Controller design method for realizing distributed cooperative control of multiple unmanned systems under sequence scaling attack and controller

Abstract

The invention belongs to the technical field of controller design, and particularly provides a controller design method for realizing distributed cooperative control of multiple unmanned systems under sequence scaling attacks and a controller, and the method comprises the steps: constructing a network system model; constructing a controller model; creating a first algorithm, performing multi-unmanned-system distributed cooperative control on the network system model by using parameters defined according to the first algorithm based on the controller model under the fixed topology and by constructing a Lyapunov function, and determining a controller under the fixed topology in which the network system is stable under a sequence scaling attack state; creating a second algorithm, and using parameters defined according to the second algorithm based on the controller model under the dynamic topology; through constructing a Lyapunov function, distributed cooperative control of multiple unmanned systems is carried out on a network system model, and a controller under a stable dynamic topology of a network system under a sequence scaling attack state is determined. The problem of a multi-agent system under sequence scaling attacks is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of distributed collaborative controller design, and in particular to a controller design method and a controller for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attacks. Background Art

[0002] In recent years, the consistency problem of linear multi-unmanned systems has attracted the attention of researchers in many fields and has played a key role in distributed consistency tracking, military aircraft control, cyber-physical systems (CPS), neural networks, opinion dynamics, and complex networks. Cyber ​​attacks are an important threat to cyber-physical systems. Among them, multi-unmanned systems attack the system by temporarily destroying the communication network or topology of the system. Different from the single attack model, the sequence scaling attack includes many types of attacks, such as DoS attacks, deception attacks, and some time series attacks. In order to defend against these malicious attacks, some control protocols have been proposed. However, most of these studies assume that only cooperative relationships exist, and ignore the existence of competitive relationships in real-world cyber-physical systems. In addition, event-triggered control methods will inevitably lead to additional trigger times and waste energy resources.

[0003] When resources are limited, it is usually more inclined to design energy-saving control strategies. Logarithmic quantizers have received widespread attention as effective control methods. At the same time, some related works have also proved that logarithmic quantizers have been effectively used in different scenarios. However, most of the work only considers attacks or quantized communications during use, and there is still little research on how to combine sequence scaling attacks with logarithmic quantizers based on symbolic networks.

[0004] The above-mentioned work on competitive relations relies on communication topology that is only applicable to a specific network structure. However, due to the possible interruption of communication patterns or the change of positions of multiple entities, the topology may be directed and time-varying. In the attack and defense process of network electronic confrontation in the military field, due to the lack of prediction of network attack patterns and reliability, the timeliness of enemy attacks is not well understood, and it is impossible to adaptively switch formations based on variable topology and symbolic graphs to counter the enemy's attack strategy, so it is impossible to effectively eliminate the impact of network attacks. Summary of the invention

[0005] In view of the problems existing in the above-mentioned existing controllers, the present invention provides a controller design method and a controller for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attacks.

[0006] In a first aspect, the technical solution of the present invention provides a controller design method for realizing distributed collaborative control of multiple unmanned systems under a sequence scaling attack, comprising the following steps: Build network system models; Constructing controller models; including controller models under fixed topology and controller models under dynamic topology; A first algorithm is created, and based on the constructed fixed topology controller model, the parameters defined according to the first algorithm are used to construct a Lyapunov function to perform distributed collaborative control of multiple unmanned systems on the network system model, and determine a controller under the fixed topology that stabilizes the network system under a sequence scaling attack; A second algorithm is created, and the controller model under the constructed dynamic topology uses the parameters defined by the second algorithm; by constructing a Lyapunov function, the network system model is subjected to distributed collaborative control of multiple unmanned systems, and a controller under the dynamic topology that stabilizes the network system when subjected to a sequence scaling attack is determined.

[0007] As a further limitation of the technical solution of the present invention, the steps of constructing the network system model include: Build a system with a leader and N A general linear multi-agent system with followers; i The dynamic equation of a follower is as follows:

[0008] In the formula, and Respectively i The state input and control input of each agent, and are constant matrices respectively.

