A Random Predefined Time Tracking Control Method for Heterogeneous Cluster Unmanned Systems

Abstract

The present invention discloses a random predefined time tracking control method for a heterogeneous cluster unmanned system, belonging to the technical field of unmanned system tracking control and used for unmanned system tracking control. It includes constructing a nonlinear leader-follower stochastic multi-follower system, designing a controller for actual preset time stochastic consensus, and conducting stability analysis and simulation verification in combination with Lyapunov stability theory; setting the unmanned systems in the heterogeneous cluster unmanned system as followers, taking the control inputs of the unmanned systems as the control inputs of the followers, and taking the control outputs of the controller for actual preset time stochastic consensus as the control information of the random predefined time tracking control. By introducing an adaptive law and a fuzzy logic system, the present invention effectively estimates and compensates for unknown dynamics and disturbances, enhancing the robustness of the system to random noise and nonlinearity.

Description

Technical Field

[0001] The present invention discloses a random predefined time tracking control method for a heterogeneous cluster unmanned system, belonging to the technical field of unmanned system tracking control. Background Art

[0002] With the wide application of heterogeneous cluster unmanned systems in fields such as robots, distributed sensor networks, and autonomous vehicles, the research on system performance and stability has become particularly important. Heterogeneous cluster unmanned systems achieve efficient and flexible task allocation and execution in complex environments by coordinating the cooperative behaviors of multiple agents, significantly improving the overall system performance. Especially in the fields of distributed control and autonomous decision-making, heterogeneous cluster unmanned systems provide new methods for the management and control of large and complex systems. However, systems in the real world are often affected by random noise or environmental disturbances, which are not only inevitable but may also pose significant challenges to system performance and stability. Summary of the Invention

[0003] The purpose of the present invention is to provide a random predefined time tracking control method for a heterogeneous cluster unmanned system, so as to solve the problem in the prior art that the performance and stability of the heterogeneous cluster unmanned system decline due to the influence of random noise or environmental disturbances.

[0004] A random predefined time tracking control method for a heterogeneous cluster unmanned system includes constructing a non-linear leader-follower random multi-follower system, designing a controller for actual preset time random consensus, and conducting stability analysis and simulation verification in combination with Lyapunov stability theory;

[0005] Set the unmanned systems in the heterogeneous cluster unmanned system as followers, set the control input of the unmanned system as the control input of the followers, and set the control output of the controller for actual preset time random consensus as the control information of the random predefined time tracking control.

[0006] The dynamic equations of the leader-follower are:

[0007] ;

[0008] ;

[0009] In the formula, is the differential symbol, is the state of the initial follower, is the follower 's state, is the follower 's control input, is the follower 's The standard Wiener process describes the random noise in the environment surrounding the follower and is an unknown continuous function of the initial follower , is an unknown continuous function of the follower , is the time, is the number of followers.

[0010] Constructing a non-linear leader-follower stochastic multi-follower system involves obtaining a connected undirected weighted graph to establish the connection between the leader and the followers.

[0011] Obtaining a connected undirected weighted graph includes using the undirected weighted graph to represent the communication between followers, , , , , is the set of followers, is the th follower, is the set of undirected edges, is the th follower and the th follower is an element of the set of undirected edges between them, , is the adjacency matrix, is the element in the rd row and th column of the adjacency matrix, represents is the -order square matrix. In the undirected weighted graph, the path connecting and is a sequence of vertices , , , where is the starting point of the path connecting and , is the ending point of the path connecting and . If there is a path between and , then the undirected weighted graph is connected.

[0012] ​Establishing the connection between the leader and the followers includes the communication weight matrix between the leader and the followers is:

[0013] ;

[0014] In the formula, represents a diagonal matrix, is diagonal elements. If the follower receives the information from the leader, define the followers who receive the information from the leader as the set , If the follower does not receive the information from the leader, define the followers who do not receive the information from the leader as the set , , and ;

[0015] The directed edge between the leader and the followers is:

[0016] ;

[0017] In the formula, is the leader;

[0018] The directed augmented communication network between the leader and the followers connects the leader and the followers, , , , is the union result of the leader and the followers sets, is the union result of the directed edge and the undirected edge sets.

