Distributed constraint formation optimal tracking method, device, equipment and medium

Abstract

The invention discloses a distributed constraint formation optimal tracking method, device and equipment and a medium, and relates to the technical field of formation tracking control of clusters, and the method comprises the steps: building a communication topological structure in a heterogeneous cluster system, building a dynamic model of the heterogeneous cluster system, and carrying out the formation tracking control of the heterogeneous cluster system based on the communication topological structure and the dynamic model. Establishing a constraint formation optimal tracking model, designing a distributed constraint formation optimal tracking control protocol, and determining control protocol parameters of the distributed constraint formation optimal tracking control protocol to ensure that a dynamic regret value and a constraint violation value are linearly increased along with time; and based on the distributed constraint formation optimal tracking control protocol and the control protocol parameters, solving the constraint formation optimal tracking model to obtain an optimal formation tracking result, thereby realizing constraint formation optimal tracking.

Description

Technical Field

[0001] The present application relates to the technical field of formation tracking control of clusters, and particularly to a distributed constrained formation optimal tracking method, device, equipment and medium for heterogeneous cluster systems. Background Art

[0002] In recent years, the problem of formation tracking of clusters has received increasing attention. In response to this problem, related technical personnel have proposed a leader-follower formation tracking method. In addition, there has also been research dedicated to various extensions, including multi-leader formation tracking, formation enclosing control, and grouped formation tracking. These methods mainly focus on scenarios where the formation reference trajectory is known in advance by the leader. However, in practical applications, the formation reference trajectory to be achieved may often change significantly over time due to different tasks assigned to the followers, rather than being determined solely by the leader. This need is more prominent when the communication link between the leader and the followers is unstable. The leaderless method based on consensus enables agents to reach a consensus in a distributed manner without a leader, but this method lacks sufficient consideration in terms of performance optimization. Therefore, for cluster systems, it is crucial to maintain formation tracking without a leader while taking into account the performance of each agent.

[0003] To solve this problem, related scholars have studied the distributed formation optimal tracking problem characterized by local objective functions and formation configuration requirements. It is assumed that each agent has a time-invariant objective function that is not disclosed to other agents, and the formation configuration requirements are transformed into a kind of constraint. In practical scenarios, the objective function may change drastically with the change of tasks and the environment. At the same time, in addition to the formation configuration requirements, there may be multiple constraints coexisting, including the dynamic model limitations of agents, obstacles or threat areas in the environment, and the limited and heterogeneous fields of view of agents. Therefore, considering the above actual influencing factors, the formation optimal tracking problem can be transformed into a distributed time-varying optimization problem with coupled constraints. In this regard, some related scholars have considered the case of coupled inequality constraints, and some related scholars have solved the problem of heterogeneous linear dynamic systems. Generally speaking, the distributed formation optimal tracking algorithm for heterogeneous linear cluster systems with coupled constraints is still worthy of further research, and there is currently a lack of practical experimental verification. In addition, predictable information has been widely used in various control fields, but there are few research results on the utilization of predictable information in formation optimal tracking. Summary of the Invention

[0004] The purpose of the present application is to provide a distributed constrained formation optimal tracking method, device, equipment and medium, which can achieve constrained formation optimal tracking.

[0005] To achieve the above purpose, the present application provides the following solutions:

[0006] In a first aspect, the present application provides a distributed constrained formation optimal tracking method, including:

[0007] Establish a communication topology structure within a heterogeneous cluster system; the heterogeneous cluster system includes a number of agents;

[0008] Establish a dynamic model of the heterogeneous cluster system;

[0009] Based on the communication topology structure and the dynamic model, establish a constrained formation optimal tracking model; the constrained formation optimal tracking model includes a global objective function and constraint conditions;

[0010] Design a distributed constrained formation optimal tracking control protocol; the distributed constrained formation optimal tracking control protocol includes a weighted average consensus mechanism, a predictive tracking controller, and a primal-dual update mechanism; the weighted average consensus mechanism is used for an agent to update the weighted average estimation of the formation center vector and the normalized left eigenvector based on neighbor information; the predictive tracking controller generates a control input based on the weighted average estimation to track the formation configuration; the primal-dual update mechanism is used to update the estimated value of the formation center vector and the estimated value of the dual vector;

[0011] Determine the control protocol parameters of the distributed constrained formation optimal tracking control protocol to ensure that the dynamic regret value and the constraint violation value increase linearly with time;

[0012] Based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters, solve the constrained formation optimal tracking model to obtain an optimal formation tracking result.