[0009] As a further limitation of the technical solution of the present invention, the step of constructing the controller model includes: Controller model under fixed topology:

[0010] In the formula, , , represents the coupling strength, is the feedback gain matrix; Controller model under dynamic topology:

[0011] In the formula, and , .

[0012] As a further limitation of the technical solution of the present invention, the steps of creating a first algorithm, using parameters defined according to the first algorithm based on the constructed controller model under the fixed topology, constructing a Lyapunov function, performing distributed collaborative control of multiple unmanned systems on the network system model, and determining the controller under the fixed topology in which the network system is stable under the state of sequence scaling attack include: Creating the first algorithm: Setting a positive scalar , , , choose the coupling strength and parameters ; Solve matrix inequalities:

[0013]

[0014] In the formula, , , , , find the positive definite matrix and ; The gain matrix is ​​defined as , ; Calculate the error function of the system under fixed topology based on the constructed controller model under fixed topology; Using the parameters defined by the first algorithm, by constructing the Lyapunov function, the network system model is subjected to distributed collaborative control of multiple unmanned systems, and the final value of the error function of the system under the fixed topology is determined to obtain the controller under the fixed topology.

[0015] As a further limitation of the technical solution of the present invention, the step of calculating the error function of the system under the fixed topology based on the constructed controller model under the fixed topology includes: Based on the constructed fixed topology controller model, we get:

[0016]

[0017] definition , represents the error value of the system, and the error function of the system under fixed topology can be obtained:

[0018] .

[0019] As a further limitation of the technical solution of the present invention, the steps of performing distributed collaborative control of multiple unmanned systems on the network system model by constructing a Lyapunov function using the parameters defined according to the first algorithm and determining the final value of the error function of the system under the fixed topology include: Lyapunov function for: ; When the system is not attacked, ,right The derivative is:

[0020] In the formula ; When a multi-unmanned system is attacked by sequence scaling, , , and we can get the following derivative: ; In the formula, ;for ,when Sometimes Then we get: Get the final value of the system's error function.

[0021] As a further limitation of the technical solution of the present invention, a second algorithm is created, and the controller model under the constructed dynamic topology uses parameters defined according to the second algorithm; by constructing a Lyapunov function, the network system model is subjected to distributed collaborative control of multiple unmanned systems, and the steps of determining the controller under the dynamic topology in which the network system is stable under the state of sequence scaling attack include: Create the second algorithm: Set a positive scalar , , , choose the coupling strength and parameters , , solve the following two matrix inequalities:

[0022]

[0023] In the formula , represents the system coupling parameter, , represents the maximum eigenvalue, , represents the minimum eigenvalue, , indicating the switching signal, , system coupling parameters, , represents the maximum eigenvalue under the switching mode, , represents the minimum eigenvalue under the switching mode, and finds the positive definite matrix and ; The gain matrix is ​​defined as , ; Calculate the error function of the system under the dynamic topology based on the constructed controller model under the dynamic topology; Using the parameters defined by the second algorithm, by constructing the Lyapunov function, the network system model is subjected to distributed collaborative control of multiple unmanned systems, the final value of the error function of the system under the dynamic topology is determined, and the controller under the dynamic topology is obtained.

[0024] As a further limitation of the technical solution of the present invention, the error function of the system under dynamic topology is: .

[0025] As a further limitation of the technical solution of the present invention, the steps of performing distributed collaborative control of multiple unmanned systems on the network system model by constructing a Lyapunov function using the parameters defined according to the second algorithm and determining the final value of the error function of the system under the dynamic topology include: Lyapunov function for ; When the system is not attacked, ,right The derivative is

[0026] Depend on get:

[0027] In the formula ; When the system is attacked by sequence scaling, , ,right The derivative is:

[0028] because

[0029] In the formula, ; for ,when hour, Get the final value of the system's error function.

[0030] In a second aspect, the technical solution of the present invention provides a controller, which is a controller designed by the method described in the first aspect.

