Distributed adaptive fixed time formation control method

Abstract

The invention provides a distributed self-adaptive fixed time formation control method, which comprises the following steps: constructing a kinetic model of a nonlinear agent system based on a leader-follower control system; establishing a networked closed-loop error agent control mechanism; a saturation control mechanism based on an Arctangent function is constructed; establishing an autonomous learning robust control mechanism; establishing a fixed time distributed formation control protocol; based on a nonlinear intelligent system model, a networked closed-loop error agent control mechanism, a saturation control mechanism based on an Arctangent function, an autonomous learning robust control mechanism, a fixed-time distributed formation control protocol, a fixed-time distributed formation control strategy, and a distributed formation control system. According to the method, the problems that when an existing intelligent agent is used for solving actual problems, the energy of an execution mechanism is limited, and the task completion time requirement, external interference and other factors directly influence the working performance of an intelligent agent system can be solved.

Description

Technical Field

[0001] The present invention relates to the field of formation control of a networked nonlinear intelligent agent cluster system, and in particular to a distributed adaptive fixed-time formation control method. Background Art

[0002] The multi-agent system is a networked complex nonlinear system that plays an important role in many practical scenarios, such as low-altitude rescue, complex sea area monitoring, intelligent collaborative assembly workshops, refined collaborative cancer treatment in the medical field, and military collaborative operations and confrontations. Compared with a single agent, when a multi-agent system is used to handle tasks, it has strong operability and redundancy, and a high degree of intelligence. The agent can use the distributed formation control method to maintain good working performance in the face of system model uncertainty and external disturbances.

[0003] Formation control is one of the important research directions in the field of collaborative control of multi-agent systems. Its control goal is to design a feasible controller for the agent to drive the agent to run along the preset target path and maintain a given position offset while overcoming other physical constraints.

[0004] At present, when intelligent agents solve practical problems, factors such as limited energy of the actuators, time requirements for task completion, and external interference directly affect the working performance of the intelligent agent system. Summary of the invention

[0005] The embodiment of the present invention provides a distributed adaptive fixed-time formation control method, which can establish a fixed-time distributed formation control strategy through a nonlinear intelligent system communication model, a networked closed-loop error intelligent agent control mechanism, a saturation control mechanism based on Arctangent function, an autonomous learning robust control mechanism and a fixed-time distributed formation control protocol, and perform formation control on the i-th intelligent agent according to the fixed-time distributed formation control strategy to ensure that the formation error converges to a smaller closed set, thereby solving the problem that when existing intelligent agents solve practical problems, factors such as limited energy of the actuator, task completion time requirements and external interference directly affect the working performance of the intelligent agent system.

[0006] An embodiment of the present invention provides a distributed adaptive fixed-time formation control method, wherein the cyber-physical system includes a plurality of subsystems, each of which is described as an intelligent agent, and the distributed adaptive fixed-time formation control method includes:

[0007] Based on the leader-follower control system, a dynamic model of nonlinear intelligent agent system is constructed;

[0008] Establish a networked closed-loop error agent control mechanism;

[0009] Construct a saturation control mechanism based on Arctangent function;

[0010] Establish autonomous learning robust control mechanism;

[0011] Establish a fixed-time distributed formation control protocol;

[0012] Based on the nonlinear intelligent system communication model, the networked closed-loop error intelligent agent control mechanism, the Arctangent function-based saturation control mechanism, the autonomous learning robust control mechanism and the fixed-time distributed formation control protocol, a fixed-time distributed formation control strategy is established, and the i-th intelligent agent is controlled in formation according to the fixed-time distributed formation control strategy.

[0013] Optionally, the step of establishing a networked closed-loop error agent control mechanism includes:

[0014] Acquire local information of adjacent intelligent agents, wherein the local information includes position information and posture information;

[0015] Performing error calculation processing on the local information of the adjacent intelligent agents to obtain local error information of the adjacent intelligent agents;

[0016] A networked closed-loop error agent control mechanism is established based on the local error information of the adjacent agents.

[0017] Optionally, the formulas of the dynamics model of the nonlinear agent system are as follows:

[0018] Mathematical model of the i-th follower

[0019]

[0020] Among them, x i ∈R 2 Indicates position, v i ∈R 2 Indicates speed, u i ∈R 2 represents the control input, f(x i ,v i ) and g(x i ,v i ) represents a known smooth function, and g(x i ,υ i ) is not equal to zero, Δ(x i ,v i ) represents the system model uncertainty, d i (t) represents the external disturbance of the system model;

[0021] Mathematical Model of Leaders

[0022]

[0023] Among them, x 0 ∈R 2 Indicates position, v 0 ∈R 2 Indicates speed, a 0 (t) represents acceleration.