[0013] In a second aspect, the present application provides a distributed constrained formation optimal tracking device, including:

[0014] A communication topology structure establishment module for establishing a communication topology structure within a heterogeneous cluster system; the heterogeneous cluster system includes a number of agents;

[0015] A dynamic model establishment module for establishing a dynamic model of the heterogeneous cluster system;

[0016] A constrained formation optimal tracking model establishment module for establishing a constrained formation optimal tracking model based on the communication topology structure and the dynamic model; the constrained formation optimal tracking model includes a global objective function and constraint conditions;

[0017] A distributed constrained formation optimal tracking control protocol design module for designing a distributed constrained formation optimal tracking control protocol; the distributed constrained formation optimal tracking control protocol includes a weighted average consensus mechanism, a predictive tracking controller, and a primal-dual update mechanism; the weighted average consensus mechanism is used for agents to update the weighted average estimates of the formation center vector and the normalized left eigenvector based on neighbor information; the predictive tracking controller generates control inputs based on the weighted average estimates to track the formation configuration; the primal-dual update mechanism is used to update the estimated values of the formation center vector and the dual vector estimate;

[0018] A control protocol parameter determination module for determining the control protocol parameters of the distributed constrained formation optimal tracking control protocol to ensure that the dynamic regret value and the constraint violation value increase linearly with time;

[0019] A constrained formation optimal tracking model solving module for solving the constrained formation optimal tracking model based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters to obtain an optimal formation tracking result.

[0020] In a third aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the computer program to implement the above-mentioned distributed constrained formation optimal tracking method.

[0021] In a fourth aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the above-mentioned distributed constrained formation optimal tracking method is implemented.

[0022] According to the specific embodiments provided by the present application, the following technical effects are disclosed in the present application:

[0023] The present application provides a distributed constrained formation optimal tracking method, device, equipment and medium, and proposes a distributed constrained formation optimal tracking control protocol. This distributed constrained formation optimal tracking control protocol uses the primal-dual mechanism to address the challenges brought by time-varying optimization tasks and various coupling constraints to the trajectory estimation layer, and introduces a predictive optimal tracking control technology to handle the problems brought by heterogeneous linear dynamics and rapidly changing trajectory estimates to the tracking control layer. By designing control inputs for the heterogeneous cluster system, each agent can perform distributed online solution of the constrained formation optimal tracking model when it knows the local information at the current moment (including its own set constraints, subgradients of local objective functions, subgradients of local inequality constraint functions) and obtains partial information of neighbors (including updated estimates of neighbor formation center vectors, normalized left eigenvector estimates) through the communication topology structure, so that both the dynamic regret value and the constraint violation value increase linearly with time, thereby achieving constrained formation optimal tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0025] Figure 1 It is an application environment diagram of a distributed constrained formation optimal tracking method in an embodiment of the present application;

[0026] Figure 2 It is a schematic flowchart of a distributed constrained formation optimal tracking method provided in an embodiment of the present application;

[0027] Figure 3 It is a schematic diagram of the specific process of a distributed constrained formation optimal tracking method provided in an embodiment of the present application;

[0028] Figure 4 It is a block diagram of a distributed constrained formation optimal tracking control protocol provided in an embodiment of the present application;

[0029] Figure 5 It is a schematic diagram of a communication topology structure provided in an embodiment of the present application;

[0030] Figure 6 It is a curve diagram of the dynamic regret value provided in an embodiment of the present application;

[0031] Figure 7 It is a curve diagram of the cumulative violation value of the formation constraint provided in an embodiment of the present application;

[0032] Figure 8 The cumulative violation value curve graph for inequality constraints provided by an embodiment of the present application;

[0033] Figure 9 The schematic diagram of the trajectory curve result provided by an embodiment of the present application;

[0034] Figure 10 The schematic diagram of the functional modules of a distributed constraint formation optimal tracking device provided by an embodiment of the present application;

[0035] Figure 11 The schematic diagram of the structure of a computer device provided by an embodiment of the present application. Detailed implementation manners

[0036] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0037] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0038] The distributed constraint formation optimal tracking method provided by the embodiments of the present application can be applied to, for example Figure 1In the application environment shown. Among them, the terminal 102 communicates with the server 104 through the network. The data storage system can store the data that the server 104 needs to process. The data storage system can be set separately, integrated on the server 104, placed on the cloud or other servers. The terminal 102 can send a tracking control request to the server 104. After receiving the tracking control request, for the tracking control request, the server 104 establishes a communication topology structure within the heterogeneous cluster system, establishes a dynamic model of the heterogeneous cluster system, based on the communication topology structure and the dynamic model, establishes a constrained formation optimal tracking model, designs a distributed constrained formation optimal tracking control protocol, determines the control protocol parameters of the distributed constrained formation optimal tracking control protocol to ensure that the dynamic regret value and the constraint violation value increase linearly with time, and based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters, solves the constrained formation optimal tracking model to obtain an optimal formation tracking result. The server 104 can feedback the obtained video tags for the video to the terminal 102. In addition, in some embodiments, the distributed constrained formation optimal tracking method can also be implemented separately by the server 104 or the terminal 102. For example, the terminal 102 can directly perform video tag processing for the tracking control request, or the server 104 can obtain the tracking control request from the data storage system and perform video tag processing for the tracking control request.

[0039] Among them, the terminal 102 can be, but is not limited to, various desktop computers, laptop computers, smart phones, tablet computers, Internet of Things devices and portable wearable devices. The Internet of Things devices can be smart speakers, smart TVs, smart air conditioners, smart in-vehicle devices, etc. The portable wearable devices can be smart watches, smart bracelets, head-mounted devices, etc. The server 104 can be implemented by an independent server or a server cluster composed of multiple servers, and can also be a cloud server.

