A Distributed Time-Varying Optimization Control Method and System for Unmanned Swarms Considering Interference

Abstract

The present invention relates to the field of unmanned flight control technology, and particularly to a distributed time-varying optimal control method and system for an unmanned cluster considering interference. The method includes: obtaining the dynamic model and cost function of each agent in the unmanned cluster; constructing an action topology model of the unmanned cluster based on the dynamic model of each agent; obtaining the first performance constant, the second performance constant, and the third performance constant of each agent based on the dynamic model, cost function, and action topology model of the unmanned cluster; constructing a time-varying controller for each agent based on the dynamic model, the first performance constant, the second performance constant, and the third performance constant of each agent. The present invention reduces the influence caused by interference information, designs a distributed time-varying optimal controller, and can achieve zero-error tracking of the optimal trajectory by the unmanned cluster system, and meets the optimal global performance index while achieving consensus.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned flight control, and in particular to a distributed time-varying optimal control method and system for an unmanned cluster considering interference. Background Art

[0002] At present, the research on the cooperative control of unmanned cluster systems has become a major focus, including consensus control, formation control, and encirclement control, etc. According to the presence or absence of a leader, the formation control of an unmanned cluster can usually be divided into two categories: leaderless control and leader-following control. In leader-following control, the formation reference information is often generated by a leader (a real leader or a virtual unknown leader). However, in actual engineering applications, an unmanned cluster system often needs to track an optimal trajectory to meet performance indicators such as optimal energy or shortest time. For example, for an unmanned aircraft cluster taking off from different positions, it is necessary to complete the assembly at the optimal formation position so that the sum of the energies consumed by the assembled cluster is minimized. At this time, the trajectory that the individuals in the cluster system need to track is not generated by a leader, but a trajectory that satisfies the optimal conditions.

[0003] The distributed optimal control of an unmanned cluster has received extensive attention and emphasis at home and abroad in recent years due to its potential application value in sensor networks, distributed parameter estimation, reinforcement learning, and power systems, etc. The research on the distributed coordinated control of an unmanned cluster system can not only reveal the internal laws of many phenomena in nature, but also provide guidance for people's work, life, and production and other practical activities. With the rapid development of technologies such as microelectronics, communication, and sensors, large-scale networks are everywhere, which greatly expands the application scope of distributed optimization algorithms.

[0004] Distributed optimization control problems usually involve finding the optimal solution of the team objective function (in terms of cost, loss, or error). In other words, in the distributed optimization problem of an unmanned cluster network system, each agent has a local cost function, and its task objective is to cooperatively minimize the global objective function composed of the sum of these objective functions. The agents optimize their own objective functions by executing distributed algorithms and perform local information interaction with their neighbors, ultimately converging their own states to an optimal solution of the global objective function. Most classical distributed optimization problems focus on discrete systems and use intelligent optimization methods for solution. However, many unmanned cluster systems, including unmanned aerial vehicles, robotic arms, and robots, are often characterized by continuous systems. Therefore, the research on distributed optimization problems for continuous systems is also very meaningful and valuable. In addition, in existing distributed optimization problems for unmanned cluster systems, it is mostly assumed that the performance functions of individuals are time-invariant, so the global performance function is also time-invariant, and in this case, what satisfies the optimal condition is often a fixed point. However, many performance functions are related not only to the states of individuals but also to time. Moreover, during the collaborative operation of an unmanned aerial vehicle cluster, affected by the battlefield environment, the unmanned aerial vehicles will inevitably be affected by unknown disturbances such as wind and waves, and at the same time, the information received by individual unmanned aerial vehicles will also contain disturbances such as noise, and at this time, the control performance of the unmanned aerial vehicles is seriously threatened. Summary of the Invention

[0005] In view of this, the present invention provides a distributed time-varying optimization control method and system for an unmanned cluster considering interference, reduces the influence of interference information, designs a distributed time-varying optimization controller, and can achieve zero-error tracking of the optimal trajectory by the unmanned cluster system, and satisfies the optimal global performance index while achieving consensus.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A distributed time-varying optimization control method for an unmanned cluster considering interference, comprising:

[0008] Obtain the dynamic model and cost function of each agent in the unmanned cluster; the dynamic model includes position, velocity, control input, and interference quantity;

[0009] Construct an action topology model of the unmanned cluster based on the dynamic model of each agent;

[0010] Obtain the first performance constant, the second performance constant, and the third performance constant of each agent based on the dynamic model, cost function of each agent, and the action topology model of the unmanned cluster;

[0011] Construct a time-varying controller for each agent based on the dynamic model of each agent, the first performance constant, the second performance constant, and the third performance constant.