[0024] Optionally, the formula of the networked closed-loop error agent control mechanism is as follows:

[0025]

[0026] in,

[0027]

[0028] h i represents the relative position deviation between the ith follower and the leader, e xi Indicates relative position, e vi Indicates speed error.

[0029] Optionally, the saturation control mechanism based on the Arctangent function is as follows:

[0030]

[0031] Among them, k is is a positive number, the formation control error and for

[0032]

[0033] h j represents the relative position deviation between the jth follower and the leader, N i represents the neighbor set of the ith follower, m ij ∈M(G) and b i0 ∈B(G), and m ij and b i0 Only 1 and 0 can be selected, M(G) represents the adjacency matrix of the directed graph, and B(G) represents the diagonal matrix.

[0034] Optionally, the autonomous learning robust control mechanism is as follows:

[0035] Robust control mechanism with online learning performance:

[0036]

[0037] Among them, |Δ(x i ,v i )|≤Δmax , Δ max is a known positive constant, |d i (t)|≤d max , d max is a known positive constant; the sliding mode control surface s ij Described as

[0038]

[0039] ε i0 ∈R + , ε ij ∈R + , γ i0 ∈(0,1), and γ ij ∈(0,1), ψ(·) is the Heaviside function, defined as follows

[0040]

[0041] mean

[0042]

[0043] Optionally, the autonomous learning robust control mechanism is as follows:

[0044] Adaptive control mechanism:

[0045]

[0046] Adaptive update law:

[0047]

[0048] in

[0049]

[0050] ρ=[ρ 1 ,ρ 2 ,…,ρ n ] T , θ=[θ 1 ,θ 2 ,…,θ n ] T ;

[0051] γ ρi ∈R+,γ θi ∈R+,ε mi ∈R + and ε θi ∈R + , respectively defined as follows:

[0052]

[0053] is an effective estimate of ρ, is a valid estimate of θ, and we define and and

[0054]

[0055] Optionally, the fixed-time distributed formation control protocol is as follows:

[0056]

[0057] Among them, μ i1 ∈R + , μ i2 ∈R + , q∈(0,1), and p∈[1,+∞).

[0058] By adopting the distributed adaptive fixed-time formation control method of the present invention, a fixed-time distributed formation control strategy can be established through the dynamic model of the nonlinear intelligent agent system, the networked closed-loop error intelligent agent control mechanism, the saturation control mechanism based on the Arctangent function, the autonomous learning robust control mechanism and the fixed-time distributed formation control protocol, and the i-th intelligent agent is controlled in formation according to the fixed-time distributed formation control strategy, which solves the problem that when the existing intelligent agent solves practical problems, the limited energy of the actuator, the task completion time requirement and the external interference and other factors directly affect the working performance of the intelligent agent system. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0060] Figure 1 It is a flow chart of a distributed adaptive fixed-time formation control method provided by an embodiment of the present invention;

[0061] Figure 2 is a flow chart of another distributed adaptive fixed-time formation control method provided by an embodiment of the present invention;

[0062] Figure 3 is a framework diagram of a smooth saturation control mechanism provided by an embodiment of the present invention;

[0063] Figure 4is a framework diagram of an adaptive control mechanism provided by an embodiment of the present invention;

[0064] Figure 5 It is a framework diagram of an autonomous learning robust control mechanism provided by an embodiment of the present invention;

[0065] Figure 6 It is a framework diagram of a distributed fixed-time distributed formation control protocol provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0066] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] like Figure 1 As shown, Figure 1 1 is a flow chart of a distributed adaptive fixed-time formation control method provided by an embodiment of the present invention. The distributed adaptive fixed-time formation control method comprises:

[0068] 101. Based on the leader-follower control system, a dynamic model of nonlinear intelligent agent system is constructed.

[0069] In an embodiment of the present invention, the above-mentioned leader-follower control system is a distributed control strategy, which includes a leader and multiple followers. The leader is responsible for formulating the overall control strategy and generating global control instructions, while the followers are responsible for performing specific operation tasks. Information exchange between the leader and the followers is required in real time so that the leader can adjust the control strategy according to the actual situation and the followers can also understand the global control instructions in a timely manner. Close cooperation is required between the leader and the followers to ensure the stable operation of the entire system and the efficient completion of tasks. Since there are multiple followers in the system, even if a follower fails, other followers can continue to perform tasks, thereby improving the stability and reliability of the system.