[0040] In an exemplary embodiment, as Figure 2 shown, a distributed constrained formation optimal tracking method is provided. This method is executed by a computer device, and can be specifically executed alone by a computer device such as a terminal or a server, or jointly executed by a terminal and a server. In the embodiments of the present application, taking this method applied to Figure 1 the server 104 in

[0041] Step 201, establish a communication topology structure within the heterogeneous cluster system; the heterogeneous cluster system includes several agents.

[0042] Step 202, establish a dynamic model of the heterogeneous cluster system.

[0043] Step 203: Based on the communication topology and the dynamic model, establish an optimal tracking model for constrained formation; the optimal tracking model for constrained formation includes a global objective function and constraint conditions.

[0044] Step 204: Design a distributed optimal tracking control protocol for constrained formation; the distributed optimal tracking control protocol for constrained formation includes a weighted average consensus mechanism, a predictive tracking controller, and a primal-dual update mechanism; the weighted average consensus mechanism is used for the agent to update the weighted average estimates of the formation center vector and the normalized left eigenvector based on neighbor information; the predictive tracking controller generates a control input based on the weighted average estimate to track the formation configuration; the primal-dual update mechanism is used to update the estimated values of the formation center vector and the dual vector.

[0045] Step 205: Determine the control protocol parameters of the distributed optimal tracking control protocol for constrained formation to ensure that the dynamic regret value and the constraint violation value increase linearly with time.

[0046] Step 206: Solve the optimal tracking model for constrained formation based on the distributed optimal tracking control protocol for constrained formation and the control protocol parameters to obtain the optimal formation tracking result.

[0047] Implementing the above steps 201 to 206, a distributed optimal tracking control protocol for constrained formation is proposed. This distributed optimal tracking control protocol uses the primal-dual mechanism to address the challenges brought by time-varying optimization tasks and various coupling constraints to the trajectory estimation layer, and introduces a predictive optimal tracking control technology to handle the problems brought by heterogeneous linear dynamics and rapidly changing trajectory estimates to the tracking control layer. By designing control inputs for heterogeneous cluster systems, each agent can perform distributed online solution of the optimal tracking model for constrained formation when knowing the local information at the current moment (including its own set of constraints, the subgradient of the local objective function, and the subgradient of the local inequality constraint function) and obtaining partial information of neighbors (including the updated estimates of the formation center vector of neighbors and the estimated normalized left eigenvector) through the communication topology, so that both the dynamic regret value and the constraint violation value increase linearly with time. In addition, this application can also use the online convex optimization theory and the discrete-time Lyapunov theory to provide a parameter determination method, which can ensure that the upper bound of the relevant error of the distributed optimal tracking control protocol for constrained formation has a linear convergence rate, that is, it can approximate the optimal solution with a bounded error within a sufficiently large time domain, thus achieving optimal tracking of the constrained formation.

[0048] As Figure 3As shown, first, the communication topology within the heterogeneous cluster system is described; second, the dynamic models of each agent in the heterogeneous cluster system are established; then, based on the above descriptions of the communication topology and dynamic models, the constrained formation optimal tracking problem in this application is clearly defined, thus laying a foundation for subsequent protocol design; next, the specific expression form of the constrained formation optimal tracking control protocol is given; finally, the control protocol parameters to be designed in the distributed constrained formation optimal tracking control protocol are determined to ensure that the heterogeneous cluster system can achieve the above-mentioned constrained formation optimal tracking under the proposed distributed constrained formation optimal tracking control protocol.

[0049] In another exemplary embodiment of this application, step 201 specifically includes: representing the internal structure of the heterogeneous cluster system in a graph-theoretic manner to obtain a directed graph; the directed graph is used to define the communication topology within the heterogeneous cluster system; the directed graph consists of a node set and an edge set; the node set includes several nodes; one node corresponds to one agent; the edge set consists of several edges; the agents corresponding to the two nodes connected by the edge can obtain each other's information.

[0050] The communication topology can be defined by a directed graph where, and respectively represent the node set and the edge set; N is a positive integer representing the number of agents; (i, j) represents an edge with the nodes corresponding to agents i and j as endpoints. If agent i can obtain the information of agent j through the communication topology, then (i, j) ∈ E; otherwise if for any agent there exists a path from agent i to agent j, then the directed graph is connected. In addition, represents the neighbor set of agent i; represents the in-degree of agent i, that is, the cardinality of the neighbor set of agent i.

[0051] It should be noted that the agents in this application can be of types such as unmanned vehicles, unmanned aerial vehicles, etc., and the heterogeneous cluster system is a cluster system composed of at least two different types of agents.

[0052] Let be a weight matrix associated with the directed graph satisfying the row-stochastic property, that is, for any agent there is represents the set of N×N dimensional real-valued matrices, and w ij represents the weight factor of agent i for agent j. For any if (i, j) ∈ E then there is wij > 0, otherwise w ij = 0, that is, when the edge between the nodes corresponding to agent i and agent j belongs to the edge set E, the weight factor w of agent i with respect to agent j ij is greater than 0, otherwise the weight factor w of agent i with respect to agent j ij equals 0. Let be the normalized left eigenvector of the weight matrix W, that is, π T W = π T and π T 1 = 1, represents the set of a-dimensional real-valued vectors, (·) T represents the transpose. It should be noted that the weight matrix W is usually set artificially in advance according to the connectivity of the directed graph .