[0019] After establishing the connection between the leader and the followers, the controller design for the actual preset time stochastic consensus includes:

[0020] ;

[0021] In the formula, is the tracking result of the follower at time is the tracking result of the leader at time is the tracking error at time is the stochastic stability time function with respect to the tracking error at time is the infimum, is the tracking result of the instantaneous follower is the tracking result of the instantaneous leader, is the set of tracking results, is a one-dimensional standard Wiener process;

[0022] When the following conditions are satisfied, the non-linear leader-follower stochastic multi-follower system is actually pre-set time stochastically consistent:

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] wherein, is an adjustable parameter determined by is the supremum, is the infimum, is the expected value, is a constant.

[0028] The controller for actual pre-set time stochastic consistency includes:

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] 0;

[0040] wherein, is the basic input quantity of the controller, is the fuzzy basis function vector, is the derivative symbol, is the sign function, , , , , are variables that can be solved, , , are adjustable variables, represents taking the maximum eigenvalue, is a positive definite matrix, follower 's aggregated neighborhood error.

[0041] Integrate into a vector :

[0042] ;

[0043] The relationship between the positive definite matrix and the aggregated neighborhood error of the follower is:

[0044] ;

[0045] In the formula, is a matrix that can be solved.

[0046] is:

[0047] ;

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] ;

[0055] ;

[0056] In the formula, is the consensus error of the follower ​ , , , , , is a matrix that can be obtained, is the functional expression in the drift term of the first follower, is the functional expression of the leader, is the functional expression in the drift term of the Nth follower, is the diffusion term function of the first follower, is the diffusion term function of the Nth follower.

[0057] Combined with Lyapunov stability theory for stability analysis and simulation verification, including that the total Lyapunov function is , if it satisfies:

[0058] ;

[0059] it is considered that has passed the stability analysis. In the formula, is the derivative of the Lyapunov function along the system trajectory, , .

[0060] Compared with the prior art, the present invention has the following beneficial effects: By introducing the adaptive law and the fuzzy logic system, the present invention effectively estimates and compensates for unknown dynamics and disturbances, and enhances the robustness of the system to random noise and nonlinearity. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is the topological structure of the leader-follower stochastic multi-follower system;

[0062] Figure 2 is the initial follower state of all followers of the present invention in the open-loop case and the states of other followers schematic diagram of the trajectory change;

[0063] Figure 3 is the initial follower state of all followers of the present invention in the closed-loop case and the states of other followers schematic diagram of the trajectory change;

[0064] Figure 4 is the consensus error of all followers of the present invention schematic diagram of the change over time;

[0065] Figure 5 is of all followers of the present invention Schematic diagram of the trajectory varying with time;

[0066] Figure 6 For all followers of the present invention Schematic diagram of the trajectory varying with time;

[0067] Figure 7 In each follower of the present invention Norm of Schematic diagram of the variation with time;

[0068] Figure 8 Control input for all followers of the present invention Schematic diagram of the trajectory varying with time. Detailed implementation manners

[0069] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be described clearly and completely below. Apparently, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without any creative effort belong to the scope of protection of the present invention.

[0070] A random predefined time tracking control method for a heterogeneous cluster unmanned system, including constructing a nonlinear leader-follower random multi-follower system, designing a controller for actual preset time random consensus, and performing stability analysis and simulation verification in combination with Lyapunov stability theory;

[0071] Set the unmanned systems in the heterogeneous cluster unmanned system as followers, set the control input of the unmanned systems as the control input of the followers, and set the control output of the controller for actual preset time random consensus as the control information of the random predefined time tracking control.

[0072] The dynamic equations of the leader-follower are:

[0073] ;

[0074] ;

[0075] In the formula, is the differential symbol, is the state of the initial follower, is the follower state of is the follower control input, is the follower of dimensional standard Wiener process, describing the surrounding of the follower Random noise in the environment, is an unknown continuous function of the initial follower, , is the follower is an unknown continuous function of, is the time, is the number of followers.