[0012] Preferably, obtaining the first performance constant, the second performance constant, and the third performance constant of each agent based on the dynamic model of each agent, the cost function, and the action topology model of the unmanned cluster includes:

[0013] Obtain the first constant value and the second constant value of each agent based on the dynamic model and the cost function of each agent;

[0014] Obtain the first performance constant, the second performance constant, and the third performance constant of each agent based on the first constant value, the second constant value of each agent, and the Laplacian matrix of the action topology model.

[0015] Preferably, the time-varying controller is as follows:

[0016]

[0017] where: i ∈ N, N is the total number of agents in the unmanned cluster, U i (t) is the time-varying controller of the i-th agent at time t, α i (t) is the first performance constant of the i-th agent at time t, · represents differentiation, q i (t) is the position of the i-th agent at time t, q j (t) represents the position of the j-th agent at time t, β i (t) is the second performance constant of the i-th agent at time t, γ i (t) is the third performance constant of the i-th agent at time t, N i is the number of agents adjacent to the i-th agent, sgn is the sign function, f i (q i (t), t) is the cost function of the i-th agent at time t, is the gradient information matrix of f i (q i (t), t), H i (q i (t), t) is the Hessian matrix of f i (q i (t), t), represents the partial derivative of the gradient information matrix with respect to time t.

[0018] Preferably, the interference quantity is calculated based on the velocity, the control input, the position matrix, and the velocity matrix of the interference system.

[0019] The present invention also provides a distributed time-varying optimization control system for an unmanned cluster considering interference, including:

[0020] A data acquisition module, configured to acquire the dynamic model and cost function of each agent in the unmanned cluster; the dynamic model includes position, velocity, control input, and interference quantity;

[0021] A topology module, configured to construct an action topology model of the unmanned cluster based on the dynamic model of each agent;

[0022] A constant module, configured to obtain the first performance constant, the second performance constant, and the third performance constant of each agent based on the dynamic model, cost function, and action topology model of the unmanned cluster of each agent;

[0023] A control module, configured to construct a time-varying controller for each agent based on the dynamic model, the first performance constant, the second performance constant, and the third performance constant of each agent.

[0024] Preferably, the constant module includes:

[0025] A first constant unit, configured to obtain the first constant value and the second constant value of each agent based on the dynamic model and cost function of each agent;

[0026] A second constant unit, configured to obtain the first performance constant, the second performance constant, and the third performance constant of each agent based on the first constant value, the second constant value of each agent, and the Laplacian matrix of the action topology model.

[0027] Preferably, the time-varying controller is as follows:

[0028]

[0029] where: i ∈ N, N is the total number of agents in the unmanned cluster, U i (t) is the time-varying controller of the i-th agent at time t, α i (t) is the first performance constant of the i-th agent at time t, · represents differentiation, q i (t) is the position of the i-th agent at time t, q j (t) represents the position of the j-th agent at time t, β i (t) is the second performance constant of the i-th agent at time t, γ i (t) is the third performance constant of the i-th agent at time t, N i is the number of agents adjacent to the i-th agent, sgn is the sign function, f i (q i$C_{i}(t)$ is the cost function of the $i$-th agent at time $t$. is $f$ i $(q$ i $(t)$ is the gradient information matrix of $C_{i}(t)$, and $H$ i $(q$ i $(t)$ is $f$ i $(q$ i $(t)$ is the Hessian matrix of $C_{i}(t)$. represents the partial derivative of the gradient information matrix with respect to time $t$.

[0030] Preferably, the interference amount is calculated based on the velocity, the control input, the position matrix and the velocity matrix of the interference system.

