Unmanned system dual-time scale security cooperative control method and system under FDI attack

Abstract

The invention discloses an unmanned system dual-time scale security cooperative control method and system under FDI attacks, and relates to the technical field of unmanned system security collaboration.The method comprises the steps that a communication topological graph and an unmanned system dynamic model with dual-time scale characteristics are established firstly, then a bounded FDI attack model and a dynamic observation error model are established, and the dynamic observation error model is established; the method comprises the following steps of: firstly, carrying out fast and slow decomposition on a follower, constructing a distributed elastic observer, then analyzing sufficient conditions of observation error convergence, secondly, carrying out fast and slow decomposition on the follower, constructing a novel composite controller and a dynamic output error system model, and finally, analyzing sufficient conditions of consistent adjustment output of a leader and the follower under FDI attack. According to the method, the ill-conditioned numerical problem of an adjustment equation caused by the dual-time scale characteristic is avoided, the FDI attack is eliminated in real time and is not influenced by the attack occurrence time and probability, and the output consistency of the leader and the follower in the unmanned system is effectively realized.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned system security cooperation, and specifically to a dual-time-scale security cooperation control method and system for unmanned systems under FDI attacks. Background Art

[0002] With the rapid development of artificial intelligence, computer, communication, and microelectronics technologies, the potential applications and research of heterogeneous multi-agent systems in fields such as sensor information fusion, UAV formation, and power system cooperative control have received extensive attention. Among them, the problem of the consistent output between the leader and followers of unmanned systems is one of the basic problems. It requires unmanned systems to use various consensus protocols or synchronization control algorithms to enable all followers to synchronize with the output of the leader. In fact, many unmanned systems have multi-time-scale characteristics. Therefore, the problem of output consensus control for unmanned systems with dual-time-scale characteristics urgently needs to be solved.

[0003] Traditional dual-time-scale security cooperation control methods and systems for unmanned systems under FDI attacks use PID controllers to achieve consistent output between the leader and followers, and limit the scope of FDI attacks by constructing a data-driven detection model. Obviously, this security cooperation control method for unmanned systems based on multi-scale control technology under FDI attacks has at least the following deficiencies: 1. The PID controllers in traditional dual-time-scale security cooperation control methods and systems for unmanned systems under FDI attacks are applicable to single-scale unmanned systems. When used in dual-time-scale unmanned systems, it will lead to ill-conditioned numerical problems when solving the corresponding output regulation equations, and cannot effectively achieve the output consistency between the leader and followers in unmanned systems.

[0004] 2. The data-driven detection model in traditional dual-time-scale security cooperation control methods and systems for unmanned systems under FDI attacks is used to limit the scope of FDI attacks and cannot eliminate the impact of FDI attacks in real time. Summary of the Invention

[0005] Aiming at the above existing technical deficiencies, the purpose of the present invention is to provide a security cooperation control method for unmanned systems based on multi-scale control technology under FDI attacks.

[0006] To solve the above technical problems, the present invention adopts the following technical solutions: In the first aspect, the present invention provides a dual-time-scale security cooperation control method for unmanned systems under FDI attacks, including the following steps: Step 1: Establish a topological graph and a dynamic model: Establish a communication topological graph based on communication nodes, and construct a dynamic model of an unmanned system with dual-time-scale characteristics.

[0007] Step 2. Construct an observer and a model: Establish a bounded FDI attack model among the follower communication channels. Meanwhile, construct a distributed resilient observer, design a filter with an adaptive compensator on each distributed resilient observer, and establish a corresponding dynamic observation error model.

[0008] Step 3. Analyze the sufficient conditions for the convergence of the observer estimation error: Analyze the unmanned system with double-time-scale characteristics under FDI attacks through Lyapunov theory, and analyze the sufficient conditions for the convergence of the observation error.

[0009] Step 4. Perform fast-slow decomposition: For the follower with double-time-scale characteristics, use the multi-scale control technique to perform fast-slow decomposition to obtain the corresponding fast subsystem and slow subsystem.

[0010] Step 5. Construct a controller and a dynamic output error system model: Obtain the state information of the fast subsystem and the state information of the slow subsystem observed by the observer, construct a new composite controller, and establish a corresponding dynamic output error system model.

[0011] Step 6. Analyze the sufficient conditions for regulating output consensus: Analyze the unmanned system with double-time-scale characteristics under FDI attacks through Lyapunov stability theory and multi-scale control technique, and analyze the sufficient conditions for the leader and the follower to have consistent regulating outputs under FDI attacks.

[0012] Preferably, the process of establishing the communication topology graph according to the communication nodes is as follows: Establish the topology graph: S11. Obtain each communication node from the database.

[0013] S12. Establish a communication topology relationship graph of the unmanned system with double-time-scale characteristics.

[0014]

[0015] In the formula, G represents the communication topology relationship graph of the unmanned system with double-time-scale characteristics, V represents the set of each communication node, then V = {v1, v2, v3,..., v N}, v i represents the i-th follower, i represents the number of each follower, i = 1, 2, 3,..., N, N represents the total number of followers, represents the set of each edge in the communication topology relationship graph of the unmanned system with double-time-scale characteristics, then

[0016] Establish the dynamic model: S21. Use sensors to obtain the state vector of the leader, the output vector of the leader, the output vector of the follower, the slow state vector and the fast state vector of the follower, and obtain each constant matrix from the database.

