Adaptive iterative learning inclusion control method for multiple mobile robots under false data injection attack

Abstract

The invention discloses a multi-mobile-robot adaptive iterative learning inclusion control method under false data injection attack, and belongs to the technical field of multi-agent control. The method mainly aims at the inclusion control problem of the multi-mobile-robot system under the false data injection attack. The control scheme comprises the following steps: establishing a multi-mobile-robot system model and a state equation of the multi-mobile-robot system model; establishing a relationship between an original system state and an attacked state; defining an expected error trajectory and coordinate transformation; constructing a Lyapunov function, introducing an echo state network, and designing a virtual controller of a first subsystem; constructing a Lyapunov function, introducing an echo state network, and designing a control input signal; constructing a composite energy function, introducing a projection operator, and designing an adaptive law; according to the adaptive iterative learning inclusion control method disclosed by the invention, all followers can converge to a convex hull formed by a leader along with the increase of the number of iterations under the false data injection attack of the multi-mobile robot system.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent control technology, and more specifically, relates to a multi-mobile robot adaptive iterative learning control method under false data injection attacks. Background Technology

[0002] In recent years, with the convergence of control, communication, and computing technologies, the control of multiple mobile robots has attracted widespread attention from scholars worldwide, resulting in significant research achievements. Compared to single-unit mobile robot systems, multiple mobile robot systems can accomplish more complex tasks and offer advantages such as high efficiency and high fault tolerance. Currently, multiple mobile robot systems and related theories have been applied in numerous fields, such as unmanned ground vehicles, unmanned aerial vehicles, and autonomous underwater robots.

[0003] Research on the control performance of multi-mobile robots needs to consider the following two aspects: 1. Due to the requirements of multiple different and complex tasks, multiple leaders are often needed to complete the coordinated control tasks of the system, so that all followers can eventually enter and remain in the convex hull formed by the leaders; 2. Multi-mobile robot communication networks are vulnerable to attacks. False data injection is a common attack mode that may occur between followers or between leaders and followers. Therefore, it is necessary to ensure the stability of the system under attack.

[0004] Currently, iterative learning control is widely used in multi-mobile robots, effectively solving their control problems and offering advantages such as learning from prior experience to improve performance and achieve high-precision tracking. Meanwhile, adaptive backstepping control can address the nonlinearity and uncertain parameters inherent in multi-mobile robots. However, these methods all require the assumption of identical initial conditions. Furthermore, traditional approaches are only applicable to strictly feedback systems; however, multi-mobile robots under network attacks exhibit strong nonlinearity and complex coupling relationships, rendering traditional methods unsuitable for direct application. Therefore, designing an inclusive control method for multi-mobile robot systems under network attacks is a pressing issue. Summary of the Invention

[0005] This invention discloses an adaptive iterative learning method for multiple mobile robots under spoofed data injection attacks, including a control method. The technical problem to be solved is to ensure that all followers of a multi-mobile robot can eventually enter and remain within the convex hull formed by the leader under a network attack, thus enabling its wider application scenarios.

[0006] To achieve the above-mentioned objectives, this application adopts the following technical solution:

[0007] S1: Establish a multi-mobile robot system model and its state equations;

[0008] S2: Establish the relationship between the original system state and the attacked state;

[0009] S3: Define the expected error trajectory and coordinate transformation;

[0010] S4: Construct a Lyapunov function, introduce an echo state network, and design a virtual controller for the first subsystem;

[0011] S5: Construct the Lyapunov function, introduce the echo state network, and design the control input signal;

[0012] S6: Construct a composite energy function, introduce a projection operator, and design an adaptive law.

[0013] In step S1, establishing the multi-mobile robot system model and its state equations specifically includes:

[0014] Consider a One leader and A multi-mobile robot system consisting of several followers, the first The dynamics model of a follower is as follows:

[0015] ;

[0016] in, ; It is the displacement of the mobile robot; It is the weight of the mobile robot; It is the damping coefficient; It is the input torque; It is the transient response coefficient;

[0017] make , and The original system can be rewritten as follows:

[0018] ;

[0019] ;

[0020] ;

[0021] in, It is the number of iterations;

[0022] To describe the communication relationships between the mobile robots in the system, we introduce graph theory: consider a directed graph. ,in, It is a set of nodes; It is an edge set; It is an adjacency matrix; if the edge ,but for The adjacent points, and adjacent matrix elements ,on the contrary Directed graph The Laplacian matrix is ​​defined as ,in, It is the in-degree matrix; It is the first The in-degree of a mobile robot.