[0070] The above-mentioned intelligent agent system consists of one or more intelligent agents, each of which has the ability to process information and perform control, but their sensing and communication capabilities are limited. Each intelligent agent has its own state information, including the position, speed, posture, etc. of the intelligent agent.

[0071] The above-mentioned dynamic model of nonlinear agent system can be a dynamic model of networked nonlinear multi-agent system with model uncertainty and external disturbance. In the nonlinear agent system model, the behavior and decision of the agent are based on nonlinear dynamic system. Nonlinearity means that the behavior of these systems cannot be simply described by linear relationships, but involves complex interactions and dependencies.

[0072] It should be noted that in many practical scenarios, the intelligent system may be affected by various uncertainties and disturbances, such as model uncertainty, external disturbances, communication delays, etc. These factors will affect the dynamic behavior and performance of the system.

[0073] 102. Establish a networked closed-loop error agent control mechanism.

[0074] In an embodiment of the present invention, the above-mentioned networked closed-loop error intelligent agent control mechanism can be a networked closed-loop error intelligent agent control system based on local measurement information, which utilizes local measurement information, networked structure and closed-loop error control to achieve efficient, reliable and flexible system control.

[0075] The above-mentioned networked closed-loop error can be understood as the networked structure adopted to enable efficient information exchange between intelligent agents, and the closed-loop error control method is adopted to adjust the control strategy of the intelligent agent by comparing the difference (i.e., error) between the actual output of the system and the expected output, so that the system can respond to changes quickly and reach the desired state.

[0076] Furthermore, the local error information of adjacent agents can be used to establish a networked closed-loop error agent control mechanism.

[0077] The local error information of the neighboring agents can be understood as the local error information obtained by each agent through error calculation based on its own information and other agents' information. The error information of the neighboring agents indicates the difference between the position or posture of an agent and the expected position or posture.

[0078] 103. Construct a saturation control mechanism based on Arctangent function.

[0079] In the embodiment of the present invention, the above-mentioned Arctangent function (tangent function) is also called the inverse tangent function, which is a trigonometric function that describes the proportional relationship between the opposite side and the adjacent side of an angle in a right triangle.

[0080] The saturation control described above is a control strategy in which, when the system state reaches a certain threshold, the system's output is "saturated" or stops growing to prevent the system from overshooting or losing control.

[0081] The above saturation control mechanism is used in control systems to prevent the output signal from exceeding a predetermined range. In signal processing and control systems, the saturation control mechanism can ensure that the output signal is within a safe and stable range.

[0082] It should be noted that the saturation control mechanism based on Arctangent function is used to deal with the local limited output constraints of the intelligent agent actuator and can accelerate the system convergence time.

[0083] 104. Establish an autonomous learning robust control mechanism.

[0084] In an embodiment of the present invention, the autonomous learning robust control mechanism can be a robust control strategy with online learning performance and an adaptive control mechanism. The robust control strategy with online learning performance is used to solve non-matching model uncertainty and external disturbances; the adaptive control mechanism is used to handle matching model uncertainty and external disturbances.

[0085] The above robust control strategy with online learning performance combines online learning and robust control strategies. Online learning allows the system to continuously learn and improve from data during operation, while robust control ensures that the system can maintain good performance in the face of model uncertainty and external disturbances. The above adaptive control mechanism allows the system to automatically adjust its parameters during operation to adapt to changing environmental or system conditions. The adaptive control mechanism can automatically adjust the controller parameters to maintain the stability and performance of the system.

[0086] 105. Establish a fixed-time distributed formation control protocol.

[0087] In an embodiment of the present invention, the above-mentioned fixed-time distributed formation control protocol is used to solve the fixed-time convergence and specified geometric formation constraints, ensuring that the relative error between intelligent agents converges to a specified closed set within a fixed time.

[0088] The above-mentioned convergence within a fixed time can be understood as the state trajectory of the system converging to a preset set within a fixed time. Convergence within a fixed time is used to ensure that the relative positions and directions between multiple agents reach a stable state within a fixed time.

[0089] 106. Based on the dynamic model of nonlinear intelligent agent system, networked closed-loop error intelligent agent control mechanism, Arctangent function-based saturation control mechanism, autonomous learning robust control mechanism and fixed-time distributed formation control protocol, a fixed-time distributed formation control strategy is established, and the i-th intelligent agent is controlled in formation according to the fixed-time distributed formation control strategy.