[0053] In step 202, for any moment where K is a positive integer, the dynamic model of the heterogeneous cluster system is:

[0054]

[0055] where, is the state of agent i at time k, is the output of agent i at time k, is the input of agent i at time k, A i , B i , C i are system matrices, p i , m, r i are positive integers, representing the state dimension, output dimension, and input dimension respectively.

[0056] Based on the above description of the communication topology and dynamic model, the constrained formation optimal tracking problem mainly concerned in this application is clarified, that is, to characterize the constrained formation optimal tracking problem.

[0057] First, the formation constraints are defined. Given the desired formation configuration For any there is is the formation constraint set, which is composed of all possible affine transformations of the formation configuration. Among them, diag represents the diagonal matrix, I m represents the m-dimensional identity matrix, and a i represents the affine transformation of the formation configuration of agent i.

[0058] Secondly, the constrained formation optimal tracking problem is defined. For any agent at any moment the local set constraint is given Local objective function \(f\) i,k : Local inequality constraint function \(g\) i,k : Denote the set of real-valued scalars. Based on this, the constrained formation optimal tracking problem is to design the control input for the heterogeneous cluster system such that the following holds, that is, the constrained formation optimal tracking model is as follows:

[0059]

[0060] where, min represents minimization; s.t. is the abbreviation of subject to, representing the constraint conditions; is the global set constraint, stacked by the local set constraints of all agents; denotes the set of agents; \(y\) k+1 is the global output vector, stacked by the output vectors of all agents; \(f\) k : is the global objective function, which is the sum of the cumulative local objective functions of all agents; \(f\) i,c \((y\) i,k+1 ) is the local objective function of agent \(i\) at time \(k + 1\); \(y\) i,k+1 ) is the output vector of agent \(i\) at time \(k + 1\); is the formation constraint; \(g\) k : is the global inequality constraint function, stacked by the cumulative local inequality constraint functions of all agents.

[0061] Furthermore, the constrained formation optimal tracking problem is equivalently transformed to facilitate the subsequent design of the distributed constrained formation optimal tracking control protocol. The constrained formation optimal tracking model shown in formula (2) can be equivalently transformed into the following formula.

[0062]

[0063] where, is the formation center vector; is the local set constraint of agent \(i\) with respect to the formation center vector, satisfying is the global set constraint with respect to the formation center vector, which is the intersection of the local set constraints of all agents with respect to the formation center vector; \(h'\) is the augmented formation configuration matrix, satisfying where horz and vert respectively represent horizontal connection and vertical connection, and 1 represents a vector of appropriate dimension; \(h'\) i is the augmented formation vector of agent \(i\), that is, the \(i\)-th row of \(h'\).

[0064] Finally, it is given whether the distributed constrained formation optimal tracking control protocol realizes the definition of the above constrained formation optimal tracking problem, that is, the performance evaluation conditions of the distributed constrained formation optimal tracking control protocol are given.

[0065] Definition 1: Given the outputs {y i,c , c = 1, 2,..., k + 1} of the heterogeneous cluster system and the estimated value of the formation center vector The dynamic regret value and constraint violation value with respect to formula (3) are shown as follows.

[0066]

[0067] Among them, is the dynamic regret value, which is used to represent the cumulative error between the actual output and the optimal value; is the local cumulative violation value of agent i with respect to the inequality constraint; is the cumulative violation value with respect to the formation constraint; y c* = h'q c* is the optimal value of the global output vector at time c; q c* is the optimal value of the formation center vector at time c; is the weighted average of the estimated values of the formation center vectors of all agents at time c, ρ is a row stochastic vector, and [·] i represents the i-th element of this row stochastic vector; Π + represents the projection on the non-negative quadrant. If the upper bounds of the above dynamic regret value and constraint violation value grow linearly with time, that is where represents the same order as k, then it is said that the heterogeneous cluster system approximates the optimal solution with a bounded error in a sufficiently large time domain, thus realizing the constrained formation optimal tracking.

[0068] To sum up, the objective of this application is: to design control inputs for the heterogeneous cluster system so that each agent, given the local information at the current time (including its own set constraints, the subgradient of the local objective function, the subgradient of the local inequality constraint function), and through the communication topology obtains partial information of its neighbors (including the updated estimate of the formation center vector of the neighbors, the estimated normalized left eigenvector), can solve formula (2) (or formula (3)) distributively and online, and makes the dynamic regret value and constraint violation value in formula (4) grow linearly with time, thus realizing the constrained formation optimal tracking. Next, step 204 will design a distributed constrained formation optimal tracking control protocol for this objective to determine the control input.

[0069] As Figure 4 shown, in step 204, for any time Each agent The distributed constrained formation optimal tracking control protocol for each agent is mainly based on the following process, including the following steps 301 to 303.