[0023] In step S2, establishing the relationship between the original system state and the attacked state specifically includes:

[0024] Because communication networks are open, multi-mobile robot systems are vulnerable to attacks; therefore, this invention considers a common type of spoofing attack that occurs simultaneously on leader-follower and follower-follower communication links; [Attacked state] And the leader's actual measurable output Defined as:

[0025] ;

[0026] ;

[0027] in, and It is unknown and false data;

[0028] Establish the original state and the state of being attacked The relationship between them, namely:

[0029] ;

[0030] in, ;

[0031] Therefore, the system state equation under a fake data injection attack is:

[0032] ;

[0033] ;

[0034] ;

[0035] in, and It is an unknown nonlinear function.

[0036] In step S3, defining the expected error trajectory and coordinate transformation specifically includes:

[0037] Define the error variable as:

[0038] ;

[0039] ;

[0040] To relax the traditional iterative learning algorithm's assumption of identical initial conditions, the desired error trajectory is designed as follows:

[0041] ;

[0042] in, It sets the time; function exist Monotonically decreasing, , ; =0 ensures the smoothness of the required error trajectory;

[0043] Define the following coordinate transformation:

[0044] ;

[0045] ;

[0046] in, It is a virtual controller.

[0047] In step S4, the construction of the Lyapunov function, the introduction of the echo state network, and the design of the virtual controller for the first subsystem specifically include:

[0048] calculate From the time derivative, we can obtain:

[0049]

[0050]

[0051]

[0052]

[0053] ;

[0054] in, It is an unknown nonlinear function;

[0055] Choose the following Lyapunov functions:

[0056] ;

[0057] Taking its derivative, we get:

[0058]

[0059] ;

[0060] Consider the following echo-state network:

[0061]

[0062]

[0063] ;

[0064] in, It is an unknown parameter; , It is an activation function; It is a weight vector; It is the number of neurons; It is an approximation error; It is an echo state network input;

[0065] Based on the above design, we can obtain:

[0066] ;

[0067] Design the following virtual controller:

[0068] ;

[0069] in, These are design parameters; yes The estimated value; the estimation error is defined as ;

[0070] Based on the designed virtual controller, we can obtain:

[0071] .

[0072] In step S5, the construction of the Lyapunov function, the introduction of the echo state network, and the design of the control input signal specifically include:

[0073] calculate From the time derivative, we can obtain:

[0074]

[0075] ;

[0076] in, = It is an unknown nonlinear function;

[0077] Choose the following Lyapunov functions:

[0078] ;

[0079] For the above Lyapunov function Taking the derivative, we get:

[0080]

[0081] ;

[0082] Consider the following echo-state network:

[0083] ;

[0084] in, It is an unknown parameter; , It is an activation function; It is a weight vector; It is the number of neurons; It is an approximation error; It is an echo state network input;

[0085] Furthermore, we can obtain:

[0086]

[0087] ;

[0088] Design the following intermediate variables:

[0089] ;

[0090] in, These are design parameters; yes The estimated value; the estimation error is defined as ;

[0091] but It can be rewritten as:

[0092]

[0093] ;

[0094] It is easy to see that the inequality Therefore, the control input is designed as follows:

[0095] ;

[0096] in, yes The boundary; yes The estimated value and The estimation error is defined as follows: ;

[0097] Based on the above design, we can obtain:

[0098]

[0099] ;

[0100] Depend on Therefore, we can conclude that:

[0101] ;

[0102] According to inequality theory, It can be calculated as:

[0103]

[0104]

[0105]

[0106] ;

[0107] Furthermore, we can obtain:

[0108] .