[0090] In the embodiment of the present invention, the above i is a serial number or an identifier, i can be an integer or other types of identifiers used to represent different intelligent agents.

[0091] The above-mentioned fixed-time distributed formation control strategy integrates the dynamic model of the nonlinear intelligent agent system to describe the kinematic and dynamic characteristics of the multi-agent system; the networked closed-loop error intelligent agent control mechanism takes the relative position and velocity errors between each intelligent agent as input, and realizes precise control of each intelligent agent through a feedback regulator; the saturation control mechanism based on the Arctangent function avoids the problem of numerical instability when calculating the saturation; the autonomous learning robust control mechanism solves the non-matching model uncertainty and external disturbance, matching model uncertainty and external disturbance; the fixed-time distributed formation control protocol ensures that the relative error between intelligent agents converges to the specified tight closed set within a fixed time.

[0092] Furthermore, the i-th agent is controlled in formation according to the fixed-time distributed formation control strategy. First, the state information of the i-th agent is obtained, including position, speed, etc.; then, the state information of other agents in the entire formation is obtained, including position, speed, etc.; then, based on the state information of the i-th agent and other agents, its control instructions for a period of time in the future are calculated, including acceleration, turning angle, etc.; finally, according to the calculated control instructions, the motion state of the i-th agent is adjusted to keep a fixed distance and relative position with other agents.

[0093] The present invention aims at the non-matching model uncertainty and unknown external disturbance obtainable by the supremum, establishes a robust learning control strategy, the learning factor is regulated by the hyperbolic tangent function, avoids the control input oscillation problem introduced by the sliding mode control method, and ensures the smooth and continuous operation of the system; for the matching model uncertainty and unknown external disturbance, constructs an adaptive control mechanism, and gives the adaptive update law of the unknown parameters; in order to characterize the limited output characteristics of the intelligent body actuator, establishes a saturation control mechanism based on the inverse tangent function; for the fixed convergence time and the specified formation constraint situation, establishes a distributed actual fixed time formation control strategy. The present invention can ensure that all parameters of the follower closed-loop error control system converge to the specified compression area within a fixed time, and realize the specified formation control problem. The present invention has the advantages of good scalability, strong robustness, good online learning ability and practicality, and has important theoretical value and practical engineering significance for nonlinear complex systems.

[0094] The embodiment of the present invention constructs a nonlinear intelligent agent system model based on a leader-follower control system; establishes a networked closed-loop error intelligent agent control mechanism; constructs a saturation control mechanism based on an Arctangent function; establishes an autonomous learning robust control mechanism; establishes a fixed-time distributed formation control strategy based on the nonlinear intelligent system model, the networked closed-loop error intelligent agent control mechanism, the saturation control mechanism based on an Arctangent function, and the autonomous learning robust control mechanism, and performs formation control on the i-th intelligent agent according to the fixed-time distributed formation control strategy. The present invention can solve the problem that when existing intelligent agents solve practical problems, factors such as limited energy of the actuator, time requirements for task completion, and external interference directly affect the working performance of the intelligent agent system.

[0095] like Figure 2 As shown, Figure 2 It is a flow chart of another distributed adaptive fixed-time formation control method provided by an embodiment of the present invention. Specifically, it includes local information acquisition of adjacent agents, relative position and speed characterization, error agent system, adaptive mechanism, autonomous learning robust control mechanism, fixed-time formation control protocol, and method stability analysis and verification. The above-mentioned local information acquisition of adjacent agents is used to solve adjacent state information and construct a control method; the above-mentioned relative position and speed characterization is used to process state information integration; the above-mentioned error agent system is used to describe the state equation of the control target; the above-mentioned adaptive mechanism is used to solve matching model uncertainty and external disturbances; the above-mentioned autonomous learning robust control mechanism is used to solve non-matching model uncertainty and external disturbances, provide smooth output, avoid ripples in control input, and ensure system performance; the above-mentioned fixed-time formation control protocol is used to solve specific task time requirements and specified geometric formation constraints; the above-mentioned method stability analysis and verification is used to give the stability mathematical analysis process and simulation result proof of the present invention. The present invention can handle model uncertainty, unknown external disturbances and formation control problems.