[0017] S22. Construct a dynamic model of an unmanned system with dual-time-scale characteristics:

[0018]

[0019] where \(x_0(t)\) represents the state vector of the leader at the \(t\)-th running moment, \(y_0(t)\) represents the output vector of the leader at the \(t\)-th running moment, \(A_0\) and \(B_0\) both represent constant matrices, represents the derivative of the state vector of the leader at the \(t\)-th running moment with respect to \(t\), the derivative of the slow state vector of the \(i\)-th follower at the \(t\)-th running moment with respect to \(t\), \(x\) i (t) represents the slow state vector of the \(i\)-th follower at the \(t\)-th running moment, represents the derivative of the fast state vector of the \(i\)-th follower at the \(t\)-th running moment with respect to \(t\), \(z\) i (t) represents the fast state vector of the \(i\)-th follower at the \(t\)-th running moment, \(u\) i (t) represents the control input of the \(i\)-th follower at the \(t\)-th running moment, \(y\) i (t) represents the output vector of the \(i\)-th follower at the \(t\)-th running moment, \(\varepsilon_i\) represents the separation degree of the dynamics of the fast and slow state vectors of the \(i\)-th follower on the fast and slow time scales, and both represent the constant matrix of the \(i\)-th follower, \(t\) represents the number of each running moment, \(t = 1, 2, 3, \cdots, d\), \(d\) represents the total number of running moments, \(i\) represents the number of each follower, and \(i\in V\), \(t\), \(d\) and \(i\) are all positive integers.

[0020] Preferably, for the established bounded FDI attack model, the aggregation process is as follows: S31. Construct a weighted adjacency matrix, denoted as \(A\), then \(A = [a\) ij , where both \(i\) and \(j\) represent the numbers of followers, \((i, j)\) represents the communication channel between the \(i\)-th follower and the \(j\)-th follower, \(i\in V\), \(j\in V\), and \(i\neq j\). When holds, \(a\) ij = 1; when holds, \(a\) ij = 0.

[0021] S32. Use the Laplacian matrix \(L\) to describe \(G\), denoted as \(L = [l\) ij \in R\) N×N . When \(i\neq j\), \(l\) ij = -a\) ij , otherwise

[0022] S33. Construct the coupling weights, denoted as B, then B = diag{b1, b2, b3,..., b i}, where b i represents the return value of the state received by the i-th follower. When the i-th follower can receive the status information of the leader information, b i = 1. When the i-th follower cannot receive the status information of the leader information, b i = 0.

[0023] S34. Construct the neighbor set of each follower, denoted as D, then where k represents the number of each neighbor follower following the i-th follower, v k ∈ V, and k ≠ i.

[0024] S35. Obtain the estimation of each state vector and the false data vector based on the idea of adaptive filtering.

[0025] S36. Establish a bounded FDI attack model:

[0026] η ij (t) = η j (t) + δ ij (t),

[0027]

[0028] In the formula, η ij (t) represents the state vector of the i-th follower's final estimation of the leader after the j-th follower is under FDI attack in the (i, j) channel, η j (t) represents the state vector of the j-th follower's estimation of the leader at the t-th running moment, δ ij (t) represents the false data vector generated by the FDI attack in the (i, j) channel at the t-th running moment, δ i (t) represents the vector of the sum of the false data received by each channel of the i-th follower at the t-th running moment, δ i0 (t) represents the specific false data vector of the i-th follower.

[0029] Preferably, the specific process of simultaneously constructing the distributed resilient observer is as follows: Use sensors to obtain the state vectors of each follower's estimation of the leader after being under FDI attack, then:

[0030]

[0031]

[0032] In the formula, η i$(t)$ represents the state vector of the leader observed by the observer of the $i$-th follower at the $t$-th running moment. represents $\eta$ i the derivative of $(t)$ with respect to $t$. represents the filter state of the filter with an adaptive compensator on the $i$-th follower at the $t$-th running moment. represents the derivative with respect to $t$, $\eta$ i0 $(t)$ represents the state information of the leader received by the $i$-th follower after being attacked by FDI at the $t$-th running moment. represents the compensation sum of the false data injected into each channel of the $i$-th follower at the $t$-th running moment. represents the compensation term for false data on the $(i, j)$ channel of the $i$-th follower at the $t$-th running moment, $M$ i represents the diagonal block matrix of the $i$-th follower. represents the estimated value of the upper bound of the attack signal on the $(i, j)$ channel at the $t$-th running moment. represents an arbitrary continuous positive definite bounded function of the $(i, j)$ channel at the $t$-th running moment. represents the derivative with respect to $t$, $c$ represents a fixed constant, and $T$ represents the transpose operator.

[0033] Preferably, the process of establishing the corresponding dynamic observation error model is as follows: S41. Establish a dynamic observation error vector:

[0034]

[0035] where represents the dynamic observation error vector at the $t$-th running moment;

[0036] S42. Establish a dynamic observation error model: Obtain the true value of the upper bound of the attack signal on each channel from the database, and combine the observer and filter information to obtain:

[0037]

[0038] $H = L + B$,

[0039]

[0040] where represents the dynamic observation error at the $t$-th running moment. represents the derivative with respect to $t$. represents the filter vector of the filter with an adaptive filter at the $t$-th running moment. represents The derivative with respect to t, where H represents the sum of the Laplacian matrix and the coupling weight matrix, and I p represents the p - order identity matrix, where p is a positive integer, represents the compensator vector at the t - th running time, represents the upper - bound error of the attack signal on the (i, j) channel at the t - th running time, represents the derivative with respect to t of, represents the true value of the upper - bound of the attack signal on the (i, j) channel at the t - th running time.

[0041] Preferably, the sufficient conditions for the convergence of the estimation error of the analysis observer are as follows: S51, construct the Lyapunov equation:

[0042]

[0043] M = diag{M1, M2,..., M i}

[0044] where M represents a diagonal matrix, Z represents a symmetric positive - definite matrix, and M i represents the diagonal matrix of the i - th follower.

[0045] S52, analyze the convergence conditions of the observation error of the i - th agent under FDI attacks:

[0046]

[0047] When the above - mentioned matrix inequality holds, it means that the estimation error of the i - th follower for the leader's state can converge to the preset range; when the above - mentioned matrix inequality does not hold, it means that the estimation error of the i - th follower for the leader's state cannot converge to the preset range.