[0109] In step S6, the construction of the composite energy function, the introduction of the projection operator, and the design of the adaptive law specifically include:

[0110] Based on the iterative learning law design process, the following composite energy function is selected:

[0111] ;

[0112] in, and These are design parameters;

[0113] Differences are applied to the composite energy function to obtain:

[0114]

[0115] ;

[0116] in, ;

[0117] because and We can obtain:

[0118]

[0119] ;

[0120] Based on the above backstepping design process, the derivative of the Lyapunov function is:

[0121] ;

[0122] Substitution We can obtain:

[0123]

[0124]

[0125] ;

[0126] From the inequality, we can obtain:

[0127]

[0128]

[0129]

[0130] ;

[0131] Based on the properties of the projection operator, the following adaptive iterative learning law can be designed:

[0132] ;

[0133] in, For projection operators;

[0134] Similarly, we can obtain:

[0135] ;

[0136] according to and The design yields:

[0137] .

[0138] Beneficial effects:

[0139] 1. The present invention discloses a multi-mobile robot adaptive iterative learning control method under false data injection attack, which applies the properties and inequalities of echo state network to multi-mobile robot system and solves unknown nonlinear problems.

[0140] 2. This invention discloses an adaptive iterative learning and control method for multiple mobile robots under false data injection attacks. It proposes an adaptive iterative learning and control method that enables all followers to converge to the convex hull formed by the leader as the number of iterations approaches infinity, thus solving the problem of false data injection attacks during communication.

[0141] 3. The present invention discloses an adaptive iterative learning control method for multiple mobile robots under false data injection attacks. It proposes an iterative learning control scheme based on error tracking method, thereby eliminating the assumption that the initial conditions of the iterative learning control are the same, so that the tracking error can follow the error trajectory.

[0142] Other features and advantages of the present invention will become clearer after reading the detailed embodiments of the invention in conjunction with the accompanying drawings. Attached Figure Description

[0143] Figure 1 The flowchart of the control method for adaptive iterative learning of multiple mobile robots under false data injection attacks proposed in this invention is shown below.

[0144] Figure 2 This is the network topology of the present invention;

[0145] Figure 3 The output curve of the multi-mobile robot system according to the method of the present invention;

[0146] Figure 4 This is the maximum absolute error curve of the method of the present invention;

[0147] Figure 5 This is a curve showing the state comparison before and after the 50th iteration attack of the method of this invention. Detailed Implementation

[0148] To better illustrate the purpose and advantages of the present invention, the invention will be further described in detail with reference to the embodiments and corresponding drawings.

[0149] This invention addresses the inclusion control problem of multi-mobile robot systems under spoofing data injection attacks. It employs an adaptive iterative learning control strategy, introducing an echo state network into the control of the multi-mobile robot system. To further address the spoofing data injection attack problem, an adaptive control method is introduced, improving the system's anti-interference capability. A multi-mobile robot adaptive iterative learning inclusion control method under spoofing data injection attacks is proposed. The specific implementation of the multi-mobile robot system control method is described in detail below.

[0150] See Figure 1 As shown in the figure, this embodiment discloses a multi-mobile robot adaptive iterative learning control method under fake data injection attacks, including the following steps:

[0151] Step S1: Establish a multi-mobile robot system model and its state equations.

[0152] Specifically:

[0153] Step S11: Consider a given... One leader and A multi-mobile robot system consisting of several followers, the first The dynamics model of a follower is as follows:

[0154] (1)

[0155] in, ; It is the displacement of the mobile robot; It is the weight of the mobile robot; It is the damping coefficient; It is the input torque; It is the transient response coefficient.

[0156] Step S12: Next, to facilitate subsequent controller design, the following coordinate transformation is performed on the multi-mobile robot system:

[0157] make , and The original system can be rewritten as follows:

[0158]

[0159]

[0160] (2)

[0161] in, It represents the number of iterations.

[0162] To describe the communication relationships between the mobile robots in the system, we introduce graph theory: consider a directed graph. ,in, It is a set of nodes; It is an edge set; It is an adjacency matrix; if the edge ,but for The adjacent points, and adjacent matrix elements ,on the contrary Directed graph The Laplacian matrix is ​​defined as ,in, It is the in-degree matrix; It is the first The in-degree of a mobile robot.