[0096] like Figure 3 As shown, Figure 3 is a framework diagram of a smooth saturation control mechanism provided by an embodiment of the present invention. Specifically, for the local finite constraints of the actuator, the sliding mode control surface s composed of position and attitude information ij As input information, a smooth saturation control mechanism is constructed to deal with the local limited output constraints of the intelligent agent's actuators, and at the same time it can accelerate the system convergence time.

[0097] like Figure 4 As shown, Figure 4 is a framework diagram of an adaptive control mechanism provided by an embodiment of the present invention. Specifically, in order to match the uncertainty of the model and the external disturbance, a sliding mode control surface s composed of position and attitude information is used. ijAs input information, an adaptive control mechanism is constructed to handle and resolve matching model uncertainties and external disturbances.

[0098] like Figure 5 As shown, Figure 5 is a framework diagram of an autonomous learning robust control mechanism provided by an embodiment of the present invention. In view of the uncertainty of the non-matching model and external disturbances, a sliding mode control surface s composed of position and attitude information is used. ij As input information, an autonomous learning robust control mechanism is constructed to address non-matching model uncertainties and external disturbances.

[0099] like Figure 6 As shown, Figure 6 This is a framework diagram for constructing a distributed fixed-time distributed formation control protocol provided by an embodiment of the present invention. In view of fixed-time convergence and specified geometric formation constraints, a distributed fixed-time distributed formation control protocol with position and posture information as input signals is constructed to solve fixed-time convergence and specified geometric formation constraints, and ensure that the relative error between intelligent agents converges to a specified closed set within a fixed time.

[0100] In an embodiment of the present invention, the present invention constructs a distributed adaptive fixed-time formation control strategy based on a smooth saturation control mechanism, an adaptive control mechanism, an autonomous learning robust control mechanism, and a distributed fixed-time distributed formation control protocol, which can ensure that all parameters of the follower closed-loop error control system converge to a specified compression area within a fixed time, thereby realizing the specified formation control problem.

[0101] Optionally, the steps of establishing a networked closed-loop error intelligent agent control mechanism include: obtaining local information of adjacent intelligent agents, the local information including position information and posture information; performing error calculation processing on the local information of adjacent intelligent agents to obtain local error information of adjacent intelligent agents; and establishing a networked closed-loop error intelligent agent control mechanism based on the local error information of adjacent intelligent agents.

[0102] In the embodiment of the present invention, each agent has its own state information, including the position, speed, posture, etc. of the agent. The local information of the agent can help other agents understand the state of the agent. For example, if an agent is moving, its position and posture information can tell other agents its direction and speed.

[0103] The above error calculation process can be understood as using an error algorithm to calculate the error information of the neighboring agents. The error information of the neighboring agents represents the difference between the position or posture of an agent and the expected position or posture.

[0104] The above-mentioned networked closed-loop error intelligent agent control mechanism can be a networked closed-loop error intelligent agent control system based on local measurement information, which utilizes local measurement information, networked structure and closed-loop error control to achieve efficient, reliable and flexible system control.

[0105] Optionally, the dynamics model of the nonlinear agent system is formulated as follows:

[0106] Mathematical model of the i-th follower

[0107]

[0108] Among them, x i ∈R 2 Indicates position, v i ∈R 2 Indicates speed, u i ∈R 2 represents the control input, f(x i ,v i ) and g(x i ,v i ) represents a known smooth function, and g(x i ,v i ) is not equal to zero, Δ(x i ,v i ) represents the system model uncertainty, d i (t) represents the external disturbance of the system model;

[0109] Mathematical Model of Leaders

[0110]

[0111] Among them, x 0 ∈R 2 Indicates position, v 0 ∈R 2 Indicates speed, a 0 (t) represents acceleration.

[0112] In the embodiment of the present invention, the above R 2 It can be understood as a two-dimensional real number space. i represents the position of the ith follower; the above v i represents the speed of the ith follower; the above u i represents the control input of the ith follower, that is, according to the current state of the system, the motion trajectory of the ith follower can be changed by adjusting the control input.

[0113] The above function f(x i ,v i ) and g(x i ,v i) represents a known smooth function, which is used to describe the motion law or physical characteristics of the i-th follower.

[0114] The above Δ(x i ,υ i ) represents the uncertainty of the system model, which may be caused by measurement error, calculation error, etc.; the above d i (t) represents the external disturbance of the system model, such as the impact of wind on the aircraft, or the impact of other uncontrollable factors on the motion trajectory of the follower.

[0115] The above-mentioned smoothing function refers to a function used to deal with data fluctuations.