[0048] Preferably, the use of multi - scale control technology for fast - slow decomposition to obtain the corresponding fast and slow subsystems is as follows: Use multi - scale control technology to obtain the state variables of the slow subsystem and the state variables of the fast subsystem, then:

[0049]

[0050]

[0051] where represents the slow - state variable of the slow subsystem of the i - th follower at the t - th running time, represents the control variable of the slow subsystem of the i - th follower at the t - th running time, represents the derivative with respect to t, and s represents the symbol for identifying variables related to the slow subsystem. The state quantity of the tachyonic subsystem representing the i-th follower at the t-th running moment, The control quantity of the tachyonic subsystem representing the i-th follower at the t-th running moment, represents The derivative with respect to t, and f represents the symbol for identifying the relevant variables of the tachyonic subsystem.

[0052] Preferably, the construction of the controller and the dynamic output error system model is as follows: S61. Construct a new type of composite controller: Use sensors to obtain the state quantities of each follower, and obtain the constant matrix in the output equation of each follower and the constant matrix in the leader's output equation from the database. Then:

[0053]

[0054] where u i (t) represents the control input of the i-th follower at the t-th running moment, x i (t) represents the fast and slow state quantities of the system of the i-th follower at the t-th running moment, z i (t) represents the state quantity of the i-th follower at the t-th running moment, and both represent gain matrices, and and are both Hurwiz.

[0055] According to the matrix regulation equation, solve and :

[0056]

[0057]

[0058] where C i represents the constant matrix in the output equation of the i-th follower, and C0 represents the constant matrix in the leader's output equation.

[0059] S62. Establish the corresponding dynamic output error system model:

[0060]

[0061] where represents the error vector of the slow subsystem of the i-th follower at the t-th running moment, X s i represents the constant matrix of the i-th follower, obtained from S61.

[0062] Preferably, the sufficient conditions for the analysis to adjust the output to be consistent are as follows: S71. Construct the corresponding Lyapunov equation:

[0063]

[0064] where W i (t) represents the Lyapunov function of the i-th follower at the t-th running moment, and R i represents the symmetric positive definite matrix of the i-th follower.

[0065] S72. The sufficient conditions for the leader and followers to adjust the output to be consistent under FDI attacks are:

[0066]

[0067] where He is an operator representing the Hermite part of the matrix, and μ is a given scalar. When the above inequality holds, it means that the i-th follower and the leader adjust the output to be consistent under FDI attacks. When the above inequality does not hold, it means that the i-th follower and the leader do not adjust the output to be consistent under FDI attacks.

[0068] Second, the present invention provides a dual-time-scale secure cooperative control system for an unmanned system under FDI attacks, including the following modules: The topology graph and dynamic model establishment module is used to establish a communication topology graph according to communication nodes and construct a dynamic model of the unmanned system with dual-time-scale characteristics.

[0069] The observer and model construction module is used to establish a bounded FDI attack model between the follower communication channels, construct a distributed resilient observer, design a filter with an adaptive compensator on each distributed resilient observer, and establish a corresponding dynamic observation error model.

[0070] The module for analyzing the sufficient conditions for the convergence of the observer estimation error is used to analyze the unmanned system with dual-time-scale characteristics under FDI attacks through Lyapunov theory and analyze the sufficient conditions for the convergence of the observer estimation error.

[0071] The fast-slow decomposition module is used to perform fast-slow decomposition on the followers with dual-time-scale characteristics using multi-scale control technology to obtain the corresponding fast subsystem and slow subsystem.

[0072] The controller and dynamic output error system model construction module is used to obtain the state information of the fast subsystem and the state information of the slow subsystem observed by the observer, construct a new composite controller, and establish a corresponding dynamic output error system model.

[0073] The sufficient condition analysis module for regulating output consistency is used to analyze the unmanned system with double-time-scale characteristics under FDI attacks through Lyapunov stability theory and multi-scale control technology, and analyze the sufficient conditions for the regulating output consistency between the leader and the followers under FDI attacks.

[0074] The database is used to store various constant matrices, the control inputs of each follower, various gain matrices, the control quantities of the slow subsystems of each follower, the control quantities of the fast subsystems of each follower, symmetric positive definite matrices, the diagonal matrices of each follower, the estimated upper bounds of the attack signals, continuously positive definite bounded functions, and fixed constants.

[0075] The beneficial effects of the present invention are as follows: 1. The present invention provides a double-time-scale secure cooperative control method and system for unmanned systems under FDI attacks. First, a communication topology graph and a dynamic model of the unmanned system with double-time-scale characteristics are established. Then, a bounded FDI attack model and a dynamic observation error model are established, and a distributed resilient observer is constructed. Next, the sufficient conditions for the convergence of the observation error are analyzed. Secondly, the followers are decomposed into fast and slow parts, and a new type of composite controller and a dynamic output error system model are constructed. Finally, the sufficient conditions for the regulating output consistency between the leader and the followers under FDI attacks are analyzed, avoiding the ill-conditioned numerical problems of the regulating equations caused by the double-time-scale characteristics, eliminating FDI attacks in real time and being unaffected by the time and probability of the attacks occurring, and effectively realizing the output consistency between the leader and the followers in the unmanned system.

[0076] 2. The present invention uses multi-scale control technology to decompose each follower with double-time-scale characteristics into corresponding fast and slow subsystems, avoiding the ill-conditioned numerical problems of the regulating equations caused by the double-time-scale characteristics.

[0077] 3. The present invention combines the information of the slow subsystems of each follower and the information of the fast subsystems of each follower, and designs a new type of composite controller, which can effectively realize the output consistency between the leader and the followers in the unmanned system. Description of the Drawings

[0078] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0079] Figure 1 It is a schematic flow chart of the implementation steps of the method of the present invention.