[0031] It can be seen from the above technical solutions that the present invention has the following advantages: a control protocol based on scaling factors is constructed, which eliminates the destructive effects of external attacks and state changes on the multi-agent system and effectively solves the problem of the multi-agent system under sequence scaling attacks.

[0032] In addition, the invention has a reliable design principle, a simple structure and a very broad application prospect.

[0033] It can be seen that compared with the prior art, the present invention has outstanding substantive features and significant progress, and the beneficial effects of its implementation are also obvious. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 It is a basic diagram of the topology of 12 individuals in one embodiment of the present invention.

[0036] Figure 2 Graph showing the state change process of a linear dynamics agent with fixed topology.

[0037] Figure 3 This is a diagram of the state change process of a linear dynamics agent with dynamic topology.

[0038] Figure 4 FIG. 1 is a diagram of a linear dynamic state change process of a fixed topology in an embodiment.

[0039] Figure 5 For Figure 4 Graph showing the linear dynamic state change process of the corresponding dynamic topology.

[0040] Figure 6 This is a diagram of the linear dynamic state change process of a fixed topology.

[0041] Figure 7 For Figure 6 Graph showing the linear dynamic state change process of the corresponding dynamic topology.

[0042] Figure 8 This is the error evolution diagram without quantization and attack under fixed topology.

[0043] Fig. 9 Error evolution diagram with quantization and attack under fixed topology.

[0044] Fig.10This is the error evolution diagram without quantization and attack under dynamic topology.

[0045] Fig.11 Error evolution diagram with quantization and attack under dynamic topology.

[0046] Fig.12 This is the error evolution diagram without quantization and attack under dynamic topology when the number of agents reaches 40.

[0047] Fig.13 Error evolution diagram with quantization and attack under dynamic topology when the number of agents reaches 40.

[0048] Fig.14 It is a schematic flow chart of the method provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0049] In order to enable those skilled in the art to better understand the technical solutions in the present invention, 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. 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 creative work should fall within the scope of protection of the present invention.

[0050] like Fig.14 As shown, an embodiment of the present invention provides a controller design method for realizing distributed collaborative control of multiple unmanned systems under a sequence scaling attack, comprising the following steps: Build network system models; It should be noted that in digital control / hybrid control / network control systems, information transmission between components is carried out through communication channels. In order for information to be transmitted in the channel, it must first be quantized and encoded. At the same time, considering that the bandwidth of the channel in practical applications is limited, in order to ensure that the system can operate normally within a given bandwidth, quantization technology is needed to reduce the communication rate, so quantization is very basic and important. The specific model of the logarithmic quantizer is: A. Logarithmic Quantizer set up is a real number The associated function, quantization level is: (1) In the formula, is the scaling factor, is the quantization accuracy. Specifically, the quantizer model is defined as follows: (2) According to the definition of quantizer, we can get , .definition and , we can get , where , indicating the quantization accuracy , represents the quantization sector boundary.

[0051] B. Network Attack: Sequence Scaling Attack It is assumed that sequence scaling attacks can temporarily disrupt communication and network topology. Each network attack occurs within a certain time interval, called the attack interval. After the attack, the multi-agent system can be restored to its original state. Therefore, the sequence scaling attack contains multiple sequence scaling attack sequences, and its number is defined as .

[0052] Then, The attack interval is recorded as ,in Indicates the start time. Indicates k The duration of the attack.

[0053] When the internal attack begins, you can get (3); Its complement is , On the other hand, the definition , where The effective sequence scaling attack time interval set is: ; ; Assume that the corresponding system topology set is , which is used to describe the evolution of topological connection disconnection when the sequence scaling attack is active and topological connection recovery when the sequence scaling attack is dormant. is the number of connected topologies that have not been attacked, and its switching topology set is . is the total number of switching topologies. Let represents the number of disconnected topologies affected by the sequence scaling attack, and the corresponding set of switching topologies is The disconnected topology set when the attack exists and the connected topology set when the attack is dormant satisfy Next, we consider attacks with scaling properties:

[0054] In the formula, represents the scaling factor, . It is a DoS attack.

[0055] set up Indicates the interval The number of attacks during the sequence scaling is defined as .

