Predefined time consistency control method of random pure feedback multi-agent system under time-varying constraint

Abstract

The invention relates to a predefined time consistency control method of a random pure feedback multi-agent system under time-varying constraint, and belongs to the technical field of control engineering. The control method comprises the following steps: S1, determining a random pure feedback multi-agent system and designing an error variable under multi-agent consistency control; s2, designing a proper fuzzy logic system, and performing accurate estimation and compensation on unknown nonlinear terms in the system; s3, selecting a proper obstacle Lyapunov function, and judging a condition which needs to be met when the practical predefined time is stable; s4, based on the steps S1, S2 and S3, controller design is carried out in combination with a backstepping method, a barrier Lyapunov function and a fuzzy control technology; and S5, carrying out stability analysis to prove that the system meets predefined time stability conditions. According to the method, the backstepping method can be effectively popularized to a random nonlinear multi-agent system with asymmetric time-varying full-state constraints, a pure feedback structure and unknown nonlinear terms, and the method has the advantages of being high in control precision and high in response speed.

Description

Technical Field

[0001] The present invention relates to a predefined time consistency control method for a random pure feedback multi-agent system under time-varying constraints, and belongs to the field of control engineering technology. Background Art

[0002] With the rapid development of modern industrial technology, the control problem of random nonlinear systems has become increasingly important in engineering practice. Such systems are widely present in fields such as robotic control, aerospace, power systems, and intelligent transportation. Their dynamic characteristics usually have a high degree of uncertainty, randomness, and complex nonlinear behavior. The control of random nonlinear systems not only needs to consider the nonlinear characteristics of the system itself, but also needs to deal with external random disturbances, parameter uncertainties, and various constraints (such as state constraints, input and output dead zones, etc.). These factors make traditional control methods difficult to apply directly, especially in scenarios that require high-precision tracking, fast convergence, and stability. Therefore, how to design effective control strategies to solve these problems has become a hot topic and difficulty in control theory research and engineering applications.

[0003] State constraints are a common challenge in the control of random nonlinear systems. State constraints mean that the system's state variables (such as position, velocity, temperature, etc.) must operate within a specific range to avoid system failure or damage. For example, in robotic control, the joint angles and angular velocities of the manipulator must be limited to a safe range; in the aerospace field, the attitude and velocity of the aircraft must meet strict constraints. Traditional control methods often have difficulty directly handling these constraints, especially when there are random disturbances and unknown nonlinear terms in the system. These nonlinear characteristics can seriously affect the control performance of the system, especially in scenarios that require high-precision tracking.

[0004] With the development of the times, people's demands for system control efficiency are becoming increasingly stringent. Many practical applications are no longer satisfied with asymptotic convergence and stability, but instead place higher demands on the system's convergence speed. Therefore, finite-time control, fixed-time control, and preset-time control have emerged, each with significant theoretical research significance and practical application value. Compared to finite-time control, preset-time control has a convergence time that is independent of the system's initial state, offering faster convergence speed and improved interference resistance, meeting the performance requirements of most control systems. Predefined-time control, in particular, can achieve system stability within any predefined time, making it applicable to a wide range of complex systems.

[0005] To address the uncertainties and constraints in random nonlinear systems, fuzzy logic systems and adaptive control methods are widely used in the design of control strategies. Fuzzy logic systems, through fuzzy rules and fuzzy reasoning, can effectively approximate unknown nonlinear terms in the system and handle system uncertainties. Adaptive control, by adjusting controller parameters online, can dynamically adapt to system changes while ensuring system stability and performance. Combining fuzzy logic systems with adaptive control can further improve the robustness and adaptability of the controller, especially in situations where the system is subject to unknown parameters, nonlinear terms, and external disturbances.

[0006] With the continuous maturity of single-system control theory, the study of control problems has gradually expanded from single systems to multi-agent systems. Multi-agent systems are composed of multiple interacting agents, each of which may have different dynamic characteristics and complex coupling relationships. Compared with single systems, the control problem of multi-agent systems is more complex, especially when the system has time-varying state constraints, pure feedback structures, and unknown nonlinear terms. Time-varying state constraints mean that the system's state constraints not only exist but also change over time; pure feedback structures mean that the system's output cannot be directly used for feedback control, further increasing the difficulty of controller design. Therefore, designing a control strategy that can ensure the consistency of multi-agent systems under time-varying state constraints and pure feedback structures is of great theoretical and practical significance. Summary of the invention

[0007] Technical issues:

[0008] The primary technical problem addressed by this invention is how to use adaptive techniques to design input signals and adaptive laws for a class of stochastic, purely feedback multi-agent systems while satisfying time-varying state constraints. Notably, the backstepping method employed in this invention not only considers the case where the system is purely feedback-based rather than strictly feedback-based, but also considers how to ensure the system's stability over a predefined timeframe.

[0009] Technical solution:

[0010] In order to solve the above technical problems, the present invention provides a predefined time consistency control method for a random pure feedback multi-agent system under time-varying constraints.

