the output is:

[0127] |y - y d | < p1(t) = (0.5 - 0.01)e -0.5t + 0.01

[0128] The preset performance function of the system state is:

[0129] |x2 - x 2,d | < p2(t) = (2 - 0.01)e -0.5t + 0.01

[0130] The actual state error of the system when suffering from a spoofing attack is:

[0131] z i (t) = x i - x i,d , i = 1,..., n.

[0132] Design the following controller:

[0133] x i+1,d = λ i N(χ i )h i (t), i = 1,..., n

[0134] v = x n+1,d

[0135]

[0136] Among them, the value of the adaptive parameter is set to χ i (0) = 0, λ i = 2.

[0137] In this embodiment, the designed fixed-time controller based on the preset performance method can make the system output error converge within a fixed time, and the convergence effect of the error is as shown in Figure 4 , and the constraint effect of the state is as shown in Figure 5 . As shown in Figure 4 and Figure 5 , the system output and state can track the reference signal within a fixed time and then always remain within the constraint range. The control input and control signal of the system are as shown in Figure 6 , and the system output, state, and values of the adaptive parameters are as shown in Figure 7 . From the above results, it can be seen that in the case of the coexistence of external disturbances, deception attacks, and component failures in the inverted pendulum system, the control strategy of the present invention can keep all signals in the system bounded. Thus, it can be seen that the method proposed by the present invention has strong robustness.

[0138] Second Embodiment

[0139] This embodiment provides an electronic device, as shown in Figure 8 , the electronic device includes: a processor and a memory; wherein, the processor and the memory can be connected through a communication bus; at least one instruction is stored in the memory, and the instruction is loaded and executed by the processor to implement the method of the first embodiment above. In addition, the electronic device may further include a transceiver, and the processor and the transceiver can be connected through a communication bus, and the transceiver is used to communicate with other devices.

[0140] Next, the specific components of the electronic device will be introduced in combination with Figure 8 :

[0141] Among them, the processor is the control center of the electronic device. The electronic device may include multiple processors, and each of these processors may be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). The processor here may be a single processor or a collective term for multiple processing elements. For example, the processor may be one or more central processing units (CPUs), or other general-purpose processors, application specific integrated circuits (ASICs), or one or more integrated circuits configured to implement the embodiments of the present invention. For example: one or more digital signal processors (DSPs), or one or more field programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc. The processor can execute various functions of the electronic device by running or executing software programs stored in the memory and calling data stored in the memory.

[0142] In a specific implementation, as an embodiment, the processor may include one or more CPUs. For example Figure 8 the CPU0 and CPU1 shown in

[0143] The memory is used to store the software program for implementing the solution of the present invention and is controlled by the processor for execution. The specific implementation manner may refer to the above method embodiments and will not be elaborated here.

[0144] Optionally, the memory may be a read-only memory (ROM) or other types of static storage devices that can store static information and instructions, a random access memory (RAM) or other types of dynamic storage devices that can store information and instructions, or may also be an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM), or other optical disc storage, optical disc storage (including compact discs, laser discs, optical discs, digital versatile discs, Blu-ray discs, etc.), magnetic disk storage media, or other magnetic storage devices, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory may be integrated with the processor or exist independently and be coupled to the processor through the interface circuit of the electronic device ( Figure 8 not shown in the figure), and the embodiments of the present invention do not make specific limitations on this.

[0145] The transceiver may include a receiver and a transmitter ( Figure 8 not shown separately in the figure). Among them, the receiver is used to implement the receiving function, and the transmitter is used to implement the transmitting function. The transceiver may be integrated with the processor or exist independently and be coupled to the processor through the interface circuit of the electronic device ( Figure 8 not shown in the figure), and the embodiments of the present invention do not make specific limitations on this.

[0146] In addition, it should be noted that Figure 8 the structure of the electronic device shown in the figure does not constitute a limitation on the device. The actual device may include more or fewer components than shown in the figure, or combine some components, or have a different component layout. In addition, the technical effects achieved by the electronic device when executing the method of the first embodiment above may refer to the technical effects described in the first embodiment above, so they will not be elaborated here.