[0080] Figure 2This is a schematic diagram of the system structure connection of the present invention.

[0081] Figure 3 It is a control structure block diagram of a security cooperative control method for an unmanned system based on multi-scale control technology under FDI attacks provided by the present invention.

[0082] Figure 4 It is a schematic diagram of FDI attack modeling in an embodiment of the present invention.

[0083] Figure 5 It is a schematic diagram of the communication topology structure among four multi-agents in an embodiment of the present invention.

[0084] Figure 6 It is a state curve diagram of an observer without a compensator in an embodiment of the present invention.

[0085] Figure 7 It is a state curve diagram of an observer with a compensator in an embodiment of the present invention.

[0086] Figure 8 It is an observation error curve diagram without a compensator in an embodiment of the present invention.

[0087] Figure 9 It is an observation error curve diagram with a compensator in an embodiment of the present invention.

[0088] Figure 10 It is an output consistency effect diagram without a compensator in an embodiment of the present invention.

[0089] Figure 11 It is an output consistency effect diagram with a compensator in an embodiment of the present invention. Detailed implementation manners

[0090] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0091] Please refer to Figure 1 As shown, in the first aspect, the present invention provides a dual-time-scale security cooperative control method for an unmanned system under FDI attacks, including the following steps: Step 1: Establish a topology graph and a dynamic model: Establish a communication topology graph according to communication nodes, and construct a dynamic model of the unmanned system with dual-time-scale characteristics.

[0092] In a specific embodiment, the process of establishing the communication topology graph according to communication nodes is as follows: Establishing the topology graph: S11. Obtain each communication node from the database.

[0093] S12. Establish the communication topology graph of the unmanned system with dual-time-scale characteristics:

[0094]

[0095] In the formula, G represents the communication topology graph of the unmanned system with dual-time-scale characteristics, and V represents the set of each communication node. Then V = {v1, v2, v3,..., v N}, v i represents the i-th follower, i represents the number of each follower, i = 1, 2, 3,..., N, and N represents the total number of followers. represents the set of each edge in the communication topology graph of the unmanned system with dual-time-scale characteristics. Then

[0096] Establish a dynamic model: S21. Use sensors to obtain the state vector of the leader, the output vector of the leader, the output vector of the follower, the slow state vector and the fast state vector of the follower, and obtain each constant matrix from the database.

[0097] S22. Construct the dynamic model of the unmanned system with dual-time-scale characteristics:

[0098]

[0099] In the formula, x0(t) represents the state vector of the leader at the t-th running moment, y0(t) represents the output vector of the leader at the t-th running moment, and both A0 and B0 represent constant matrices. represents the derivative of the state vector of the leader at the t-th running moment with respect to t. The derivative of the slow state vector of the i-th follower at the t-th running moment with respect to t, x i (t) represents the slow state vector of the i-th follower at the t-th running moment. represents the derivative of the fast state vector of the i-th follower at the t-th running moment with respect to t, z i (t) represents the fast state vector of the i-th follower at the t-th running moment, u i (t) represents the control input of the i-th follower at the t-th running moment, y i (t) represents the output vector of the i-th follower at the t-th running moment, and εi represents the separation degree of the dynamics of the fast state vector and the slow state vector of the i-th follower on the fast and slow time scales. and Both represent the constant matrix of the i-th follower, t represents the number of each running time, t = 1, 2, 3,..., d, d represents the total number of running times, i represents the number of each follower, and i ∈ V. Both t, d, and i are positive integers.

[0100] It should be noted that each communication node represents each follower.

[0101] It should be noted that each of the above constant matrices is obtained by the designer based on experiments.

[0102] It should also be noted that each of the above derivatives is obtained by the designer through calculation.

[0103] It should also be noted that the separation degree of the dynamics of the fast state vector and the slow state vector of the follower on the fast and slow time scales is set by the designer referring to the existing data and conclusions.

[0104] It should also be noted that represents the first constant matrix of the slow state vector of each follower, represents the first constant matrix of the control input vector of each follower, represents the second constant matrix of the slow state vector of each follower, represents the second constant matrix of the control input vector of each follower, represents the first constant matrix of the fast state vector of each follower, represents the second constant matrix of the fast state vector of each follower.

[0105] Step 2: Construct an observer and a model: Establish a bounded FDI attack model between the follower communication channels, and at the same time construct a distributed resilient observer, and design a filter with an adaptive compensator on each distributed resilient observer to establish a corresponding dynamic observation error model.

[0106] In a specific embodiment, the establishment of the bounded FDI attack model is as follows: S31. Construct a weighted adjacency matrix, denoted as A, then A = [a ij , where both i and j represent the numbers of followers, (i, j) represents the communication channel between the i-th follower and the j-th follower, i ∈ V, j ∈ V, and i ≠ j. When holds, a ij = 1, and when holds, a ij = 0.

[0107] It should be noted that represents that there is a communication channel between the i-th follower and the j-th follower, represents that there is no communication channel between the i-th follower and the j-th follower.

[0108] S32. Use the Laplacian matrix L to describe G, denoted as When i ≠ j, l ij = -a ij , otherwise

[0109] S33. Construct the coupling weights, denoted as B, then B = diag{b1, b2, b3,..., b i}}, where b i represents the return value of the received state of the i-th follower. When the i-th follower can receive the state information of the leader information, b i = 1. When the i-th follower cannot receive the state information of the leader information, b i = 0.

[0110] It should be noted that diag represents extracting the diagonal elements of the matrix.

[0111] S34. Construct the neighbor set of each follower, denoted as D, then where k represents the number of each neighbor follower following the i-th follower, v k ∈ V, and k ≠ i.

[0112] S35. Obtain the estimation of each state vector and the false data vector based on the idea of adaptive filtering.