[0116] The above external disturbances refer to factors from the external environment of the system that affect the system output. External disturbances may cause changes in the system output, thereby affecting the performance and stability of the system. The above external disturbances are unpredictable and occur randomly.

[0117] The above x 0 represents the position of the leader in two-dimensional space, the above υ 0 represents the speed of the leader, the above a 0 (t) represents the acceleration of the leader. 0 (t) can describe the rate of change of the leader's velocity.

[0118] Alternatively, the networked closed-loop error agent control mechanism is formulated as follows:

[0119]

[0120] in,

[0121]

[0122] h i represents the relative position deviation between the ith follower and the leader, e xi Indicates relative position, e vi Indicates speed error.

[0123] In the embodiment of the present invention, the relative position deviation can be understood as the difference between the positions of the follower and the leader. The relative position deviation can be used to analyze group structure, identify leader individuals, study migration and diffusion behaviors, etc.

[0124] The above relative position can be understood as the relative position relationship between an object or individual and other objects or individuals in space.

[0125] The above speed error can be understood as the difference between the expected value and the actual output value of the steady-state output of the control system under the action of the input signal.

[0126] Optionally, the saturation control mechanism based on the Arctangent function is as follows:

[0127]

[0128] Among them, k is is a positive number, the formation control error and for

[0129]

[0130] h j represents the relative position deviation between the jth follower and the leader, N i represents the neighbor set of the ith follower, m ij ∈M(G) and b i0 ∈B(G), and m ij and b i0 Only 1 and 0 can be selected, M(G) represents the adjacency matrix of the directed graph, and B(G) represents the diagonal matrix.

[0131] In the embodiment of the present invention, the above k is As a positive constant, it can be understood as k is is a constant greater than zero. In control theory and mathematical models, k is Used to adjust the behavior of the model, because k is is a constant, so its size directly affects the overall scale of the model. is is a positive constant, then no matter what value k takes, k is This helps to ensure the stability and consistency of the model.

[0132] The above formation control error can be understood as the relative position deviation between the follower agent and the leader agent, that is, the distance or angle difference between them.

[0133] In a multi-agent system, each agent has a neighbor set, which represents other agents that are directly connected to it.

[0134] The Arctangent function is also called the inverse tangent function, which is a trigonometric function. The inverse tangent function takes an angle as input and returns the tangent of the angle.

[0135] The purpose of the above saturation control mechanism is to enable multiple agents to adapt to different flight environments and mission requirements while maintaining formation. is The value of can balance the sensitivity and anti-saturation ability of the control strategy, thereby improving the stability and performance of the entire group.

[0136] In the embodiment of the present invention, the above 1 represents yes, and the above 0 represents no.

[0137] The above M(G) represents the adjacency matrix of the directed graph, and B(G) represents the diagonal matrix, which is used to describe whether there is a dependency relationship between followers and leaders.

[0138] The above directed graph is used to describe the directional relationship between objects. In a directed graph, each node represents an object, and each edge represents the directional relationship between two objects.

[0139] The adjacency matrix of the directed graph mentioned above is a method of using a matrix to represent the structural features of a directed graph. A matrix can be used to describe the connection between each pair of nodes in a directed graph. Specifically, assuming that a directed graph has n nodes, the adjacency matrix A of the directed graph is an n×n square matrix, where A[i][j] indicates that there is an edge from node i to node j. If there is no edge from node i to node j, then A[i][j] = 0; if there is a directed edge from node i to node j, then A[i][j] = 1.

[0140] The above diagonal matrix can be understood as a square matrix where all elements except the main diagonal are 0. Assume that the directed graph contains 3 nodes: A, B, and C. If there is a directed edge from node A to node B, and there is no other path from node A to node B, then the out-degree of A is 1 and the in-degree of B is 1. Therefore, a 3×3 diagonal matrix can be constructed as follows:

[0141]

[0142] Among them, A[1][1]=1, A[2][2]=2, A[3][3]=0, and A[1][2]=0, A[2][1]=0, A[2][3]=0, A[3][2]=0, A[3][1]=0.

[0143] It can be seen that only the elements on the main diagonal of the matrix are not 0, and the elements in other positions are all 0.

