Random predefined time tracking control method for heterogeneous cluster unmanned system

Abstract

The invention discloses a random predefined time tracking control method for a heterogeneous cluster unmanned system, which belongs to the technical field of unmanned system tracking control, is used for unmanned system tracking control, and comprises the following steps: constructing a nonlinear leader-follower random multi-follower system, carrying out controller design of actual preset time random consistency, and carrying out time tracking control. Carrying out stability analysis and simulation verification by combining a Lyapunov stability theory; and setting the unmanned system in the heterogeneous cluster unmanned system as a follower, taking the control input of the unmanned system as the control input of the follower, and taking the control output of the controller with the random consistency of the actual preset time as the control information of the random predefined time tracking control. By introducing the adaptive law and the fuzzy logic system, unknown dynamics and interference are effectively estimated and compensated, and the robustness of the system to random noise and nonlinearity is enhanced.

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 interference, 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 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 interference.

[0004] A random predefined time tracking control method for a heterogeneous cluster unmanned system includes constructing a nonlinear 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 system in the heterogeneous cluster unmanned system as the follower, set the control input of the unmanned system as the control input of the follower, 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 equation of the leader-follower is:

[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 A 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 , where is the time and 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, where is the set of followers, is the -th follower, is the -th follower, is the set of undirected edges, is the -th follower and the -th follower in the element of the set of undirected edges between them, where is the adjacency matrix, is the element in the -th row and -th column of the adjacency matrix, indicating that is an -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.

[0012] Establishing the connection between the leader and the followers includes the communication weight matrix between the leader and the followers as follows:

[0013] ;

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

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

[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 design of the controller 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-specified time stochastically consistent:

[0023] ;

[0024] ;

[0025] ;

[0026] ;

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

[0028] The controller for actual pre-specified 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 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.

[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 existing technology, 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 with time;

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

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

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

[0068] Figure 8 Control input of all followers of the present invention Schematic diagram of the trajectory changing 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 clearly and completely described 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 making creative efforts shall fall within the protection scope 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 the 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 equation of the leader-follower is:

[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 follower Random noise in the environment, 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.

[0076] 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.

[0077] Obtaining a connected undirected weighted graph includes using the undirected weighted graph to represent the communication between , , , , 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 's adjacency matrix, is the element in the th row and th column of the adjacency matrix, represents is 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 design of the controller 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 of is the tracking result of the leader at time a set of tracking results, is a one-dimensional standard Wiener process;

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

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] where 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] where 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 obtained, 、 、 is the adjustable variable, represents taking the maximum eigenvalue, is a positive definite matrix, follower 's aggregated neighborhood error.

[0107] Combine 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 obtained.

[0112] is:

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] In the formula, is the consistency error of the follower 's, 、 、 , , , are matrices 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.

[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 embodiment of the present invention verifies the above content, conducts simulation experiments for verification using MATLAB, and makes detailed explanations through the attached drawings. The embodiment of the present invention simulates 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, where Leader represents the leader, and 1, 2, 3, 4, 5, 6 represent 6 followers. The adjacency matrix and the communication weight matrix are selected as follows:

[0127] ;

[0128] ;

[0129] ;

[0130] According to it is obtained that . Assume that the initial value of the leader is 2, and 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 in the open-loop case of the present invention and the trajectory changes of other follower states Figure 2 are as shown in . The initial follower state of all followers in the closed-loop case of the present invention Figure 3 and the trajectory changes of other follower states are as shown in . It can be seen that can track Figure 4 within 0.5 seconds, achieving a good tracking effect and achieving the required practical predefined time stochastic consistency. The consistency error of all followers of the present invention Figure 5 changes with time as shown in . The trajectory of Figure 6 in each follower of the present invention changes with time as shown in Figure 7 . The trajectory of the control input (speed in the embodiment) of all followers of the present inventionchanges with time as shown in Figure 8 . It can be seen that each control quantity (all control quantities in the present invention take dimensionless values 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 Itô's formula as follows:

[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 trajectory of the leader 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: (7);

[0153] ;

[0154] Let :

[0155] (8);

[0156] be the derivative of;

[0157] According to Equation (8), we get:

[0158] (9);

[0159] ;

[0160] ;

[0161] ;

[0162] Rewrite as:

[0163] ;

[0164] (9);

[0165] If , then for any , :

[0166] ;

[0167] If , then for any , :

[0168] ;

[0169] So we have:

[0170] (10);

[0171] (11);

[0172] Substitute Equation (10) and Equation (11) into Equation (9), we get Equation (12):

[0173] (12);

[0174] If then for any There are:

[0175] ;

[0176] If , then for any there are:

[0177] ;

[0178] For any 、 , there are:

[0179] ;

[0180] ;

[0181] In the formula, 、 、 .