[0070] Step 301: First, based on the updated estimates in step 303 at the previous moment (i.e., the updated estimates of the formation center vector estimate and the dual vector estimate) and the neighbor information obtained using the communication topology, a weighted average consensus mechanism is designed to obtain the weighted average estimate at the current moment, so as to ensure that the estimates of the heterogeneous cluster system can reach an overall consensus; the neighbor information includes the updated estimates of the neighbors (neighbor agents).

[0071] Specifically: the weighted average consensus mechanism. Agent i calculates the weighted average estimate of the formation center vector and the weighted average estimate of the normalized left eigenvector through communication with neighbor agents. The calculation formula of the weighted average consensus mechanism is:

[0072]

[0073] Among them, represents the weighted average estimate of the formation center vector of agent i at time k for time k + v - 1; N is the number of agents, w ij represents the weight factor of agent i for agent j; q j,k+v-1 represents the updated estimate of the formation center vector of agent j at time k - 1 for time k + v - 1; κ i,k+v represents the weighted average estimate (or updated estimate) of the normalized left eigenvector of agent i at time k for time k + v; κ j,k+v-1 represents the weighted average estimate (or updated estimate) of the normalized left eigenvector of agent j at time k - 1 for time k + v - 1, q j,k+v-1 and κ j,k+v-1 are both obtained through the communication between agent i and agent j. The initial values are selected as q i,l = 0, κ i,l = e i , l = 1,..., v, where 0 represents a 0 vector or 0 matrix with appropriate dimensions, and e i represents a vector with appropriate dimensions, whose i-th element is 1 and the rest of the elements are all 0.

[0074] Step 302: Based on the weighted average estimate of the formation center vector obtained in step 301 and the first local information, a predictive tracking controller is formulated, and the output of the agent can track the estimated information at the next moment through this predictive tracking controller; the first local information includes its own state, output, and formation configuration vector.

[0075] Specifically, the predictive tracking control protocol. Agent i calculates the control input at the (k + 1)-th moment based on the weighted average estimation of the formation center vector. The control input of the predictive tracking controller is as follows:

[0076]

[0077] where, Δu i,k = u i,k+1 - u i,k represents the difference in the control input of agent i at the k-th moment, u i,k+1 represents the control input of agent i at the (k + 1)-th moment, u i,k represents the control input of agent i at the k-th moment, represents the optimal control gain, represents the augmented state of agent i at the k-th moment, represents the augmented error, represents the tracking error, Δx i,k = x i,k+1 - x i,k represents the state difference, x i,k+1 represents the state of agent i at the (k + 1)-th moment, x i,k represents the state of agent i at the k-th moment, represents the augmented predicted state estimate, and T represents the transpose.

[0078] Specifically, the evolution equation of the augmented state is shown as follows:

[0079]

[0080] where, X i,k+1 represents the augmented state of agent i at the (k + 1)-th moment, and represent system matrices with appropriate dimensions, and the formula is as follows:

[0081]

[0082] In the formula, G i ′ ,q 、 A i ′, G i =, G i,q represent intermediate variable matrices; A i 、B i 、C i are system matrices, 0 represents a 0 vector or 0 matrix with appropriate dimensions; I represents an identity matrix with appropriate dimensions.

[0083] The calculation formula of the optimal control gain is shown as follows:

[0084]

[0085] Among them, argmin represents the parameter that minimizes the function, and K i represents the control gain of agent i, and J i,k represents the quadratic objective function for evaluating the optimal control gain, and the formula is as follows:

[0086]

[0087] Among them, X i,c represents the augmented state of agent i at time c, represents the augmented evaluation matrix with respect to the augmented state, and Q i represents the evaluation matrix with respect to the state, and R i represents the evaluation matrix with respect to the control input difference.

[0088] Step 303: Based on the weighted average estimation in Step 301 and the second local information, design a primal-dual based update mechanism to update the weighted average estimation in Step 301, so as to be used as the input at the next moment 1). The second local information includes the subgradient of its own local objective function, the subgradient of the local inequality constraint function, the local set constraint, and the formation configuration vector.

[0089] It should be noted that each agent can predict the information of the local objective function and the local inequality constraint function v steps in advance, where v is a positive integer representing the prediction time step.

[0090] Specifically, for the primal-dual based update mechanism. Agent i updates the estimated value of the formation center vector at the (k + v)-th moment and the estimated value of the dual vector for handling constraints respectively based on the weighted average estimation of the formation center vector and the weighted average estimation of the normalized left eigenvector. Then the primal-dual update mechanism includes the update of the estimated value of the formation center vector and the update of the estimated value of the dual vector, which are respectively expressed as follows:

[0091]

[0092] Among them, q i,k+v represents the updated estimate of the formation center vector of agent i at the (k + v)-th moment at time k, and Π M represents the projection onto M, represents the weighted average estimation of the formation center vector of agent i at the (k + v - 1)-th moment at time k, and α k and δ k are control protocol parameters, h′ is the augmented formation configuration matrix, and λ i,k+v represents the updated estimate of the dual vector of agent i at the (k + v)-th moment at time k, and Π +Denote the projection on the non - negative quadrant, λ i,k+v-1 Denote the estimated update of the dual vector of agent i at time k - 1 for time k + v - 1, and Denote the sub - gradient of the Lagrangian function with respect to the formation center vector and the sub - gradient of the Lagrangian function with respect to the dual vector respectively. The calculation formulas are shown as follows.