[0163] Step S2: Establish the relationship between the original system state and the attacked state.

[0164] Specifically:

[0165] Because communication networks are open, multi-mobile robot systems are vulnerable to attacks; therefore, this invention considers a common type of spoofing attack that occurs simultaneously on leader-follower and follower-follower communication links; [Attacked state] And the leader's actual measurable output Defined as:

[0166]

[0167] (3)

[0168] in, and It is unknown and false data.

[0169] Establish the original state and the state of being attacked The relationship between them, namely:

[0170] (4)

[0171] in, .

[0172] Therefore, the system state equation under a fake data injection attack is:

[0173]

[0174]

[0175] (5)

[0176] in, and It is an unknown nonlinear function.

[0177] Step S3: Define the desired error trajectory and coordinate transformation.

[0178] Specifically:

[0179] Step S31: Define the error variable as:

[0180]

[0181] (6)

[0182] To relax the traditional iterative learning algorithm's assumption of identical initial conditions, the desired error trajectory is designed as follows:

[0183] (7)

[0184] in, It sets the time; function exist Monotonically decreasing, , ; =0 ensures the smoothness of the required error trajectory.

[0185] Step S32: Define the following coordinate transformation:

[0186]

[0187] (8)

[0188] in, It is a virtual controller.

[0189] Step S4: Construct the Lyapunov function, introduce the echo state network, and design the virtual controller for the first subsystem.

[0190] Specifically:

[0191] Step S41: Calculate From the time derivative, we can obtain:

[0192]

[0193]

[0194]

[0195]

[0196] (9)

[0197] in, It is an unknown nonlinear function.

[0198] Step S42: Select the following Lyapunov function:

[0199] (10)

[0200] Taking its derivative, we get:

[0201]

[0202] (11)

[0203] Step S43: Consider the following echo state network:

[0204]

[0205]

[0206] (12)

[0207] in, It is an unknown parameter; , It is an activation function; It is a weight vector; It is the number of neurons; It is an approximation error; It is an echo state network input.

[0208] Based on the above design, we can obtain:

[0209] (13)

[0210] Step S44: Design the following virtual controller:

[0211] (14)

[0212] in, These are design parameters; yes The estimated value; the estimation error is defined as ;

[0213] Based on the designed virtual controller, we can obtain:

[0214] (15)

[0215] Step S5: Construct the Lyapunov function, introduce the echo state network, and design the control input signal.

[0216] Specifically, it includes:

[0217] Step S51: Calculation From the time derivative, we can obtain:

[0218]

[0219] (16)

[0220] in, = It is an unknown nonlinear function;

[0221] Step S52: Select the following Lyapunov function:

[0222] (17)

[0223] For the above Lyapunov function Taking the derivative, we get:

[0224]

[0225] (18)

[0226] Step S53: Similar to step S43, consider the following echo state network:

[0227] (19)

[0228] in, It is an unknown parameter; , It is an activation function; It is a weight vector; It is the number of neurons; It is an approximation error; It is an echo state network input.

[0229] Furthermore, we can obtain:

[0230]

[0231]

[0232] (20)

[0233] Step S54: Design the following intermediate variables:

[0234] (twenty one)

[0235] in, These are design parameters; yes The estimated value; the estimation error is defined as .

[0236] but It can be rewritten as:

[0237]

[0238] (twenty two)

[0239] Step S55: It is easy to see that the inequality Therefore, the control input is designed as follows:

[0240] (twenty three)

[0241] in, yes The boundary; yes The estimated value and The estimation error is defined as follows: .

[0242] Based on the above design, we can obtain:

[0243]

[0244] (twenty four)

[0245] Depend on Therefore, we can conclude that:

[0246] (25)

[0247] According to inequality theory, It can be calculated as:

[0248]

[0249]

[0250]

[0251] (26)

[0252] Furthermore, we can obtain:

[0253]

[0254] (27)

[0255] Step S6: Construct a composite energy function, introduce a projection operator, and design an adaptive law.