[0113] S36. Establish a bounded FDI attack model:

[0114] η ij (t) = η j (t) + δ ij (t),

[0115]

[0116] In the formula, η ij (t) represents the state vector of the i-th follower's final estimation of the leader after the j-th follower is under FDI attack in the (i, j) channel, η j (t) represents the state vector of the j-th follower's estimation of the leader at the t-th running moment, δ ij (t) represents the false data vector generated by the FDI attack on the (i, j) channel at the t-th running moment, δ i (t) represents the vector of the sum of the false data received by each channel of the i-th follower at the t-th running moment, δ i0 (t) represents the specific false data vector of the i-th follower.

[0117] It should be noted that the false data vectors generated by each follower being attacked by FDI on each channel are added together to obtain the vector of the sum of the false data received by each follower on each channel.

[0118] It should also be noted that the specific false data vectors of each follower are set by the designer.

[0119] In another specific embodiment, the simultaneous construction of the distributed resilient observer is as follows: Use sensors to obtain the state vectors of each follower after being attacked by FDI, then:

[0120]

[0121]

[0122] where η i (t) represents the state vector of the leader observed by the observer of the i-th follower at the t-th running moment, represents η i (t) derivative with respect to t, represents the filter's own state of the filter with an adaptive compensator on the i-th follower at the t-th running moment, represents derivative with respect to t, η i0 (t) represents the state information of the leader received by the i-th follower after being attacked by FDI at the t-th running moment, represents the compensation sum of the false data injected into each channel of the i-th follower at the t-th running moment, represents the compensation term for the false data on the (i, j) channel of the i-th follower at the t-th running moment, M i represents the diagonal block matrix of the i-th follower, represents the estimated value of the upper bound of the attack signal on the (i, j) channel at the t-th running moment, represents an arbitrary continuous positive definite bounded function on the (i, j) channel at the t-th running moment, represents derivative with respect to t, c represents a fixed constant, and T represents the transpose operator.

[0123] It should be noted that the above derivatives are obtained by the designer through calculation.

[0124] It should also be noted that the compensation for the attack signal, the compensation term for the false data, the diagonal block matrix, the estimated value of the upper bound of the attack signal, the continuous positive definite bounded function, and the fixed constant are all set by the designer.

[0125] It should also be noted that the compensations of the filters with adaptive compensators on each follower for the attack signal are added together to obtain the compensation sum of the false data injected by each follower in each channel.

[0126] In another specific embodiment, the process of establishing the corresponding dynamic observation error model is as follows: Establish a dynamic observation error model: Obtain the true value of the upper bound of the attack signal on each channel from the database. Combining the observer and filter information, we can get:

[0127]

[0128] H = L + B,

[0129]

[0130] where represents the dynamic observation error at the t-th running moment, represents the derivative with respect to t, represents the filter vector of the adaptive filter at the t-th running moment, represents the derivative with respect to t, H represents the sum of the Laplacian matrix and the coupling weight matrix, I p represents the p-order identity matrix, where p is a positive integer, represents the compensator vector at the t-th running moment, represents the upper bound error of the attack signal on the (i, j) channel at the t-th running moment, represents the derivative with respect to t, represents the true value of the upper bound of the attack signal on the (i, j) channel at the t-th running moment.

[0131] It should be noted that the above derivatives are calculated by designers.

[0132] It should also be noted that when using a machine learning algorithm to obtain the true value of the upper bound of the attack signal on each channel, first use a feature selection algorithm to select the most representative and discriminative feature subset from the extracted features, then remove redundant and irrelevant features, and finally select a regression model to predict the upper bound of the attack signal strength.

[0133] Step 3: Analyze the sufficient conditions for the convergence of the observer estimation error: Through Lyapunov theory, analyze the unmanned system with double-time-scale characteristics under FDI attacks and give the sufficient conditions for the convergence of the observer estimation error.

[0134] In a specific embodiment, the sufficient conditions for the convergence of the estimation error of the analysis observer are as follows: S51. Construct the Lyapunov equation:

[0135]

[0136] M = diag{M1, M2,..., M i},

[0137] where M represents a diagonal matrix, Z represents a symmetric positive definite matrix, and M i represents the diagonal matrix of the i-th follower.

[0138] It should be noted that the symmetric positive definite matrix and the diagonal matrices of each follower are set by the designer.

[0139] S52. Analyze the convergence conditions of the observation error of the i-th agent under FDI attacks:

[0140]

[0141] When the above matrix inequality holds, it means that the estimation error of the i-th follower for the leader state can converge to the preset range. When the above matrix inequality does not hold, it means that the estimation error of the i-th follower for the leader state cannot converge to the preset range.

[0142] Step 4. Perform fast-slow decomposition: For followers with double time-scale characteristics, use multi-scale control technology to perform fast-slow decomposition to obtain the corresponding fast subsystem and slow subsystem.

[0143] In a specific embodiment, the process of using multi-scale control technology to perform fast-slow decomposition to obtain the corresponding fast subsystem and slow subsystem is as follows: Use multi-scale control technology to obtain the state variables of the slow subsystem and the state variables of the fast subsystem. Then:

[0144]

[0145] where represents the slow state variable of the slow subsystem of the i-th follower at the t-th running moment, represents the control variable of the slow subsystem of the i-th follower at the t-th running moment, represents the derivative with respect to t, s represents the symbol for identifying the relevant variables of the slow subsystem, represents the state variable of the fast subsystem of the i-th follower at the t-th running moment, represents the control variable of the fast subsystem of the i-th follower at the t-th running moment, represents The derivative with respect to t, where f represents the symbol for identifying the variables related to the fast subsystem.

[0146] It should be noted that the control quantities of the slow subsystems of each follower and the control quantities of the fast subsystems of each follower are all designed and controlled by the designers.