[0076] Constructing a non - linear leader - follower stochastic multi - follower system includes obtaining a connected undirected weighted graph , establishing the connection between the leader and the followers.

[0077] Obtaining a connected undirected weighted graph includes using the undirected weighted graph to express the communication between followers, , , , , is the set of followers, is the th follower, is the set of undirected edges, is the th follower and the th follower is an element of the set of undirected edges between them, , is the adjacency matrix of, is the element in the th row and th column of the adjacency matrix, represents is an n - order square matrix. In the undirected weighted graph, the path connecting and is a sequence composed of vertices , , where is the starting point of the path connecting and , is the ending point of the path connecting and . If there is a path between and , then the undirected weighted graph is connected.

[0078] Establishing the connection between the leader and the followers includes the communication weight matrix between the leader and the followers is:

[0079] ;

[0080] In the formula, represents a diagonal matrix, is diagonal elements. If the follower receives the information of the leader, , define the follower who receives the information of the leader as the set , If the follower does not receive the information of the leader, , define the follower who does not receive the information of the leader as the set , , and ;

[0081] The directed edge between the leader and the follower is:

[0082] ;

[0083] In the formula, is the leader;

[0084] The directed augmented communication network between the leader and the follower connects the leader and the follower, , , , is the union result of the leader and follower sets, is the union result of the directed edge and undirected edge sets.

[0085] After establishing the connection between the leader and the follower, the controller design for actual preset time stochastic consensus includes:

[0086] ;

[0087] In the formula, is the tracking result of the follower at time is the tracking result of the leader at time is the tracking error at time is the stochastic stability time function with respect to the tracking error at time is the infimum, is the follower at time The tracking result, is the tracking result of the leader at time is the set of tracking results, is a one-dimensional standard Wiener process;

[0088] When the following conditions are satisfied, the non-linear leader-follower stochastic multi-follower system is actually pre-set time stochastically consistent:

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] wherein, is an adjustable parameter determined by , is the supremum, is the expected value, is a constant.

[0094] The controller for actual pre-set time stochastic consistency includes:

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] ;

[0105] 0;

[0106] wherein, is the basic input quantity of the controller, is the fuzzy basis function vector, is the derivative symbol, is the sign function, 、 、 、 、 is the variable to be solved, 、 、 is the adjustable variable, represents taking the maximum eigenvalue, is the positive definite matrix, follower 's aggregated neighborhood error.

[0107] Integrate into a vector :

[0108] ;

[0109] The relationship between the positive definite matrix and the aggregated neighborhood error of the follower is:

[0110] ;

[0111] In the formula, is the matrix to be solved.

[0112] is:

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] In the formula, is the consistency error of the follower , 、 、 , , , are matrices that can be obtained. is the function expression in the drift term of the first follower. is the function expression of the leader. is the function expression in the drift term of the Nth follower. is the diffusion term function of the first follower. is the diffusion term function of the Nth follower.

[0123] Combined with Lyapunov stability theory for stability analysis and simulation verification, including that the total Lyapunov function is . If it satisfies:

[0124] ;

[0125] it is considered that has passed the stability analysis. In the formula, is the derivative of the Lyapunov function along the system trajectory. , .

[0126] The embodiments of the present invention verified the above content, carried out simulation experiments using MATLAB for verification, and made detailed explanations through the attached drawings. The embodiments of the present invention simulated the control system of 6 unmanned aerial vehicles, that is, there are 6 followers. The control system of the unmanned aerial vehicle is regarded as an unmanned system, and the control input of the unmanned aerial vehicle is the control input of the follower. The topological structure of the leader-follower random multi-follower system in the embodiment is as Figure 1 shown, Leader represents the leader, 1, 2, 3, 4, 5, 6 represent 6 followers, and the adjacency matrix and the communication weight matrix are selected as follows:

[0127] ;

[0128] ;