[0056] set up for The total time of the intra-sequence scaling attack. And there is , , , , so that , .

[0057] Lemma 1: is positive definite, and there exists a matrix , , so that ,in ,and .

[0058] Having a leader and N A general linear multi-agent system with followers. i The dynamic equation of a follower is as follows: (4) In the formula, and Respectively i The state input and control input of each agent, and are constant matrices respectively. Similarly, (5) Definition 3: For some In this case, the leader-follower safe bipartite consistency problem expressed by equations (4) and (5) can be solved if the following equations are satisfied:

[0059]

[0060] The above formula can be further written as: .

[0061] Constructing a controller model; including a controller model under a fixed topology and a controller model under a dynamic topology; (6) In the formula, , , represents the coupling strength, As the feedback gain matrix, we can get (7)

[0062] definition , represents the error value of the system, we can get: (8) (9) The system can remain stable only when the error value between the leader and the follower in the system tends to 0 or a certain value.

[0063] A first algorithm is created, and based on the constructed fixed topology controller model, the parameters defined according to the first algorithm are used to construct a Lyapunov function to perform distributed collaborative control of multiple unmanned systems on the network system model, and determine a controller under the fixed topology that stabilizes the network system under a sequence scaling attack; First algorithm: 1) Set the following positive scalar , , , choose the coupling strength and parameters , From Lemma 1; 2) Solve the following two matrix inequalities: (10) (11) In the formula , , , , find the positive definite matrix and .

[0064] 3) Define the gain matrix as , .

[0065] Based on the control model (6), using the parameters defined according to the first algorithm, the multi-unmanned system (4) and (5) achieves secure bipartite consistency under sequence scaling attacks.

[0066] Lyapunov function for ; When the system is not attacked, ,right The derivative is Can get (12) In the formula .

[0067] When a multi-unmanned system is attacked by sequence scaling, , Similar to the above analysis, The derivative is:

[0068] therefore,

[0069] In the formula, .

[0070] for ,when Sometimes

[0071] Further deduction can be obtained Based on the above derivation, it is not difficult to find the final value of the system's error function.

[0072] Create a second algorithm, based on the controller model under the constructed dynamic topology using the parameters defined by the second algorithm; construct a Lyapunov function to perform distributed collaborative control of multiple unmanned systems on the network system model, and determine the controller under the dynamic topology that is stable for the network system under the state of sequence scaling attack; assume All graphs in contain a directed spanning tree with a leader at the root, are structurally balanced, and have the same set of binary elements. and .

[0073] Applying Lemma 1 to For all the graphs in , we can directly draw the following results.

[0074] Lemma 2: Diagonal matrices , If it exists, then , where , , .

[0075] Construct the input function: (13) In the formula (19) and , , similar to the fixed topology, we have: (20) Formula (20) represents the system function under the switching topology condition.

[0076] Second algorithm: 1) Assume the following positive scalar , , , choose the coupling strength and parameters , ; 2) Solve the following two matrix inequalities: (14) (15) In the formula , represents the system coupling parameter, , represents the maximum eigenvalue, , represents the minimum eigenvalue, , indicating the switching signal, , system coupling parameters, , represents the maximum eigenvalue under the switching mode, , represents the minimum eigenvalue under the switching mode, and finds the positive definite matrix and .

[0077] 3) Define the gain matrix as , .

[0078] In the controller model (13), a control input signal suitable for the target system is selected, and combined with the quantitative control information of the system, the second algorithm is used and the corresponding variable parameters are selected. By constructing the Lyapunov function, the stability of the system under the state of sequence scaling attack is determined, and the system safety bisection consistency is achieved. Compared with general control systems, this system can not only maintain stability under continuous mode switching, but also effectively eliminate external interference of the system. After adding the quantitative controller, the adjustability of the system is enhanced, and the convergence rate of the system can be improved by adjusting the variable parameters in the algorithm.

[0079] Lyapunov function for ; When the system is not attacked, ,right The derivative is:

[0080] because ; According to the derivation, we can get ; In the formula .