[0147] Step Five: Construct a controller and a dynamic output error system model: Obtain the state information of the fast subsystem and the state information of the slow subsystem through an observer, construct a new type of composite controller, and establish a corresponding dynamic output error system model.

[0148] In a specific embodiment, the process of constructing the controller and the dynamic output error system model is as follows: S61, S61, construct a new type of composite controller: Use sensors to obtain the state quantities of each follower, and obtain the constant matrix in the output equation of each follower and the constant matrix in the output equation of the leader from the database, then:

[0149]

[0150] In the formula, u i (t) represents the control input of the i-th follower at the t-th running moment, x i (t) represents the fast and slow state quantities of the system of the i-th follower at the t-th running moment, z i (t) represents the state quantity of the i-th follower at the t-th running moment, and both represent gain matrices, and and are both Hurwiz.

[0151] It should be noted that Hurwiz is a kind of matrix, representing that the corresponding system is asymptotically stable, which is the condition to ensure the stability of the design of the new type of composite controller.

[0152] It should also be noted that represents the gain matrix of the slow state vector of each follower, represents the gain matrix of the state vector of the leader observed by the observer of each follower, represents the first gain matrix, represents the second gain matrix, represents the third gain matrix.

[0153] According to the matrix adjustment equation, solve and :

[0154]

[0155] In the formula, C i$C_i$ represents the constant matrix in the output equation of the $i$-th follower, and $C_0$ represents the constant matrix in the output equation of the leader.

[0156] It should be noted that the constant matrices in the output equations of each follower and the constant matrix in the output equation of the leader are all set by the designer.

[0157] S62. Establish the corresponding dynamic output error system model:

[0158]

[0159]

[0160] In the formula $\widetilde{e}_i(t)$ represents the error vector of the slow subsystem of the $i$-th follower at the $t$-th running moment, $C_i$ represents the constant matrix of the $i$-th follower, obtained from S61.

[0161] It should also be noted that the difference between the estimated vector of the state of each follower's slow subsystem and the state vector of each follower's slow subsystem is used as the error vector of each follower's slow subsystem.

[0162] It should also be noted that the constant matrices of each follower are set by the designer.

[0163] Step Six. Analyze the sufficient conditions for regulating output consensus: Through the Lyapunov stability theory and multi-scale control technology, analyze the unmanned system with double-time-scale characteristics under FDI attacks, and analyze the sufficient conditions for the leader and followers to regulate output consensus under FDI attacks.

[0164] In a specific embodiment, the process of analyzing the sufficient conditions for regulating output consensus is as follows: S71. Construct the corresponding Lyapunov equation:

[0165]

[0166] In the formula, $W_i(t)$ i represents the Lyapunov function of the $i$-th follower at the $t$-th running moment, and $R_i$ i represents the symmetric positive definite matrix of the $i$-th follower.

[0167] It should be noted that the symmetric positive definite matrices of each follower are set by the designer.

[0168] S72. The sufficient conditions for the leader and followers to regulate output consensus under FDI attacks are:

[0169]

[0170] In the formula, He is an operator representing the Hermite part of a matrix, and μ represents a given scalar. When the above inequality holds, it means that the output regulation of the i-th follower is consistent with that of the leader under the FDI attack. When the above inequality does not hold, it means that the output regulation of the i-th follower is inconsistent with that of the leader under the FDI attack.

[0171] It should be noted that the given scalar is set by the designer.

[0172] The second aspect of the present invention provides a dual-time-scale secure cooperative control system for an unmanned system under FDI attack, including the following modules: The topology graph and dynamic model establishment module is used to establish a communication topology graph according to communication nodes and construct a dynamic model of the unmanned system with dual-time-scale characteristics.

[0173] The observer and model construction module is used to establish a bounded FDI attack model between the follower communication channels, construct a distributed resilient observer at the same time, design a filter with an adaptive compensator on each distributed resilient observer, and establish a corresponding dynamic observation error model.

[0174] The module for analyzing the sufficient conditions for the convergence of the observer estimation error is used to analyze the unmanned system with dual-time-scale characteristics under FDI attack through Lyapunov theory and analyze the sufficient conditions for the convergence of the observer estimation error.

[0175] The fast-slow decomposition module is used to perform fast-slow decomposition on the follower with dual-time-scale characteristics using multi-scale control technology to obtain the corresponding fast subsystem and slow subsystem.

[0176] The controller and dynamic output error system model construction module is used to obtain the state information of the fast subsystem and the state information of the slow subsystem observed by the observer, construct a new type of composite controller, and establish a corresponding dynamic output error system model.

[0177] The module for analyzing the sufficient conditions for consistent output regulation is used to analyze the unmanned system with dual-time-scale characteristics under FDI attack through Lyapunov stability theory and multi-scale control technology, and analyze the sufficient conditions for the output regulation of the leader and the follower to be consistent under FDI attack.

[0178] The database is used to store various constant matrices, the control inputs of each follower, various gain matrices, the control quantities of the slow subsystems of each follower, the control quantities of the fast subsystems of each follower, symmetric positive definite matrices, the diagonal matrices of each follower, the estimated values of the upper bounds of the attack signals, continuous positive definite bounded functions, and fixed constants.

[0179] In the embodiments of the present invention, a communication topology graph and a dynamic model of an unmanned system with double-time-scale characteristics are first established. Then, a bounded FDI attack model and a dynamic observation error model are established, and a distributed resilient observer is constructed. Next, the sufficient conditions for the convergence of the observation error are analyzed. Secondly, the followers are decomposed into fast and slow components, and a new composite controller and a dynamic output error system model are constructed. Finally, the sufficient conditions for the consistent adjustment output of the leader and the followers under FDI attacks are analyzed, avoiding the ill-conditioned numerical problems of the adjustment equations caused by the double-time-scale characteristics, eliminating FDI attacks in real time and being unaffected by the time and probability of the occurrence of the attacks, and effectively realizing the output consistency between the leader and the followers in the unmanned system.