[0129] ;

[0130] According to it is obtained that . Assuming that the initial value of the leader is 2, the vector containing the initial values of the leader and the followers is . Since the functions and is unknown and is processed using a fuzzy logic system approach. The Gaussian function is used as the fuzzy basis function, and a total of 21 fuzzy rules are selected. The center of each Gaussian function is set to , and the standard deviation is uniformly set to 0.05 to control the width of each fuzzy set. Select , , . To achieve the consistency of the predefined time, a distributed adaptive fuzzy controller and an adaptive update law are adopted and processed by MATLAB with a step size of 0.0001. The initial follower state of all followers of the present invention and other follower states trajectory changes are as Figure 2 shown. The initial follower state of all followers of the present invention in the closed-loop case and other follower states trajectory changes are as Figure 3 shown. It can be seen that can track within 0.5 seconds, achieving a good tracking effect and achieving the required actual predefined time stochastic consistency. The consistency error of all followers of the present invention changes with time as Figure 4 shown. The trajectory of all followers of the present invention changes with time as Figure 5 shown. The trajectory of all followers of the present invention changes with time as Figure 6 shown. The norm of in each follower of the present invention changes with time as Figure 7 shown. The control input (speed in the embodiment) of all followers of the present invention changes with time as Figure 8 shown. It can be seen that each control quantity (each control quantity in the present invention takes a dimensionless value for convenient experimental comparison) is relatively stable.

[0131] The present invention also proves that the system is actually preset time stochastically consistent according to the distributed adaptive fuzzy controller and the adaptive update law. Let , and the infinitesimal operator is obtained through the Ito formula:

[0132] (1);

[0133] (2);

[0134] Based on the following formula:

[0135] (3);

[0136] where , is a positive Lipschitz constant;

[0137] , ;

[0138] ;

[0139] ;

[0140] ;

[0141] where is the fuzzy weighted vector, is a constant, is dimensional Euclidean space.

[0142] Substitute into :

[0143] (4);

[0144] The following inequality is derived:

[0145] (5);

[0146] ;

[0147] ; is a positive Lipschitz constant.

[0148] Assume that the leader's trajectory is uniformly bounded. There exists such that . According to the property of continuous functions, there must exist a constant such that trace . Substitute Eqs. (3), (4) and (5) into Eq. (2):

[0149] (6);

[0150] ;

[0151] ;

[0152] Considering the controller, Eq. (6) is rewritten as:

[0153] (7);

[0154] ;

[0155] Let :

[0156] (8);

[0157] be the derivative of;

[0158] According to Equation (8), we get:

[0159] (9);

[0160] ;

[0161] ;

[0162] ;

[0163] Rewrite as:

[0164] ;

[0165] (9);

[0166] If , then for any , :

[0167] ;

[0168] If , then for any , :

[0169] ;

[0170] So we have:

[0171] (10);

[0172] (11);

[0173] Substitute Equation (10) and Equation (11) into Equation (9), we get Equation (12):

[0174] (12);

[0175] If Then for any there is:

[0176] ;

[0177] If , then for any there is:

[0178] ;

[0179] For any 、 , there is:

[0180] ;

[0181] ;

[0182] In the formula, 、 、 .

[0183] Combined with to obtain:

[0184] (13);

[0185] Observing formula (9), formula (12) and formula (13), it is concluded that the derivative of satisfies the following conditions:

[0186] (14);

[0187] (15);

[0188] Let and , similar to the method used for , the same method also applies to and , so the following results are obtained:

[0189] (16);

[0190] (17);

[0191] In the formula, , .

[0192] (18);

[0193] (19);

[0194] According to , the total Lyapunov function is obtained :

[0195] ;

[0196] .