[0093]

[0094] where the initial value is selected as λ i,l = 0, l = 1,..., v, ▽g i,k and ▽f i,k Denote the sub - gradients of the local inequality constraint function and the local objective function with respect to the formation center vector respectively, and they are all given self - information.

[0095] In step 205, the control protocol parameters are determined by using the online convex optimization theory and the discrete - time Lyapunov theory. The specific process is as follows: The control protocol parameters include the evaluation matrix, the optimal control gain, and the step - size; Based on Definition 1 in step 203, to ensure that the distributed constrained formation optimal tracking control protocol in step 204 can achieve formula (2) (or formula (3)), that is, to ensure that the dynamic regret value and the constraint violation value increase linearly. For any time each agent the control protocol parameters in the distributed constrained formation optimal tracking control protocol can be designed as follows:

[0096] 1) Select the evaluation matrix Q i with respect to the state and the evaluation matrix R i with respect to the control input difference as symmetric positive - definite matrices, and is detectable;

[0097] 2) The optimal control gain satisfies where is the unique positive - definite solution of the Riccati equation shown as follows:

[0098]

[0099] 3) Let the step - size be α k = k -0.5 , δ k = k -0.2 .

[0100] Using the routine of the distributed constrained formation optimal tracking method provided by this application, the effects are as follows:

[0101] Consider a heterogeneous cluster system consisting of two types of agents, namely drones and unmanned vehicles. This heterogeneous cluster system specifically includes 1 drone and 4 unmanned vehicles. Based on the inner and outer loop control framework, the dynamic models of the drone and unmanned vehicles can be approximately described by Equation (1). Note that the flight altitude of the drone is assumed to be constant, so the altitude does not need to be considered in this routine. The following routine is implemented in a two-dimensional plane, that is, m = 2 in Equation (1). Specifically, the parameters of the drone (i = 1) are:

[0102]

[0103] The parameters of the unmanned vehicles (i = 2, 3, 4, 5) are:

[0104] A i = I 2 , B i = I 2 Δt, C i = I 2 (17).

[0105] where Δt = 0.02 s is the sampling interval.

[0106] The communication topology structure of the above heterogeneous cluster system is as shown in Figure 5 where the hexagon represents the drone, the circle represents the unmanned vehicle, and the numbers represent the agent numbers; the solid line represents the communication edge, and the arrow represents the information transmission direction.

[0107] The constrained formation optimal tracking task is defined by Equation (2). Specifically, f i,k (y i,k+1 ) = 0.5||a i,k + b i,k 0.05kΔt + c i,k h i - y i,k+1 || 2 , where a i,k , b i,k , c i,k are randomly generated, and h is set as a regular pentagon. The above task can be understood as: within a fixed rectangular area , there are two threat areas with strong and weak threats. Each agent is expected to maintain a regular pentagon formation configuration while completing the dynamic task characterized by f i,k in the non-threat area of the rectangular area with good global performance. In addition, each agent can only obtain partial information about the task at any given time, and has a limited and different field of view when observing the threat area, which is characterized by g i,k .

[0108] Figure 6 、 Figure 7 andFigure 8 shows the curve results of the dynamic regret value, the cumulative violation value of the formation constraint, and the cumulative violation value of the inequality constraint obtained by the heterogeneous cluster system under the distributed constrained formation optimal tracking control protocol of the present application. Among them, "Total" in the legend represents the and "Agent 1, 2, 3, 4, 5" represents the and components related to Agents 1, 2, 3, 4, 5 defined in formula (4), and "Agent 1, 2, 3, 4, 5 (Threat Area 1, Threat Area 2)" represents the components in formula (4) where i = 1, 2, 3, 4, 5 and related to Threat Area 1 and Threat Area 2. Figure 6 In (a) of Figure 6 is the evolution curve of the dynamic regret value at all times, Figure 7 In (a) of Figure 7 is the evolution curve of the cumulative violation value of the formation constraint at all times,

[0109] From Figure 6 , Figure 7 and Figure 8 it can be seen that the dynamic regret value and the formation constraint violation value can achieve linear growth, and the inequality constraint violation value can achieve sub-linear growth better than linear growth. Therefore, the distributed constrained formation optimal tracking control protocol proposed in the present application can enable the heterogeneous cluster system to achieve constrained formation optimal tracking.