[0180] The above content is only an example and illustration of the concept of the present invention. Those skilled in the art of the present technology can make various modifications or supplements to the described specific embodiments or use similar methods for substitution, as long as they do not deviate from the concept of the invention or exceed the scope defined in this specification, they should all fall within the protection scope of the present invention.

Claims

1. A dual-time-scale safety collaborative control method for unmanned systems under FDI attack, characterized in that: The steps include: Step 1: Establish a topology map and dynamic model: Establish a communication topology map based on the communication nodes, and construct an unmanned system dynamic model with dual time scale characteristics; Step 2: Construct observers and models: Establish a bounded FDI attack model between follower communication channels, construct distributed elastic observers, design filters with adaptive compensators on each distributed elastic observer, and establish the corresponding dynamic observation error model; Step 3: Analyze the sufficient conditions for the convergence of the observer estimation error: Through the Lyapunov theory, analyze the unmanned system with dual time scale characteristics under FDI attack, and analyze the sufficient conditions for the convergence of the observation error; Step 4: Decompose the fast and slow subsystems: For followers with dual time scale characteristics, use multi-scale control technology to decompose the fast and slow subsystems to obtain the corresponding fast subsystems and slow subsystems. Step 5: Construct a controller and a dynamic output error system model: obtain the state information of the fast subsystem and the slow subsystem observed by the observer, construct a new composite controller, and establish a corresponding dynamic output error system model; Step 6. Analyze the sufficient conditions for the consistency of regulation output: Through Lyapunov stability theory and multi-scale control technology, analyze the unmanned system with dual time scale characteristics under FDI attack, and analyze the sufficient conditions for the consistency of the regulation output of the leader and follower under FDI attack.

2. The dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to claim 1 is characterized in that: The specific process of establishing a communication topology diagram based on communication nodes is as follows: Create a topology map: S11, obtaining each communication node from the database; S12. Establish the communication topology diagram of the unmanned system with dual time scale characteristics: Where G represents the communication topology diagram of the unmanned system with dual time scale characteristics, V represents the set of communication nodes, then V = {v1,v2,v3,...,v N },v i represents the ith follower, i represents the number of each follower, i=1,2,3,...,N, N represents the total number of followers, The set of edges in the communication topology graph representing an unmanned system with dual time scale characteristics, then Building a dynamic model: S21, using sensors to obtain the state vector of the leader, the output vector of the leader, the output vector of the follower, the slow state vector and the fast state vector of the follower, and obtaining each constant matrix from a database; S22. Constructing a dynamic model of an unmanned system with dual time scale characteristics: Where x0(t) represents the state vector of the leader at the tth running time, y0(t) represents the output vector of the leader at the tth running time, A0 and B0 both represent constant matrices, represents the derivative of the leader's state vector at the tth running time with respect to t, The derivative of the slow state vector of the ith follower at the tth running time with respect to t, x i (t) represents the slow state vector of the ith follower at the tth running time, represents the derivative of the fast state vector of the ith follower at the tth running time with respect to t, z i (t) represents the fast state vector of the ith follower at the tth running time, u i (t) represents the control input of the ith follower at the tth running time, y i (t) represents the output vector of the ith follower at the tth running moment, εi represents the separation of the dynamics of the fast state vector and the slow state vector of the ith follower on the fast and slow time scales, and They all represent the constant matrix of the i-th follower, t represents the number of each running time, t=1,2,3,…,d, d represents the total number of running times, i represents the number of each follower, and i∈V, t, d and i are all positive integers.

3. The dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to claim 2 is characterized in that: The process of establishing a bounded FDI attack model is as follows: S31. Construct a weighted adjacency matrix, denoted as A, then A=[a ij ], where i and j represent the numbers of the followers, (i, j) represents the communication channel between the ith follower and the jth follower, i∈V, j∈V, and i≠j, when When ij =1, when When ij =0; S32, use the Laplace matrix L to describe G, denoted as L = [l ij ]∈R N×N , when i≠j, l ij =-a ij ,otherwise S33, construct coupling weight, denoted as B, then B = diag{b1,b2,b3,...,b i }, where b i Represents the return value of the i-th follower receiving status. When the i-th follower can receive the status information of the leader information, b i = 1, when the i-th follower cannot receive the status information of the leader, b i =0; S34. Construct the neighbor set of each follower, denoted as D, then Where k represents the number of each neighbor follower following the ith follower, v k ∈V, and k≠i; S35, obtaining estimates of each state vector and false data vector based on the adaptive filtering concept; S36. Establish a bounded FDI attack model: or ij (t)=η j (t)+δ ij (t), Where η ij (t) represents the state vector of the leader’s estimate that the i-th follower finally receives after the j-th follower is attacked by FDI on the (i, j) channel, η j (t) represents the state vector estimated by the j-th follower at the t-th running time of the leader, δ ij (t) represents the false data vector generated by the FDI attack on the (i, j) channel at the tth running time, δ i (t) represents the vector of the sum of the false data received by each channel of the ith follower at the tth running time, δ i0 (t) represents the specific false data vector of the i-th follower.

4. The dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to claim 3 is characterized in that: The distributed elastic observer is constructed at the same time, and the specific process is as follows: Use sensors to obtain the state vector of the leader estimated by each follower after being attacked by FDI, then: Where η i (t) represents the state vector of the leader observed by the observer of the i-th follower at the t-th running time, Represents η i The derivative of (t) with respect to t, represents the state of the filter with adaptive compensator on the ith follower at the tth running time, represent The derivative with respect to t, η i0 (t) represents the state information received by the leader after the i-th follower is attacked by FDI at the t-th running time, represents the compensation sum of the false data injected by each channel of the i-th follower at the t-th running time, represents the compensation term for false data on the (i, j) channel by the i-th follower at the t-th running time, M i represents the diagonal block matrix of the ith follower, represents the estimated value of the upper bound of the attack signal on the (i, j) channel at the t-th running time, represents any continuous positive definite bounded function of the (i, j) channel at the tth running time, represent The derivative with respect to t, c represents a fixed constant, and T represents the transpose operator.