[0197] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A random predefined time tracking control method for heterogeneous cluster unmanned systems, characterized in that Including constructing a non-linear leader-follower stochastic multi-follower system, designing a controller for practical preset-time stochastic consensus, and conducting stability analysis and simulation verification by combining Lyapunov stability theory; Regarding the unmanned systems in the heterogeneous cluster unmanned system as followers, taking the control inputs of the unmanned systems as the control inputs of the followers, and taking the control outputs of the controller for practical preset-time stochastic consensus as the control information for stochastic predefined-time tracking control; The controller for practical preset-time stochastic consensus includes: ； ； ； ； ； ； ； ； ； ； 0； wherein, is the control input of the follower ; is the basic input quantity of the controller ; is the derivative symbol ; is a set representing the followers who receive the information of the leader ; is the number of followers ; ; ; is the sign function ; ; ; ; ; ; ; ; represents taking the maximum eigenvalue ; is the aggregated neighborhood error of the follower ; is the state of the follower .

2. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 1, wherein, The dynamic equation of the leader-follower is: ； ； In the formula, is the differential symbol, is the follower, 's dimensional standard Wiener process, which describes the random noise in the environment around the follower , is an unknown continuous function of the initial follower, , is an unknown continuous function of the follower , is the time.

3. A random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 2, characterized in that Constructing a non-linear leader-follower stochastic multi-follower system includes obtaining a connected undirected weighted graph , and establishing the connection between the leader and the followers.

4. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 3, wherein Obtain a connected undirected weighted graph including using an undirected weighted graph to represent the communication between followers , , , , where \(V\) is the set of followers and \(v_i\) is the \(i\)-th follower and \(E\) is the set of undirected edges and \(e_{ij}\) is the undirected edge element between the \(i\)-th follower and the \(j\)-th follower , and \(A\) is the adjacency matrix of \(G\) which indicates that \(A\) is an \(n\times n\) square matrix. In the undirected weighted graph, a path connecting \(v_i\) and \(v_j\) is a sequence of \(k\) vertices , , wherein \(v_{i_0}\) is the starting point of the path connecting \(v_i\) and \(v_{i_1}\), and \(v_{i_k}\) is the ending point of the path connecting \(v_{i_{k - 1}}\) and \(v_j\). If there exists a path between \(v_i\) and \(v_j\), then the undirected weighted graph is connected.

5. A random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 4, characterized in that Establishing the connection between the leader and the follower includes the communication weight matrix between the leader and the follower as follows: ； wherein, represents a diagonal matrix, is diagonal elements. If the follower receives the information of the leader, , , if the follower does not receive the information of the leader, , , and ; Directed edge between the leader and the follower is as follows: ； In the formula, is the leader; Communication network between directed augmented leaders and followers , connecting the leaders and followers, , , , is the union result of the leader and follower sets, is the union result of the directed edge and undirected edge sets.

6. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 5, characterized in that, After establishing the connection between the leader and the followers, the design of the controller for practical preset-time stochastic consensus includes: ； In the formula, is the tracking result of the follower at time is the tracking result of the leader at time is the tracking error at time is a random stability time function with respect to the tracking error at time is the infimum, is the tracking result of the follower at time is the tracking result of the leader at time is the set of tracking results, is a one-dimensional standard Wiener process; When the following conditions are satisfied, the non-linear leader-follower stochastic multi-follower system is of practical preset-time stochastic consensus: ； ； ； ； In the formula, is an adjustable parameter determined by , is the supremum, is the expected value, is a constant.

7. A random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 6, characterized in that Integrate into a vector : ； Positive definite matrix and follower The relationship of the aggregated neighborhood error is as follows: ； In the formula, is a matrix that can be obtained.

8. A random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 7, characterized in that is as follows: ； ； ； ； ； ； ； ； ； wherein, is the consistency error of the follower , , , , , , are matrices that can be obtained, is the function expression in the drift term of the first follower, is the function expression of the leader, is the function expression in the drift term of the Nth follower, is the diffusion term function of the first follower, is the diffusion term function of the Nth follower.

9. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 8, characterized in that, Stability analysis and simulation verification are carried out in combination with Lyapunov stability theory, including that the total Lyapunov function is , if the following conditions are met: ； It is considered that has passed the stability analysis, where the Lyapunov function is the derivative along the system trajectory, , .

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