[0110] In addition, to more intuitively present the implementation process of constrained formation optimal tracking, Figure 9 shows the trajectory curve results obtained by the heterogeneous cluster system under the distributed constrained formation optimal tracking control protocol of the present application. Figure 9 In Figure 9 the rhombus represents the initial position of the agent, the pentagram represents the end position of the agent, the line represents the trajectory curve of the agent, the abscissa represents the state component along the X-axis, and the ordinate represents the state component along the Y-axis. The formation configurations of all agents are shown at times k = 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000. The gray area represents the threat area. From

[0111] The present application also provides an application scenario, which applies the above-mentioned distributed constrained formation optimal tracking method. Specifically: The distributed constrained formation optimal tracking method provided in this embodiment can be applied in the formation optimal tracking scenario. The formation optimal tracking scenario includes a request generation link, a formation optimal tracking processing link, and a formation control link; the tracking control request enters the formation optimal tracking link from the request generation link, obtains corresponding content features through a human-machine collaboration method, and enters the downstream formation control link. The distributed constrained formation optimal tracking method provided in this embodiment belongs to the formation optimal tracking link. Specifically, in the process of the formation optimal tracking link for the tracking control request, a communication topology structure inside the heterogeneous cluster system can be established, a dynamic model of the heterogeneous cluster system can be established, based on the communication topology structure and the dynamic model, a constrained formation optimal tracking model can be established, a distributed constrained formation optimal tracking control protocol can be designed, the control protocol parameters of the distributed constrained formation optimal tracking control protocol can be determined to ensure that the dynamic regret value and the constraint violation value increase linearly with time, and based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters, the constrained formation optimal tracking model can be solved to obtain the optimal formation tracking result.

[0112] Based on the same inventive concept, the embodiment of the present application also provides a distributed constrained formation optimal tracking device for implementing the above-mentioned distributed constrained formation optimal tracking method. The implementation solution provided by this device for solving problems is similar to the implementation solution described in the above method. Therefore, the specific limitations in one or more embodiments of the distributed constrained formation optimal tracking device provided below can refer to the limitations on the distributed constrained formation optimal tracking method in the above text, and will not be repeated here.

[0113] In an exemplary embodiment, as Figure 10 shown, a distributed constrained formation optimal tracking device is provided, which includes the following modules:

[0114] A communication topology structure establishment module T1, which is used to establish a communication topology structure inside the heterogeneous cluster system; the heterogeneous cluster system includes several agents;

[0115] A dynamic model establishment module T2, which is used to establish a dynamic model of the heterogeneous cluster system;

[0116] A constrained formation optimal tracking model establishment module T3, which is used to establish a constrained formation optimal tracking model based on the communication topology structure and the dynamic model; the constrained formation optimal tracking model includes a global objective function and constraint conditions;

[0117] The distributed constrained formation optimal tracking control protocol design module T4 is used to design a distributed constrained formation optimal tracking control protocol; the distributed constrained formation optimal tracking control protocol includes a weighted average consensus mechanism, a predictive tracking controller, and a primal-dual update mechanism; the weighted average consensus mechanism is used for agents to update the weighted average estimates of the formation center vector and the normalized left eigenvector based on neighbor information; the predictive tracking controller generates control inputs based on the weighted average estimates to track the formation configuration; the primal-dual update mechanism is used to update the estimated values of the formation center vector and the dual vector.

[0118] The control protocol parameter determination module T5 is used to determine the control protocol parameters of the distributed constrained formation optimal tracking control protocol to ensure that the dynamic regret value and the constraint violation value increase linearly with time.

[0119] The constrained formation optimal tracking model solving module T6 is used to solve the constrained formation optimal tracking model based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters to obtain the optimal formation tracking result.

[0120] In an exemplary embodiment, a computer device is provided. The computer device can be a server or a terminal, and its internal structure diagram can be as Figure 11 shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store distributed constrained formation optimal tracking processing data. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals through a network connection. When the computer program is executed by the processor, it implements a distributed constrained formation optimal tracking method.

[0121] Those skilled in the art can understand that Figure 11 the structure shown in

[0122] In an exemplary embodiment, a computer device is provided, which includes a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0123] In an exemplary embodiment, a computer-readable storage medium is provided, which stores a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0124] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use, and processing of relevant data need to comply with relevant regulations.

[0125] Those of ordinary skill in the art can understand that all or part of the processes in the above method embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above method embodiments. Among them, any reference to a memory, database, or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memories. Non-volatile memory can include Read-Only Memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0126] In each of the embodiments provided in this application, the database involved may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., without limitation. In each of the embodiments provided in this application, the processor may be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., without limitation.

[0127] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0128] Specific examples are used in this article to elaborate on the principles and implementation manners of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, 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 to this application.

Claims

1. A distributed constrained formation optimal tracking method, characterized in that: The distributed constrained formation optimal tracking method comprises: Establishing a communication topology structure within a heterogeneous cluster system; the heterogeneous cluster system includes a plurality of intelligent agents; Establishing a dynamic model of the heterogeneous cluster system; Based on the communication topology and the dynamic model, an optimal tracking model for a constrained formation is established; the optimal tracking model for a constrained formation includes a global objective function and constraint conditions; Design a distributed constrained formation optimal tracking control protocol; the distributed constrained formation optimal tracking control protocol includes a weighted average consensus mechanism, a predictive tracking controller and a primal-dual update mechanism; the weighted average consensus mechanism is used for the agent to update the weighted average estimate of the formation center vector and the normalized left eigenvector based on the neighbor information; the predictive tracking controller generates a control input based on the weighted average estimate to track the formation configuration; the primal-dual update mechanism is used to update the formation center vector estimate and the dual vector estimate; Determining control protocol parameters of the distributed constrained formation optimal tracking control protocol to ensure that dynamic regret values ​​and constraint violation values ​​grow linearly over time; Based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters, the constrained formation optimal tracking model is solved to obtain an optimal formation tracking result.