[0031] According to the specific embodiments provided by the present invention, the following technical effects are disclosed:

[0032] The present invention relates to the technical field of unmanned flight control, and particularly to a distributed time-varying optimization control method and system for an unmanned cluster considering interference. The method includes: obtaining the dynamic model and cost function of each agent in the unmanned cluster; constructing the action topology model of the unmanned cluster based on the dynamic model of each agent; obtaining the first performance constant, the second performance constant and the third performance constant of each agent based on the dynamic model, the cost function and the action topology model of the unmanned cluster; and constructing a time-varying controller for each agent based on the dynamic model, the first performance constant, the second performance constant and the third performance constant of each agent. The present invention reduces the influence caused by interference information, designs a distributed time-varying optimization controller, and can achieve zero-error tracking of the optimal trajectory by the unmanned cluster system, and meet the optimal global performance index while achieving consensus. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] 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 in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings without creative efforts based on these drawings.

[0034] Figure 1 is a flowchart of the distributed time-varying optimization control method for an unmanned cluster considering interference according to the present invention;

[0035] Figure 2 is a schematic diagram of the action topology model according to the present invention;

[0036] Figure 3 is a schematic diagram of the estimated value and the actual value of the $x$-axis component of the interference amount of each agent according to the present invention;

[0037] Figure 4 Schematic diagram of the estimated value and actual value of the y-axis component of the interference amount of each agent of the present invention;

[0038] Figure 5 Control trajectory diagram of the x coordinate of the positions of the agents of the present invention;

[0039] Figure 6 Control trajectory diagram of the y coordinate of the positions of the agents of the present invention;

[0040] Figure 7 Schematic diagram of the gradient change of combining the cost function of the first agent and the cost function of the second agent of the present invention.

[0041] Figure 8 Structural diagram of the distributed time-varying optimization control system for unmanned clusters considering interference of the present invention.

[0042] Symbol description: 1. Data acquisition module; 2. Topology module; 3. Constant module; 4. Control module. Detailed implementation manners

[0043] 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 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.

[0044] The purpose of the present invention is to provide a distributed time-varying optimization control method and system for unmanned clusters considering interference, reduce the influence caused by interference information, design a distributed time-varying optimization controller, and be able to achieve zero-error tracking of the optimal trajectory by the unmanned cluster system, and meet the optimal global performance index while achieving consistency.

[0045] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0046] Figure 1 Flowchart of the distributed time-varying optimization control method for unmanned clusters considering interference of the present invention. As Figure 1 shown, the present invention provides a distributed time-varying optimization control method for unmanned clusters considering interference, including:

[0047] Step S1, obtaining the dynamic model and cost function of each agent in the unmanned cluster; the dynamic model includes position, velocity, control input, and interference amount.

[0048] The dynamic model is as follows:

[0049]

[0050] where: \(i\in N\), \(N\) is the total number of agents in the unmanned cluster, \(q\) i (t) is the position of the \(i\)-th agent at time \(t\), \(u\) i (t) is the control input of the \(i\)-th agent at time \(t\), \(v\) i (t) is the velocity of the \(i\)-th agent at time \(t\), \(\cdot\) represents differentiation, is the estimated value of the disturbance quantity of the \(i\)-th agent at time \(t\), V i (t) represents the velocity matrix of the disturbance system that generates interference to the \(i\)-th agent at time \(t\), \(S\) i (t) represents the position matrix of the disturbance system that generates interference to the \(i\)-th agent at time \(t\), \(K\) i (t) represents the gain matrix of the disturbance system that generates interference to the \(i\)-th agent at time \(t\), \(K\) i (t) satisfies \(W\) i (t)=(S i (t)+K i (t)V i (t)), \(W\) i (t) is a Hurwitz matrix.

[0051] Step S2: Construct the action topology model of the unmanned cluster based on the dynamic model of each agent.

[0052] In this embodiment, the action topology model is described by a topological graph \(G = \{Z, E, C\}\) composed of nodes and edges to represent the communication relationship between agents in the cluster system. Where \(A=\{z_1,z_2,\cdots,z\) N} represents the node set, and the nodes are the serial numbers of the agents, represents the edge set, \(C = [c\) ij \(\in L\) N×N represents the adjacency matrix with non-negative weight \(c\) ij . Define the in-degree matrix of graph \(G\) as \(D = diag\{deg\) in (z_1),\cdots,deg\) in (z\) N )\}, where, represents the in-degree of node \(z\) i . Define the Laplacian matrix of graph \(G\) as \(L = D - C\). The established topological graph is an undirected graph.