[0256] Specifically, it includes:

[0257] Step S61: Combining the iterative learning law design process, select the following composite energy function:

[0258] (28)

[0259] in, and These are design parameters.

[0260] Differences are applied to the composite energy function to obtain:

[0261]

[0262] (29)

[0263] in, .

[0264] because and We can obtain:

[0265]

[0266] (30)

[0267] Step S62: Combining the above backstepping design process, the derivative of the Lyapunov function is:

[0268]

[0269] (31)

[0270] Substitution We can obtain:

[0271]

[0272]

[0273] (32)

[0274] Step S63: From the inequality, we can obtain:

[0275]

[0276]

[0277]

[0278] (33)

[0279] Based on the properties of the projection operator, the following adaptive iterative learning law can be designed:

[0280] (34)

[0281] in, This is the projection operator.

[0282] Step S64: Similarly, we can obtain:

[0283] (35)

[0284] according to and The design yields:

[0285] (36)

[0286] The parameters of the mobile robot system used in this embodiment are set as follows: , and .

[0287] The fake data injection attack is set up as follows: .function Defined as:

[0288] .

[0289] The output of the two leaders is set as follows: , .

[0290] The controller-related parameters are set as follows: 0.6, , , , , , , , , .

[0291] The initial conditions are: , , , , , .

[0292] Depend on Figure 2 It can be known that: Figure 2 The network topology of multiple mobile robots is shown.

[0293] Depend on Figure 3 It can be known that: Figure 3 Given the leader and follower displacement curves, and considering spoofing attacks, under the inclusion control strategy proposed in this invention, the follower converges to the convex hull formed by the leader at the 50th iteration. Therefore, the inclusion control strategy proposed in this invention enables the follower to converge to the convex hull formed by the leader as the number of iterations increases.

[0294] Depend on Figure 4 It can be seen that the maximum absolute error is defined as follows: , The simulation curves are as follows Figure 4 As shown, observations reveal that, with increasing iteration count, the maximum tracking error of the three followers tends towards zero.

[0295] Depend on Figure 5 It can be known that: Figure 5 The state at the 50th iteration before and after the attack. In this invention, all states before and after the attack are bounded. Therefore, the method proposed in this invention can effectively solve the problem of fake data injection attacks.

[0296] This embodiment primarily uses the system output as a performance parameter. Figure 2 The network topology for multiple mobile robots is given. Figure 3 The output curves of each mobile robot under the adaptive iterative learning control strategy are given. Figure 4 Provide the curve of the maximum absolute error. Figure 5 The control method of this invention is presented with output state comparison curves before and after the attack. Figure 5 It can be seen that the control method provided by this invention can effectively handle false data injection attacks and improve the anti-interference capability of multi-mobile robot systems.

[0297] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the embodiments are only used to explain the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., that are based on the same principles and concepts as the present invention should be included within the scope of protection of the present invention.

Claims

1. A control method for adaptive iterative learning of multiple mobile robots under a fake data injection attack, characterized in that: Includes the following steps: S1: Establish a multi-mobile robot system model and its state equations; S2: Establish the relationship between the original system state and the attacked state; S3: Define the expected error trajectory and coordinate transformation; S4: Construct a Lyapunov function, introduce an echo state network, and design a virtual controller for the first subsystem; S5: Construct the Lyapunov function, introduce the echo state network, and design the control input signal; S6: Construct a composite energy function, introduce a projection operator, and design an adaptive law.

2. The adaptive iterative learning method for multiple mobile robots under false data injection attacks according to claim 1 includes a control method, characterized in that, In S1, a multi-mobile robot system model and its state equations are established, specifically including: Consider a One leader and A multi-mobile robot system consisting of several followers, the first The dynamics model of a follower is as follows: ； in, ; It is the displacement of the mobile robot; It is the weight of the mobile robot; It is the damping coefficient; It is the input torque; It is the transient response coefficient; make , and The original system can be rewritten as follows: ； ； ； in, It is the number of iterations; To describe the communication relationships between the mobile robots in the system, we introduce graph theory: consider a directed graph. ,in, It is a set of nodes; It is an edge set; It is an adjacency matrix; if the edge ,but for The adjacent points, and adjacent matrix elements ,on the contrary Directed graph The Laplacian matrix is ​​defined as ,in, It is the in-degree matrix; It is the first The in-degree of a mobile robot.