5. The dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to claim 4 is characterized in that: The specific process of establishing the corresponding dynamic observation error model is as follows: S41. Establishing dynamic observation error vector: In the formula Represents the dynamic observation error vector at the tth running time; S42, establish a dynamic observation error model: obtain the true value of the upper bound of the attack signal on each channel from the database, and combine the observer and filter information to obtain: H=L+B, In the formula represents the dynamic observation error at the tth running time, represent The derivative with respect to t is represents the filter vector with the adaptive filter at the tth running time, represent The derivative with respect to t, H represents the sum of the Laplacian matrix and the coupling weight matrix, I p represents the p-order identity matrix, where p is a positive integer. represents the compensator vector at the tth running time, represents the upper bound error of the attack signal on the (i, j) channel at the t-th running time, represent The t-derivative of with respect to Represents the true value of the upper bound of the attack signal on the (i, j) channel at the t-th running time.

6. The dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to claim 5 is characterized in that: The sufficient condition for the convergence of the analysis observer estimation error is as follows: S51. Construct Lyapunov equation: M=diag{M1,M2,...,M i }, Where M represents a diagonal matrix, Z represents a symmetric positive definite matrix, and M i Represents the diagonal matrix of the i-th follower; S52. Analyze the convergence condition of the observation error of the i-th agent under FDI attack: When the above matrix inequality holds true, it means that the estimation error of the i-th follower to the leader's state can converge to a preset range. When the above matrix inequality does not hold true, it means that the estimation error of the i-th follower to the leader's state cannot converge to a preset range.

7. The dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to claim 2 is characterized in that: The multi-scale control technology is used to perform fast-slow decomposition to obtain the corresponding fast subsystem and slow subsystem. The specific process is as follows: Use multi-scale control technology to obtain the state quantity of the slow subsystem and the state quantity of the fast subsystem, then: In the formula represents the slow state of the slow subsystem of the ith follower at the tth running time, represents the control amount of the slow subsystem of the ith follower at the tth running time, represent The derivative with respect to t, s represents the sign of the variable that identifies the slow subsystem, represents the state quantity of the fast subsystem of the ith follower at the tth running time, represents the control quantity of the fast subsystem of the ith follower at the tth running time, represent The derivative with respect to t, f, represents the symbol identifying the variable of interest in the fast subsystem.

8. The dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to claim 7 is characterized in that: The specific process of constructing the controller and the dynamic output error system model is as follows: S61. Construct a new composite controller: Use sensors to obtain the state of each follower, and obtain the constant matrix in the output equation of each follower and the constant matrix in the output equation of the leader from the database: Where u i (t) represents the control input of the ith follower at the tth running time, x i (t) represents the fast and slow state of the system of the ith follower at the tth running time, z i (t) represents the state of the ith follower at the tth running time, and represent the gain matrix, and and All are from Hurwiz; According to the matrix adjustment equation, solve and Where C i represents the constant matrix in the output equation of the ith follower, and C0 represents the constant matrix in the output equation of the leader; S62. Establish the corresponding dynamic output error system model: In the formula represents the error vector of the ith follower slow subsystem at the tth running time, The constant matrix representing the i-th follower is obtained from S61.

9. The dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to claim 7 is characterized in that: The sufficient conditions for the analysis and adjustment output to be consistent are as follows: S71. Construct the corresponding Lyapunov equation: Where W i (t) represents the Lyapunov function of the ith follower at the tth running time, R i represents the symmetric positive definite matrix of the i-th follower; S72. The sufficient condition for the leader and follower to adjust their outputs in a consistent manner under FDI attack is: Where He is an operator representing the Hermite part of the matrix, μ represents a given scalar, and when the above inequality holds, it means that the ith follower and the leader have the same adjusted output under the FDI attack, and when the above inequality does not hold, it means that the ith follower and the leader have different adjusted outputs under the FDI attack.

10. A collaborative control system for executing the dual-time-scale safety collaborative control method for unmanned systems under FDI attack according to any one of claims 1 to 9, characterized in that: include: The topology map and dynamic model building module is used to build a communication topology map according to the communication nodes and construct a dynamic model of the unmanned system with dual time scale characteristics; The observer and model building module is used to establish a bounded FDI attack model between follower communication channels, build distributed elastic observers, design filters with adaptive compensators on each distributed elastic observer, and establish the corresponding dynamic observation error model; The module for analyzing sufficient conditions for the convergence of observer estimation errors is used to analyze unmanned systems with dual time scale characteristics under FDI attacks through Lyapunov theory, and analyze sufficient conditions for the convergence of observer estimation errors; The fast-slow decomposition module is used to decompose the follower with dual time scale characteristics using multi-scale control technology to obtain the corresponding fast subsystem and slow subsystem; The controller and dynamic output error system model building module is used to obtain the state information of the fast subsystem and the slow subsystem observed by the observer, build a new composite controller, and establish the corresponding dynamic output error system model; The sufficient condition analysis module for consistent regulation output is used to analyze the unmanned system with dual time scale characteristics under FDI attack through Lyapunov stability theory and multi-scale control technology, and analyze the sufficient conditions for the consistent regulation output of the leader and follower under FDI attack; The database is used to store various constant matrices, control inputs of various followers, various gain matrices, control quantities of various follower slow subsystems, control quantities of various follower fast subsystems, symmetric positive definite matrices, diagonal matrices of various followers, estimates of the upper bounds of attack signals, continuous positive definite bounded functions and fixed constants.

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