[0144] Optionally, the self-learning robust control mechanism is as follows:

[0145] Robust control strategy with online learning capability

[0146]

[0147] Among them, |Δ(x i ,υ i )|≤Δ max , Δ max is a known positive constant, |d i (t)|≤d max , dmax is a known positive constant; the sliding mode control surface s ij Described as:

[0148]

[0149] ε i0 ∈R + ,ε ij ∈R + ,γ i0 ∈(0,1), and γ ij ∈(0,1), ψ(·) is the Heaviside function, defined as follows

[0150]

[0151] mean

[0152]

[0153] In an embodiment of the present invention, the above-mentioned robust control strategy with online learning performance combines online learning and robust control strategies, where online learning allows the system to continuously learn and improve from data during operation, while robust control ensures that the system can maintain good performance in the face of model uncertainty and external disturbances. The robust control strategy with online learning performance is used to solve non-matching model uncertainty and external disturbances.

[0154] The above sliding mode control surface is used to describe the state change trend and performance indicators of the system. It is a hyperplane composed of state variables. By designing a controller, the state trajectory of the system slides on the sliding mode surface, thereby achieving control of the system.

[0155] The above Heaviside function is a step function. When the input signal is greater than or equal to 0, the output is 1; when the input signal is less than 0, the output is 0. The Heaviside function is used to represent the sliding mode control surface s ij The function properties of .

[0156] Optionally, the self-learning robust control mechanism is as follows:

[0157] Adaptive control mechanism:

[0158]

[0159] Adaptive update law:

[0160]

[0161] in:

[0162]

[0163] ρ=[ρ 1 ,ρ 2 ,…,ρ n ] T , θ=[θ 1 ,θ 2 ,…,θ n ] T ;

[0164] γ ρi ∈R+,γ θi ∈R+,ε mi ∈R + and ε θi ∈R + , respectively defined as follows:

[0165]

[0166] is an effective estimate of ρ, is a valid estimate of θ, and we define and and

[0167]

[0168] In the embodiment of the present invention, the above-mentioned adaptive update law can be understood as a law for updating the state estimation value according to the current observation data. The adaptive update law enables the control system to better adapt to uncertain or changing systems by continuously updating the system state estimation value.

[0169] The above-mentioned effective estimated value refers to the value of an unknown parameter or state that can be accurately estimated on a given data set. is an effective estimate of ρ, that is, The value of ρ can be accurately estimated. Specifically, ρ is a random variable representing an unknown parameter or state, and is a function or operator of ρ, representing the estimated value calculated using the observed data of ρ. is a valid estimate of θ, that is The value of θ can be accurately estimated. Specifically, θ is a random variable representing an unknown parameter or state, and It is a function or operator of θ, representing the estimated value calculated using the observed data of θ.

[0170] Optional, fixed-time distributed formation control protocol, as follows:

[0171]

[0172] Among them, μi1 ∈R + , μ i2 ∈R + , q∈(0,1), and p∈[1,+∞).

[0173] In an embodiment of the present invention, the above-mentioned fixed-time distributed formation control protocol is used to solve the fixed-time convergence and specified geometric formation constraints, ensuring that the relative error between intelligent agents converges to a specified closed set within a fixed time.

[0174] In one embodiment, the feasibility of the present invention is verified through theoretical and simulation experiments. The present invention can ensure that all parameters of the follower closed-loop error control system converge to a specified compression region within a fixed time, thereby realizing a specified formation control problem.

[0175] In the embodiment of the present invention, the present invention establishes a robust learning control strategy for the non-matching model uncertainty and unknown external disturbance that can be obtained by the supremum, and the learning factor is regulated by the hyperbolic tangent function to avoid the control input oscillation problem introduced by the sliding mode control method, so as to ensure the smooth and continuous operation of the system; for the matching model uncertainty and unknown external disturbance, an adaptive control mechanism is constructed to give the adaptive update law of the unknown parameters; in order to characterize the limited output characteristics of the intelligent body actuator, a saturation control mechanism based on the inverse tangent function is established; for the fixed convergence time and the specified formation constraint situation, a distributed actual fixed time formation control strategy is established. The present invention can ensure that all parameters of the follower closed-loop error control system converge to the specified compression area within a fixed time, and realize the specified formation control problem. The present invention has the advantages of good scalability, strong robustness, good online learning ability and practicality, and has important theoretical value and practical engineering significance for nonlinear complex systems.

[0176] An embodiment of the present invention also provides an electronic device, including: a memory, a processor, and a computer program of a distributed adaptive fixed-time formation control method stored in the memory and executable on the processor.

[0177] The electronic device provided in the embodiment of the present invention can implement each process implemented by the distributed adaptive fixed-time formation control method in the above method embodiment, and can achieve the same beneficial effect. To avoid repetition, it will not be described here.