3. The adaptive iterative learning method for multiple mobile robots under false data injection attacks according to claim 1 includes a control method, characterized in that, In S2, the relationship between the original system state and the attacked state is established, specifically including: Because communication networks are open, multi-mobile robot systems are vulnerable to attacks; therefore, this invention considers a common type of spoofing attack that occurs simultaneously on leader-follower and follower-follower communication links; [Attacked state] And the leader's actual measurable output Defined as: ； ； in, and It is unknown and false data; Establish the original state and the state of being attacked The relationship between them, namely: ； in, ; Therefore, the system state equation under a fake data injection attack is: ； ； ； in, and It is an unknown nonlinear function.

4. The adaptive iterative learning method for multiple mobile robots under false data injection attacks according to claim 1 includes a control method, characterized in that, In S3, the expected error trajectory and coordinate transformation are defined, specifically including: Define the error variable as: ； ； To relax the traditional iterative learning algorithm's assumption of identical initial conditions, the desired error trajectory is designed as follows: ； in, It sets the time; function exist Monotonically decreasing, , ; =0 ensures the smoothness of the required error trajectory; Define the following coordinate transformation: ； ； in, It is a virtual controller.

5. The adaptive iterative learning method for multiple mobile robots under false data injection attacks according to claim 1 includes a control method, characterized in that, In S4, a Lyapunov function is constructed, an echo state network is introduced, and the virtual controller for the first subsystem is designed, specifically including: calculate From the time derivative, we can obtain: ； in, It is an unknown nonlinear function; Choose the following Lyapunov functions: ； Taking its derivative, we get: ； Consider the following echo-state network: ； in, It is an unknown parameter; , It is an activation function; It is a weight vector; It is the number of neurons; It is an approximation error; It is an echo state network input; Based on the above design, we can obtain: ； Design the following virtual controller: ； in, These are design parameters; yes The estimated value; the estimation error is defined as ; Based on the designed virtual controller, we can obtain: 。 6. The adaptive iterative learning method for multiple mobile robots under false data injection attacks according to claim 1 includes a control method, characterized in that, In S5, a Lyapunov function is constructed, an echo state network is introduced, and the control input signal is designed, specifically including: calculate From the time derivative, we can obtain: ； in, = It is an unknown nonlinear function; Choose the following Lyapunov functions: ； For the above Lyapunov function Taking the derivative, we get: ； Consider the following echo-state network: ； in, It is an unknown parameter; , It is an activation function; It is a weight vector; It is the number of neurons; It is an approximation error; It is an echo state network input; Furthermore, we can obtain: ； Design the following intermediate variables: ； in, These are design parameters; yes The estimated value; the estimation error is defined as ; but It can be rewritten as: ； It is easy to see that the inequality Therefore, the control input is designed as follows: ； in, yes The boundary; yes The estimated value and The estimation error is defined as follows: ; Based on the above design, we can obtain: ； Depend on Therefore, we can conclude that: ； According to inequality theory, It can be calculated as: ； Furthermore, we can obtain: 。 7. The adaptive iterative learning method for multiple mobile robots under false data injection attacks according to claim 1 includes a control method, characterized in that, In S6, a composite energy function is constructed, a projection operator is introduced, and an adaptive law is designed, specifically including: Based on the iterative learning law design process, the following composite energy function is selected: ； in, and These are design parameters; Differences are applied to the composite energy function to obtain: ； in, ; because and We can obtain: ； Based on the above backstepping design process, the derivative of the Lyapunov function is: ； Substitution We can obtain: ； From the inequality, we can obtain: ； Based on the properties of the projection operator, the following adaptive iterative learning law can be designed: ； in, For projection operators; Similarly, we can obtain: ； according to and The design yields: 。

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