[0147] Third Embodiment

[0148] This embodiment provides a computer-readable storage medium in which at least one instruction is stored. The instruction is loaded and executed by the processor to implement the method of the first embodiment above. Among them, the computer-readable storage medium may be a ROM, a random access memory, a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device, etc. The instructions stored therein can be loaded and executed by the processor in the terminal to implement the above method.

[0149] In addition, it should be noted that the present invention can be provided as a method, an apparatus, or a computer program product. Therefore, the embodiments of the present invention can take the form of all or part of a hardware embodiment, all or part of a software embodiment, or an embodiment combining software and hardware aspects. Moreover, when implemented using software, the embodiments of the present invention can take the form of a computer program product implemented on one or more computer-usable storage media containing computer-usable program code. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the processes or functions described in the embodiments of the present invention are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wired (such as infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or a data center containing one or more collections of available media. The available media can be magnetic media (such as floppy disks, hard disks, magnetic tapes), optical media (such as DVDs), or semiconductor media. The semiconductor media can be a solid-state drive.

[0150] The embodiments of the present invention are described with reference to the flowcharts and / or block diagrams of methods, terminal devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, and the combination of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, an embedded processor, or other programmable data processing terminal device to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing terminal device generate a device for implementing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0151] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing terminal device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device that implements the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1The functions specified in one or more boxes. These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device, so that a series of operation steps are executed on the computer or other programmable terminal device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable terminal device provide for implementing the steps of the functions specified in one or more processes and / or boxes. Figure 1 One process or more processes and / or boxes Figure 1 The steps of the functions specified in one box or more boxes.

[0152] It should also be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or terminal device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or terminal device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or terminal device comprising the element. In addition, the term "and / or" is merely a description of the associated relationship of the associated objects, indicating that three relationships may exist. For example, A and / or B may mean: A exists alone, A and B exist simultaneously, and B exists alone. Among them, A and B may be singular or plural. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship, but it may also indicate an "and / or" relationship, which can be understood specifically with reference to the context. "At least one" means one or more, and "a plurality" means two or more. "At least one of the following (items)" or similar expressions refer to any combination of these items, including any combination of single (item) or plural (items). For example, at least one of a, b or c may mean: a, b, c, a - b, a - c, b - c, or a - b - c, where a, b, c may be single or plural.

[0153] In addition, it can be understood that in various embodiments of the present invention, the magnitudes of the serial numbers of the above processes do not mean the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

[0154] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0155] In the several embodiments provided herein, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of functional modules / units is merely a logical functional division. In actual implementation, other division methods may be used, such as multiple units or components being combined or integrated into another device, or some features being ignored or not implemented. Furthermore, the coupling or direct coupling or communication connection shown or discussed between each other may be through some interface, indirect coupling or communication connection between devices or units, and may be electrical, mechanical, or other forms. Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, i.e., they may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of the present embodiment according to actual needs. In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit.

[0156] If the method is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0157] Finally, it should be noted that the above description is only a preferred embodiment of the present invention. It should be pointed out that although the preferred embodiments of the present invention have been described, for those of ordinary skill in the art, once they know the basic creative concept of the present invention, without departing from the principle described in the present invention, several improvements and refinements can still be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Therefore, the appended claims are intended to be construed to include the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present invention.

Claims

1. A performance control method for a constrained nonlinear cyber-physical system, characterized in that Including: Establish a control-oriented dynamic model of a constrained nonlinear cyber-physical system with external disturbances under deception attacks, and mathematically characterize bounded multiplicative and additive deception attacks; Construct a Lyapunov function based on the preset performance control method, and give a method for determining the system stability based on the Nussbaum inequality; Introduce coordinate transformation to satisfy the full-state constraints, and use the backstepping method to design a fixed-time controller to achieve the preset performance control of the constrained nonlinear cyber-physical system under deception attacks and external disturbances.