[0178] An embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the various processes of the distributed adaptive fixed-time formation control method provided by the embodiment of the present invention are implemented, and the same technical effect can be achieved. To avoid repetition, it will not be repeated here.

[0179] A person skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, the computer-readable storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0180] The above disclosure is only the preferred embodiment of the present invention, which certainly cannot be used to limit the scope of the present invention. Therefore, equivalent changes made according to the claims of the present invention are still within the scope of the present invention.

Claims

1. A distributed adaptive fixed-time formation control method, characterized in that ,,The distributed adaptive fixed-time formation control method comprises the following steps: Based on the leader-follower control system, a dynamic model of nonlinear intelligent agent system is constructed; Establish a networked closed-loop error agent control mechanism; Construct a saturation control mechanism based on Arctangent function; Establish autonomous learning robust control mechanism; Establish a fixed-time distributed formation control protocol; Based on the nonlinear intelligent system communication model, the networked closed-loop error intelligent agent control mechanism, the Arctangent function-based saturation control mechanism, the autonomous learning robust control mechanism and the establishment of a fixed-time distributed formation control protocol, a fixed-time distributed formation control strategy is established, and the i-th intelligent agent is controlled in formation according to the fixed-time distributed formation control strategy.

2. The distributed adaptive fixed-time formation control method according to claim 1, characterized in that: The steps of establishing a networked closed-loop error agent control mechanism include: Acquire local information of adjacent intelligent agents, wherein the local information includes position information and posture information; Performing error calculation processing on the local information of the adjacent intelligent agents to obtain local error information of the adjacent intelligent agents; A networked closed-loop error agent control mechanism is established based on the local error information of the adjacent agents.

3. The distributed adaptive fixed-time formation control method according to claim 2, characterized in that: The formulas of the dynamic model of the nonlinear agent system are as follows: Mathematical model of the i-th follower Among them, x i ∈R 2 Indicates position, v i ∈R 2 Indicates speed, u i ∈R 2 represents the control input, f(x i ,v i ) and g(x i ,v i ) represents a known smooth function, and g(x i ,υ i ) is not equal to zero, Δ(x i ,v i ) represents the system model uncertainty, d i (t) represents the external disturbance of the system model; Mathematical Model of Leaders Where x0∈R 2 represents the position, υ0∈R 2 represents velocity and a0(t) represents acceleration.

4. The distributed adaptive fixed-time formation control method according to claim 3, characterized in that: The formula of the networked closed-loop error agent control mechanism is as follows: in, h i represents the relative position deviation between the ith follower and the leader, e xi Indicates relative position, e υi They represent the speed errors respectively.

5. The distributed adaptive fixed-time formation control method according to claim 4, characterized in that: The saturation control mechanism based on Arctangent function is as follows: Among them, k is is a positive number, the formation control error and for h j represents the relative position deviation between the jth follower and the leader, N i represents the neighbor set of the ith follower, m ij ∈M(G) and b i0 ∈B(G), and m ij and b i0 Only 1 and 0 can be selected, M(G) represents the adjacency matrix of the directed graph, and B(G) represents the diagonal matrix.

6. The distributed adaptive fixed-time formation control method according to claim 5, characterized in that: The autonomous learning robust control mechanism is as follows: Robust control strategy with online learning capability Among them, |Δ(x i ,v i )|≤Δ max , Δ max is a known positive constant; |d i (t)|≤d max , d max is a known positive constant; the sliding mode control surface s ij Described as: ε i0 ∈R + , ε ij ∈R + , γ i0 ∈(0,1), and γ ij ∈(0,1), ψ(·) is the Heaviside function, defined as follows mean 7. The distributed adaptive fixed-time formation control method according to claim 6, characterized in that: The autonomous learning robust control mechanism is as follows: Adaptive control mechanism: Adaptive update law: in: p=[p1,p2,…,p n ] T ,θ=[θ1,θ2,…,θ n ] T ; γ ρi ∈R+,γ θi ∈R+,ε mi ∈R + and ε θi ∈R + , respectively defined as follows: is an effective estimate of ρ, is a valid estimate of θ, and we define and and 8. The distributed adaptive fixed-time formation control method according to claim 7, characterized in that: The fixed-time distributed formation control protocol is as follows: Among them, μ i1 ∈R + , μ i2 ∈R + , q∈(0,1), and p∈[1,+∞).

Images