[0081] When the system is attacked by sequence scaling, , , similar to the above analysis, The derivative is:

[0082]

[0083] In the formula, .for ,when After mathematical derivation, we get .

[0084] Therefore, the multi-agent system can achieve secure bipartite consistency under the directed switching topology when subjected to sequence scaling attacks. The final value of the system's error function is bounded within any time range. The directed switching topology in this application is a dynamic topology.

[0085] The embodiment of the present invention also provides a controller designed by the method described in the above embodiment. A numerical example is given to illustrate that the constructed controller can guarantee convergence to safe bipartite consistency. Consider a large-scale multi-unmanned system consisting of 12 and 40 unmanned combat aircraft with adversarial edges, respectively. The topology of the 12 individuals is as follows Figure 1 As shown, negative edges represent competition. When the system is not attacked, the directed topology of the system always contains directed spanning trees. After being attacked, the topological connections change, the topology is paralyzed, and no longer contains directed spanning trees. The corresponding Laplace matrix is ​​obtained and solved to obtain , , , The state vector of an individual , respectively, velocity, angle of attack, pitch velocity and pitch angle. Given the input equation (19), the dynamic equation of the unmanned aerial vehicle is: , , , , , , , , , , , , , The communication channels (1,3)(4,6)(5,9)(7,8)(10,11)(2,12) are affected by the attack interference, and the corresponding scaling factors are 0.8, 0.6, 0.3, 0, 0.5, 0.9. By solving the linear matrix inequality, we get K =[−0.7319 0.6831 0.5512 0.4623], .

[0086] Different from the current research that only considers fixed topology and is not vulnerable to any attack damage, this paper considers switching topology and sequence scaling attacks. Under the controller equations (6) and (13), the 12 individual trajectories with positive and negative edges and sequence scaling attacks are as follows: Figure 2 and Figure 3 shown. Figure 4 , Figure 5 and Figure 6 , Figure 7 The trajectories of 12 agents with only positive edges and attacks are shown, which shows that the proposed method can solve the problem of secure bisection consistency of linear / nonlinear multi-unmanned systems under sequence scaling attacks and DoS attacks. Figure 8 reflects the error change process under the non-sequential scaling attack, and Fig. 9 It depicts the error change process of the linear dynamics individual using the logarithmic quantizer proposed in this paper under the sequence scaling attack.

[0087] Fig.10 and Fig.11 This shows that, regardless of whether there is a sequence scaling attack, the controller of the present application can effectively solve the security bipartite consistency under the switching topology. When the system scale is expanded, the same simulation parameters as the above settings can be selected. And Fig.12 and Fig.13 It is described that when the number of agents reaches 40, the controller formula (13) can also effectively achieve safe bipartite consistency under quantized information and switching topology.

[0088] Although the present invention has been described in detail with reference to the accompanying drawings and in combination with the preferred embodiments, the present invention is not limited thereto. Without departing from the spirit and essence of the present invention, a person of ordinary skill in the art may make various equivalent modifications or substitutions to the embodiments of the present invention, and these modifications or substitutions shall be within the scope of the present invention. Any person of ordinary skill in the art may easily think of changes or substitutions within the technical scope disclosed by the present invention, and these shall be within the scope of protection of the present invention.

Claims

1. A controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attacks, characterized in that: The steps include: Build network system models; Constructing a controller model; including a controller model under a fixed topology and a controller model under a dynamic topology; A first algorithm is created, and based on the constructed fixed topology controller model, the parameters defined according to the first algorithm are used to construct a Lyapunov function to perform distributed collaborative control of multiple unmanned systems on the network system model, and determine a controller under the fixed topology that stabilizes the network system under a sequence scaling attack; Creating a second algorithm based on the controller model under the constructed dynamic topology using parameters defined according to the second algorithm; By constructing the Lyapunov function, the distributed collaborative control of multiple unmanned systems in the network system model is carried out, and the controller under the dynamic topology that stabilizes the network system under the state of sequence scaling attack is determined.