2. The performance control method of the constrained nonlinear cyber-physical system according to claim 1, characterized in that The expression of the dynamic model is: y = x1 Among them, represents the derivative of the \(i\)-th state with respect to time; represents the derivative of the \(n\)-th state with respect to time; \(x\) i+1 represents the \((i + 1)\)-th state; \(n\) represents the highest order of the system; and are both unknown nonlinear functions; \(u\) represents the control input; \(x_1\) represents the first state; is the system state variable; \(x\) i represents the \(i\)-th state; \(T\) represents matrix transpose; \(R\) i represents the set of real numbers; \(y\) is the system output; \(d\) i (t) is the external disturbance; and are both unknown functions, defined as bounded; The deception attack on the system control output is given by: u = ζ(t)v + τ(t) where \(v\) is the actual control input; \(\zeta(t)\) and \(\tau(t)\) are the bounded multiplicative and additive attack coefficients, respectively; \(\zeta(t)\) is defined as bounded, i.e., where and are arbitrary positive constants.

3. The performance control method of the constrained nonlinear cyber-physical system according to claim 2, characterized in that The constructing a Lyapunov function based on the preset performance control method, and giving a method for determining the system stability based on the Nussbaum inequality includes: Set the preset performance function p i (t): where p i0 , p i∞ and β i are all normal constants and satisfy p i0 > p i∞ ; e represents the natural constant, t represents time; n represents the highest order of the system; Express the actual state error of the system when suffering from deception attacks as: z i (t) = x i -x i,d , i = 1, ..., n Among them, z i (t) represents the error of state x i ; x i represents the i-th state; x i,d represents the virtual controller of state x i ; Design a Lyapunov function: where, V i is the designed Lyapunov function; z i (t) represents the error of state x i ; p i (t) represents the preset performance function of state x i . If there exists a positive definite and unbounded Lyapunov function V that satisfies the following formula, then both V and χ are bounded; where, m0 and m1 are positive constants; g(γ) is a bounded function that is always positive or always negative; χ is a smooth function; N(χ) is a smooth Nussbaum-type function; t represents time; represents the adaptive parameter; dγ represents the integration variable; If V is bounded and the actual state error satisfies |z i (t)| < p i (t), then there must exist a positive constant p i such that |z i (t)| is maintained at a distance of p i from the predefined performance function p i ; that is, it satisfies: |z i (t)| < p i (t) - p i < p i (t) Means the limit does not exist; thus the condition for system stability is that this limit exists; where, t0 represents any positive constant; z s (t) represents the state error; p s (t) represents the preset performance function.

4. The performance control method of the constrained nonlinear cyber-physical system according to claim 3, wherein The introducing coordinate transformation to satisfy the full-state constraints, and using the backstepping method to design a fixed-time controller includes: Implement coordinate transformation using the following formula: Among them, h i (t) represents the coordinate transformation function; z i (t) is the actual state error of the system; p i (t) is the preset performance function; To achieve the preset control objective, design the following controller using the backstepping method: x i+1,d = λ i N(χ i )h i (t), i = 1, ..., n v = x n+1,d Among them, the preset control objective includes that all signals satisfy the preset constraint conditions and all signals in the closed-loop system are bounded; x i+1,d represents the state x i+1 of the virtual controller; h i (t) represents the coordinate transformation function; v represents the actual controller; x n+1,d represents the state x n+1 of the virtual controller; λ i is a constant variable; N(χ i ) is a Nussbaum-type function, χ i is a monotonically increasing smooth function, and its derivative with respect to time is:

5. The performance control method of the constrained nonlinear cyber-physical system according to claim 1, characterized in that After introducing coordinate transformation to facilitate the satisfaction of full-state constraints and using the backstepping method to design a fixed-time controller, the performance control method of the constrained nonlinear cyber-physical system further includes: Prove the system stability conditions to ensure the stable operation of the controlled system under deception attacks.

6. The performance control method for the constrained nonlinear cyber-physical system according to claim 5, characterized in that, The proving the system stability conditions to ensure the stable operation of the controlled system under deception attacks includes: Prove the system stability conditions by contradiction to ensure the stable operation of the controlled system under deception attacks.

7. The performance control method of the constrained nonlinear cyber-physical system according to claim 1, characterized in that The performance control method of the constrained nonlinear cyber-physical system further includes: Use MATLAB to simulate the constrained nonlinear cyber-physical system under deception attacks and external disturbances, and verify the effectiveness of the performance control method of the constrained nonlinear cyber-physical system with an inverted pendulum as an example.

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