[0053] Step S3: Obtain the first performance constant, the second performance constant and the third performance constant of each agent based on the dynamic model of each agent, the cost function and the action topology model of the unmanned cluster.

[0054] Specifically, step S3 includes:

[0055] Step S31: Obtain the first constant value and the second constant value of each agent based on the dynamic model and the cost function of each agent.

[0056] The calculation formula is as follows:

[0057]

[0058] In the formula: is the first constant value of the i-th agent at time t, is the second constant value of the i-th agent at time t, f i (q i (t), t) is the cost function of the i-th agent at time t, is the gradient information matrix of f i (q i (t), t), H i (q i (t), t) is the Hessian matrix of f i (q i (t), t), represents the partial derivative of the gradient information matrix with respect to time t, q j (t) is the position of the j-th agent at time t, j ∈ N, Γ j (t) has the same calculation formula as Γ i (t).

[0059] Step S32: Obtain the first performance constant, the second performance constant, and the third performance constant of each agent based on the first constant value, the second constant value of each agent, and the Laplacian matrix of the action topology model.

[0060] First, calculate the constant value of the action topology model. The calculation formula is as follows:

[0061]

[0062] In the formula, k1 is the constant value of the action topology model, ε is the total number of edges of the action topology model, n is the dimension of the position of the agent, λ N (L) is the maximum eigenvalue in the Laplacian matrix of the action topology model.

[0063] Then, calculate the constant mean of each agent at time t. The calculation formula is as follows:

[0064]

[0065] In the formula: k i(t) is the constant mean of the i-th agent at time t.

[0066]

[0067]

[0068]

[0069] Where: λ2(L) is the minimum eigenvalue in the Laplacian matrix of the action topology model, and the minimum eigenvalue is non-zero.

[0070] Step S4, construct a time-varying controller for each agent based on the dynamic model, the first performance constant, the second performance constant, and the third performance constant of each agent.

[0071] The time-varying controller is as follows:

[0072]

[0073] Where: U i (t) is the time-varying controller of the i-th agent at time t, N i is the number of agents adjacent to the i-th agent, and sgn is the sign function.

[0074] Figure 8 This is the structure diagram of the distributed time-varying optimization control system for an unmanned cluster considering interference in the present invention. As Figure 8 shown, the present invention provides a distributed time-varying optimization control system for an unmanned cluster considering interference, including: a data acquisition module 1, a topology module 2, a constant module 3, and a control module 4.

[0075] The data acquisition module 1 is used to acquire the dynamic model and cost function of each agent in the unmanned cluster; the dynamic model includes position, velocity, control input, and disturbance quantity.

[0076] The topology module 2 is used to construct an action topology model of the unmanned cluster based on the dynamic model of each agent.

[0077] The constant module 3 is used to obtain the first performance constant, the second performance constant, and the third performance constant of each agent based on the dynamic model, cost function of each agent, and the action topology model of the unmanned cluster.

[0078] The control module 4 is used to construct a time-varying controller for each agent based on the dynamic model, the first performance constant, the second performance constant, and the third performance constant of each agent.

[0079] Optionally, the constant module 3 includes: a first constant unit and a second constant unit.

[0080] The first constant unit is configured to obtain a first constant value and a second constant value for each agent based on the dynamic model and cost function of each agent.

[0081] The second constant unit is configured to obtain a first performance constant, a second performance constant, and a third performance constant for each agent based on the first constant value, the second constant value of each agent, and the Laplacian matrix of the action topology model.