[0182] Combined with to obtain:

[0183] (13);

[0184] Observing formula (9), formula (12) and formula (13), it is concluded that the derivative of

[0185] (14);

[0186] (15);

[0187] Let and , similar to the method for , the same method also applies to and , so the following results are obtained:

[0188] (16);

[0189] (17);

[0190] In the formula, , .

[0191] (18);

[0192] (19);

[0193] According to , the total Lyapunov function is obtained :

[0194] ;

[0195] .

[0196] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than 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 recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features, and these modifications or replacements do not make the essence of the corresponding technical solutions 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 a heterogeneous cluster unmanned system, characterized in that: This includes constructing a nonlinear leader-follower random multi-follower system, designing a controller with actual preset time random consistency, and performing stability analysis and simulation verification in combination with Lyapunov stability theory; The unmanned system in the heterogeneous cluster unmanned system is set as a follower, the control input of the unmanned system is used as the control input of the follower, and the control output of the controller with actual preset time random consistency is used as the control information of random predefined time tracking control.

2. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 1 is characterized in that: The leader-follower dynamic equation is: ； ； In the formula, is the differential symbol, is the initial follower state, Is a follower status, Is a follower The control input, Is a follower of The standard Wiener process, which describes the The random noise in the environment, is an unknown continuous function of the initial follower, , Is a follower An unknown continuous function of It's time. is the number of followers.

3. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 2 is characterized in that: Constructing a nonlinear leader-follower random multi-follower system involves obtaining a connected undirected weighted graph , building connections between leaders and followers.

4. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 3 is characterized in that: Get a connected undirected weighted graph Including, using undirected weighted graph Express The communication between followers , , , , is the set of followers, It is Followers, is an undirected edge set, It is Followers and Followers The undirected edge set elements between , yes The adjacency matrix of is the first Line The elements of the column, express yes Order square matrix, undirected weighted graph, connection and The path is A sequence of vertices , , , where Yes Connect and The initial point of the path, Yes Connect and The final point of the path, if and If there is a path between are connected.

5. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 4 is characterized in that: Establishing the connection between the leader and the follower includes the communication weight matrix between the leader and the follower for: ； In the formula, represents a diagonal matrix, yes diagonal elements, if the follower Receive the leader's message, , define the followers who receive the leader's information as a set , , if the follower No message from the leader was received. , define the followers who have not received the leader's information as a set , , and ; Directed edges between leaders and followers for: ； In the formula, Be a leader; Directed augmentation of the communication network between leaders and followers , connecting leaders and followers, , , , is the union of the leader and follower sets, It is the union of the directed edge set and the undirected edge set.

6. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 5 is characterized in that: After establishing the connection between the leader and followers, the controller design for actual preset time random consistency includes: ； In the formula, yes Time Follower The tracking results, yes The leader's tracking results, yes The tracking error is About The random settling time function of the tracking error at is the infimum, yes Always Follower The tracking results, yes Tracking results of the moment leaders, is a collection of tracking results, is a one-dimensional standard Wiener process; A nonlinear leader-follower random multi-follower system is actually temporally stochastically consistent if the following conditions are met: ； ； ； ； In the formula, Is The adjustable parameters that determine is the supremum, is the expected value, is a constant.

7. The random predefined time tracking control method for a heterogeneous cluster unmanned system according to claim 6 is characterized in that: The controllers that actually preset the random consistency of time include: ； ； ； ； ； ； ； ； ； ； 0； In the formula, is the basic input of the controller, is the fuzzy basis function vector, is the derivative symbol, is a sign function, , , , , is a variable that can be sought, , , is an adjustable variable, It means taking the maximum eigenvalue. is a positive definite matrix, Followers Aggregate neighborhood error.

8. The random predefined time tracking control method for heterogeneous cluster unmanned system according to claim 7 is characterized in that: Will Integrate into vectors : ； Positive definite matrices and followers The relationship between the aggregated neighborhood error of is: ； In the formula, It is a findable matrix.

9. The random predefined time tracking control method for heterogeneous cluster unmanned system according to claim 8 is characterized in that: for: ； ； ； ； ； ； ； ； ； In the formula, Is a follower The consistency error, , , , , , is a searchable matrix, 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 function of the first follower, is the diffusion function of the Nth follower.

10. The random predefined time tracking control method for heterogeneous cluster unmanned system according to claim 9, characterized in that: Combining Lyapunov stability theory to carry out stability analysis and simulation verification includes: the total Lyapunov function is , if it satisfies: ； think Through the stability analysis, the formula is: is the Lyapunov function The derivative along the trajectory of the system, , .

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