2. The controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attack according to claim 1 is characterized in that: The steps to construct the network system model include: Build a system with a leader and N A general linear multi-agent system with followers; i The dynamic equation of a follower is as follows: In the formula, and Respectively i The state input and control input of each agent, and are constant matrices respectively.

3. The controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attack according to claim 2 is characterized in that: The steps to build a controller model include: Controller model under fixed topology: In the formula, , , represents the coupling strength, is the feedback gain matrix; Controller model under dynamic topology: In the formula, and , .

4. The controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attack according to claim 3 is characterized in that: The steps of creating a first algorithm, performing distributed collaborative control of multiple unmanned systems on the network system model based on the constructed controller model under the fixed topology using parameters defined according to the first algorithm by constructing a Lyapunov function, and determining the controller under the fixed topology in which the network system is stable under the state of sequence scaling attack include: Creating the first algorithm: Setting a positive scalar , , , choose the coupling strength and parameters ; Solve matrix inequalities: In the formula, , , , , find the positive definite matrix and ; The gain matrix is ​​defined as , ; Calculate the error function of the system under fixed topology based on the constructed controller model under fixed topology; Using the parameters defined by the first algorithm, by constructing the Lyapunov function, the network system model is subjected to distributed collaborative control of multiple unmanned systems, and the final value of the error function of the system under the fixed topology is determined to obtain the controller under the fixed topology.

5. The controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attack according to claim 4 is characterized in that: The steps of calculating the error function of the system under the fixed topology based on the constructed controller model under the fixed topology include: Based on the constructed fixed topology controller model, we get: definition , represents the error value of the system, and the error function of the system under fixed topology can be obtained: 。 6. The controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attack according to claim 5 is characterized in that: The steps of performing distributed collaborative control of multiple unmanned systems on the network system model by constructing a Lyapunov function using the parameters defined according to the first algorithm and determining a final value of the error function of the system under a fixed topology include: Lyapunov function for: ; When the system is not attacked, ,right The derivative is: In the formula ; When a multi-unmanned system is attacked by sequence scaling, , , and we can get the following derivative: ； In the formula, ;for ,when Sometimes: Then we get: Get the final value of the system's error function.

7. The controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attack according to claim 6 is characterized in that: Creating a second algorithm based on the controller model under the constructed dynamic topology using parameters defined according to the second algorithm; By constructing the Lyapunov function, the distributed collaborative control of multiple unmanned systems in the network system model is carried out, and the steps of determining the controller under the dynamic topology of the network system under the state of sequence scaling attack include: Create the second algorithm: Set a positive scalar , , , choose the coupling strength and parameters , , solve the following two matrix inequalities: In the formula , represents the system coupling parameter, , represents the maximum eigenvalue, , represents the minimum eigenvalue, , indicating the switching signal, , system coupling parameters, , represents the maximum eigenvalue under the switching mode, , represents the minimum eigenvalue under the switching mode, and finds the positive definite matrix and ; The gain matrix is ​​defined as , ; Calculate the error function of the system under the dynamic topology based on the constructed controller model under the dynamic topology; Using the parameters defined by the second algorithm, by constructing the Lyapunov function, the network system model is subjected to distributed collaborative control of multiple unmanned systems, the final value of the error function of the system under the dynamic topology is determined, and the controller under the dynamic topology is obtained.

8. The controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attack according to claim 7 is characterized in that: Error function of the system under dynamic topology: .

9. The controller design method for realizing distributed collaborative control of multiple unmanned systems under sequence scaling attack according to claim 8 is characterized in that: The steps of performing distributed collaborative control of multiple unmanned systems on the network system model by constructing a Lyapunov function using the parameters defined according to the second algorithm and determining a final value of the error function of the system under the dynamic topology include: Lyapunov function for ; When the system is not attacked, ,right The derivative is: Depend on get: In the formula ; When the system is attacked by sequence scaling, , ,right The derivative is: because In the formula, ; for ,when hour, Get the final value of the system's error function.

10. A controller, characterized in that: The controller is a controller designed by the method according to claims 1-9.

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