[0082] Optionally, the time-varying controller is as follows:

[0083]

[0084] where: i ∈ N, N is the total number of agents in the unmanned cluster, U i (t) is the time-varying controller of the i-th agent at time t, α i (t) is the first performance constant of the i-th agent at time t, · represents differentiation, q i (t) is the position of the i-th agent at time t, q j (t) represents the position of the j-th agent at time t, β i (t) is the second performance constant of the i-th agent at time t, γ i (t) is the third performance constant of the i-th agent at time t, N i is the number of agents adjacent to the i-th agent, sgn is the sign function,

[0085] f i (q i (t), t) is the cost function of the i-th agent at time t, is the gradient information matrix of f i (q i (t), t), H i (q i (t), t) is the Hessian matrix of f i (q i (t), t), represents the partial derivative of the gradient information matrix with respect to time t.

[0086] Optionally, the interference quantity is calculated based on the velocity, the control input, the position matrix, and the velocity matrix of the interference system.

[0087] Taking an unmanned cluster including 6 agents as an example, its action topology model is as Figure 2 shown, The initial values of the position and velocity of each agent are randomly taken in [-6, 6], and ηi The initial value of (t) is set to 0, α i (t) takes 350, β i (t) takes 200, γ i (t) takes 1500.

[0088] Among them, the actual value and the estimated value of the x-axis component of the interference amount of each agent are as Figure 3 shown, and the actual value and the estimated value of the y-axis component of the interference amount of each agent are as Figure 4 shown. Figure 3 and Figure 4 In, the solid line represents the actual value of each agent, and the dashed line represents the estimated value of each agent. It can be seen from Figure 3 and Figure 4 that the method in the present invention can well obtain the estimated value of the interference amount.

[0089] The position of each agent is reflected by the x coordinate and the y coordinate. Figure 5 gives the x coordinate trajectories of 6 agents, Figure 6 gives the y coordinate trajectories of 6 agents. Figure 5 In, q 11 is the x coordinate trajectory of the 1st agent, q 21 is the x coordinate trajectory of the 2nd agent, q 31 is the x coordinate trajectory of the 3rd agent, q 41 is the x coordinate trajectory of the 4th agent, q 51 is the x coordinate trajectory of the 5th agent, q 61 is the x coordinate trajectory of the 6th agent; Figure 6 In, q 12 is the y coordinate trajectory of the 1st agent, q 22 is the y coordinate trajectory of the 2nd agent, q 32 is the y coordinate trajectory of the 3rd agent, q 42 is the y coordinate trajectory of the 4th agent, q 52 is the y coordinate trajectory of the 5th agent, q 62 is the y coordinate trajectory of the 6th agent; It can be seen from Figure 5 and Figure 6 that the positions of the 6 agents in the unmanned cluster are finally consistent. Figure 7 In, the cost function of the 1st agent and the cost function of the 2nd agent are added as the global cost function. Figure 7 is the gradient value of the global cost function. It can be seen from Figure 7 that the gradient of the global cost function finally gradually becomes 0. According to the optimal condition of the strongly convex function, it can be known that the unmanned cluster can track the optimal trajectory.

[0090] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

[0091] In this article, specific examples are used to elaborate on the principles and implementation manners of the present invention. The descriptions of the above embodiments are only used to help understand the method of the present invention and its core idea. At the same time, for those of ordinary skill in the art, based on the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation on the present invention.