2. The distributed constrained formation optimal tracking method according to claim 1, characterized in that: Establish the internal communication topology of the heterogeneous cluster system, including: Based on the graph theory, the internal structure of the heterogeneous cluster system is represented to obtain a directed graph; the directed graph is used to define the communication topology structure inside the heterogeneous cluster system; the directed graph is composed of a node set and an edge set; the node set includes a number of nodes; one node corresponds to one intelligent agent; the edge set is composed of a number of edges; the intelligent agents corresponding to the two nodes connected by the edge can obtain each other's information.

3. The distributed constrained formation optimal tracking method according to claim 1, characterized in that: The kinetic model is: Among them, x i,k is the state of agent i at time k, y i,k is the output of agent i at time k, u i,k is the input of agent i at time k, A i ,B i ,C i is the system matrix.

4. The distributed constrained formation optimal tracking method according to claim 1, characterized in that: The optimal tracking model of the constrained formation is expressed as follows: Among them, min means minimization; st means constraint condition; is a global set constraint, which is a stack of local set constraints of all agents; represents the set of agents; y k+1 is the global output vector, which is formed by stacking the output vectors of all agents; f k is the global objective function; f i,c (y i,k+1 ) is the local objective function of agent i at time k+1; y i,k+1 ) is the output vector of agent i at time k+1; is the formation constraint; g k is the global inequality constraint function, which is formed by the accumulated local inequality constraint function stack of all agents.

5. The distributed constrained formation optimal tracking method according to claim 1, characterized in that: The calculation formula of the weighted average consensus mechanism is: in, represents the weighted average estimate of the formation center vector at the k+v-1th moment by agent i at time k; N is the number of agents, w ij represents the weight factor of agent i to agent j; q j,k+v-1 represents the updated estimate of the formation center vector at the k+v-1th moment by agent j at the k-1th moment; κ i,k+v represents the weighted average estimate of the normalized left eigenvector of agent i at time k for the k+vth time; κ j,k+v-1 It represents the weighted average estimate of the normalized left eigenvector of agent j at time k+v-1 at time k-1.

6. The distributed constrained formation optimal tracking method according to claim 1, characterized in that: The control input of the predictive tracking controller is: Among them, Δu i,k =u i,k+1 -u i,k represents the control input difference of agent i at time k, u i,k+1 represents the control input of agent i at time k+1, u i,k represents the control input of agent i at time k, represents the optimal control gain, X i,k Indicates the augmented state.

7. The distributed constrained formation optimal tracking method according to claim 1, characterized in that: The original dual update mechanism includes updating the estimated value of the formation center vector and updating the estimated value of the dual vector, which are respectively expressed as follows: Among them, q i,k+v represents the updated estimate of the formation center vector at time k+v by agent i at time k, Π M represents the projection on M, represents the weighted average estimate of the formation center vector at the k+v-1th moment by agent i at time k, α k and δ k To control the protocol parameters, and denote the subgradient of the Lagrangian function with respect to the formation center vector and the subgradient of the Lagrangian function with respect to the dual vector, h′ is the augmented formation configuration matrix, λ i,k+v represents the update estimate of the dual vector of agent i at time k for the k+vth time, Π + represents the projection on the non-negative quadrant, λ i,k+v-1 + represents the update estimate of the dual vector of agent i at time k-1 for the k+v-1th time.

8. A distributed constrained formation optimal tracking device, characterized in that: The distributed constrained formation optimal tracking device comprises: A communication topology structure establishment module is used to establish a communication topology structure within a heterogeneous cluster system; the heterogeneous cluster system includes a plurality of intelligent agents; A dynamic model building module, used to build a dynamic model of the heterogeneous cluster system; A constrained formation optimal tracking model establishment module, used to establish a constrained formation optimal tracking model based on the communication topology and the dynamic model; the constrained formation optimal tracking model includes a global objective function and constraint conditions; A distributed constrained formation optimal tracking control protocol design module is used to design a distributed constrained formation optimal tracking control protocol; the distributed constrained formation optimal tracking control protocol includes a weighted average consensus mechanism, a predictive tracking controller and a primal-dual update mechanism; the weighted average consensus mechanism is used for the agent to update the weighted average estimate of the formation center vector and the normalized left eigenvector based on the neighbor information; the predictive tracking controller generates a control input based on the weighted average estimate to track the formation configuration; the primal-dual update mechanism is used to update the formation center vector estimate and the dual vector estimate; A control protocol parameter determination module, used to determine the control protocol parameters of the distributed constrained formation optimal tracking control protocol to ensure that the dynamic regret value and the constraint violation value increase linearly over time; The constrained formation optimal tracking model solving module is used to solve the constrained formation optimal tracking model based on the distributed constrained formation optimal tracking control protocol and the control protocol parameters to obtain the optimal formation tracking result.

9. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the distributed constrained formation optimal tracking method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the distributed constrained formation optimal tracking method described in any one of claims 1 to 7 is implemented.

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