Claims

1. A distributed time-varying optimization control method for unmanned clusters considering interference, characterized in that Including: Obtain the dynamic model and cost function of each agent in the unmanned cluster; the dynamic model includes position, velocity, control input, and disturbance quantity; Construct the action topology model of the unmanned cluster based on the dynamic model of each agent; Obtain the first performance constant, second performance constant, and third performance constant of each agent based on the dynamic model, cost function, and action topology model of the unmanned cluster; Construct a time-varying controller for each agent based on the dynamic model, first performance constant, second performance constant, and third performance constant of each agent; The obtaining of the first performance constant, second performance constant, and third performance constant of each agent based on the dynamic model, cost function, and action topology model of the unmanned cluster includes: Obtain the first constant value and second constant value of each agent based on the dynamic model and cost function of each agent; Obtain the first performance constant, second performance constant, and third performance constant of each agent based on the first constant value, second constant value of each agent, and the Laplacian matrix of the action topology model; The constant value of the action topology model is calculated as follows: ； where \(k_1\) is a constant value of the action topology model, \(\varepsilon\) is the total number of edges of the action topology model, and \(n\) is the dimension of the position of the agent. is the largest eigenvalue in the Laplacian matrix of the action topology model; The constant mean value of each agent at time t is calculated as follows: ； where: k i (t) is the constant mean of the i-th agent at time t; is the first constant value of the i-th agent at time t, N is the total number of agents in the unmanned cluster, is the minimum eigenvalue in the Laplacian matrix of the action topology model, and the minimum eigenvalue is non-zero; is the second constant value of the i-th agent at time t; α i (t) is the first performance constant of the i-th agent at time t, β i (t) is the second performance constant of the i-th agent at time t, γ i (t) is the third performance constant of the i-th agent at time t; The time-varying controller is as follows: where: \(i\in N\), \(U i (t)\) is the time-varying controller of the \(i\)-th agent at time \(t\), \(\cdot\) represents differentiation, \(q i (t)\) is the position of the \(i\)-th agent at time \(t\), \(q j (t)\) represents the position of the \(j\)-th agent at time \(t\), \(N i is the number of agents adjacent to the \(i\)-th agent, and sgn is the sign function. , f i (q i (t), t) at time t The cost function of the $i$-th agent, $\nabla f$ i (q i (t), t) is the gradient information matrix of $f$ i (q i (t), t), H i (q i (t), t) is f i (q i (t), t)'s Hessian matrix, representing the gradient information matrix with respect to time t The partial derivative of.

2. The time-varying optimization control method for unmanned cluster distributed according to claim 1, wherein, The disturbance quantity is calculated based on the velocity, the control input, the position matrix, and the velocity matrix of the disturbance system.

3. A distributed time-varying optimization control system for unmanned clusters considering interference, characterized in that Including: A data acquisition module for obtaining the dynamic model and cost function of each agent in the unmanned cluster; the dynamic model includes position, velocity, control input, and disturbance quantity; A topology module for constructing the action topology model of the unmanned cluster based on the dynamic model of each agent; A constant module for obtaining the first performance constant, second performance constant, and third performance constant of each agent based on the dynamic model, cost function, and action topology model of the unmanned cluster; A control module for constructing a time-varying controller for each agent based on the dynamic model, first performance constant, second performance constant, and third performance constant of each agent; The constant module includes: A first constant unit for obtaining the first constant value and second constant value of each agent based on the dynamic model and cost function of each agent; A second constant unit for obtaining the first performance constant, second performance constant, and third performance constant of each agent based on the first constant value, second constant value of each agent, and the Laplacian matrix of the action topology model; The constant value of the action topology model is calculated as follows: ； where \(k_1\) is the constant value of the action topology model, \(\varepsilon\) is the total number of edges of the action topology model, and \(n\) is the dimension of the position of the agent. is the largest eigenvalue in the Laplacian matrix of the action topology model; The constant mean value of each agent at time t is calculated as follows: ； where: k i (t) is the constant mean of the i-th agent at time t; is the first constant value of the i-th agent at time t, N is the total number of agents in the unmanned cluster, is the minimum eigenvalue in the Laplacian matrix of the action topology model, and the minimum eigenvalue is non-zero; is the second constant value of the i-th agent at time t; α i (t) is the first performance constant of the i-th agent at time t, β i (t) is the second performance constant of the i-th agent at time t, γ i (t) is the third performance constant of the i-th agent at time t; The time-varying controller is as follows: where: \(i\in N\), \(U\) i (t) is the time-varying controller of the \(i\)-th agent at time \(t\), \(\cdot\) represents differentiation, \(q\) i (t) is the position of the \(i\)-th agent at time \(t\), \(q\) j (t) represents the position of the \(j\)-th agent at time \(t\), \(N\) i is the number of agents adjacent to the \(i\)-th agent, sgn is the sign function, , f i (q i (t), t) at time t The cost function of the $i$-th agent, $\nabla f$ i (q i (t), t) is the gradient information matrix of $f$ i (q i (t), t), H i (q i (t), t) is f i (q i (t), t)'s Hessian matrix, representing the partial derivative of the gradient information matrix with respect to time t.

4. The unmanned cluster distributed time-varying optimization control system according to claim 3, wherein The disturbance quantity is calculated based on the velocity, the control input, the position matrix, and the velocity matrix of the disturbance system.

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