[0011] The specific plan is as follows:

[0012] A fast finite-time control method for a non-strict feedback system under quantized input conditions, the method comprising the following steps:

[0013] S1, determine the mathematical model of a random pure feedback multi-agent system under time-varying constraints and design the error variables under the multi-agent consensus control;

[0014] S2, design a fuzzy logic system to accurately estimate and compensate for unknown nonlinear terms in a random pure feedback multi-agent system;

[0015] S3, select the barrier Lyapunov function and determine the conditions that need to be met to achieve stability for a practical predefined time;

[0016] S4, based on steps S1, S2 and S3, controller design is performed by combining backstepping method, barrier Lyapunov function and fuzzy control technology;

[0017] S5, Stability Analysis, proves that the random pure feedback multi-agent system under time-varying constraints satisfies the predefined time stability conditions.

[0018] Furthermore, step S1 includes the following contents:

[0019] (1) For a type of robot manipulator system, under the condition of considering random noise, the dynamic model obtained is:

[0020]

[0021] where x i,1 and x i,2 Represent position and velocity respectively, t represents time variable, ω represents random disturbance, J represents the mass of the object, g represents gravitational acceleration, l represents distance, u represents the control input of the robot manipulator, and D represents the damping coefficient;

[0022] (2) In order to achieve the consistency control problem under multi-agent, consider a leader agent (generating a reference signal y d ) and N follower agents (need to track the leader's state). The error variables of each subsystem of the random pure feedback multi-agent system are designed as:

[0023]

[0024] From a i,j represents the signal edge weight from the i-th system to the j-th system. If the i-th follower obtains the leader's information, then b i >0; otherwise, b i =0;y i and y j Represent the output states of the i-th and j-th followers respectively.

[0025] Furthermore, the step S2 specifically includes the following contents:

[0026] The fuzzy logic system's ability to approximate unknown functions is used to process and control the nonlinear terms in the random pure feedback multi-agent system. The Gaussian function is selected as the basis function of the fuzzy logic system:

[0027]

[0028] where χ is the basis vector, c j is the center of the receptive field, and w j is the width of the basis function;

[0029] Furthermore, the step S3 specifically includes the following content:

[0030] (1) Considering the existence of time-varying state constraints in the stochastic pure-feedback multi-agent system, it is necessary to design a barrier Lyapunov function to limit the states of the stochastic pure-feedback multi-agent system. The form adopted here is:

[0031]

[0032] where z i,1 = x i,1 - y d , is the estimate of θ i,1 , θ i,1 represents the adaptive parameter, γ i,1 is a positive constant used to adjust the weight of the error term in the Lyapunov function;. L1 and H1 are the time-varying bounds of the states, defined as L1 = y d + H1 and

[0033] After obtaining the virtual controller, it is necessary to constrain the controller to meet the constraint conditions, and the specific form is shown in formula (1.5)

[0034]

[0035] where α represents the virtual controller before constraint;

[0036] For an n-order system, the final Lyapunov function is shown in formula (1.6):

[0037]

[0038] where V i,j represents the local Lyapunov function of the i-th agent in the j-th order subsystem;

[0039] (2) Considering a general stochastic nonlinear system If there exists a positive definite and continuous function V(x) such that

[0040] 1. Satisfies

[0041]

[0042] 2. There exists max‖x‖ p = ∈, satisfying

[0043]

[0044] where 0 < k2 < 1, k4 > 1, ε > 1, η > 0, k5 > 0, then the stochastic nonlinear system is predefined-time stable and satisfies where T(x0) represents the time when the stochastic nonlinear system first converges to the desired output. The differential operator is defined as

[0045] Furthermore, the step S4 specifically includes the following content:

[0046] (1) For N n-order stochastic nonlinear systems of a class of stochastic pure-feedback type, use the backstepping method to design the control law and the adaptation law, and obtain the general model of the stochastic pure-feedback multi-agent system:

[0047]

[0048] where k = 1, 2,..., n - 1, i = 1, 2,..., N, is the state vector of the stochastic pure-feedback multi-agent system. ω is a standard Wiener process. The drift term f i,k (·) and the diffusion term ψ i,k (·) are both assumed to be unknown smooth functions. y i and u i respectively represent the output and input of the i-th subsystem.

[0049] Considering the mutual influence among agents, when designing the controller, first complete the first step in the backstepping method, then complete the remaining n - 2 steps, and finally complete the design of the n-th step;

[0050] (2) Design of the virtual control law and the adaptation law, the first step

[0051] For the general model (1.9) discussed in this method, considering the fuzzy logic system involved in step S2 and the stability conditions involved in step S3, design the virtual control law and the adaptation law;

[0052] By using the mean value theorem, the original general model (1.9) can be rewritten as:

[0053]

[0054] Processing the non - linear term using the fuzzy logic system, we can obtain:

[0055]

[0056] where Further calculation can obtain:

[0057]

[0058] The virtual controller α i,1 and the adaptation rate are:

[0059]

[0060] where the parameters respectively satisfy b i,1 > 0, γ i,1 > 0, g i,1 > 0.

[0061] (3) Design of the virtual control rate and the adaptation rate, at the k - th step

[0062] After constructing the barrier Lyapunov function, calculate

[0063]

[0064] The virtual controller and the adaptation rate are:

[0065]

[0066]

[0067] where the parameters respectively satisfy bi, k > 0, γ i,k > 0, g i,k > 0.

[0068] (4) Design of the actual control rate and the adaptation rate, at the n - th step

[0069] After performing the corresponding calculations, the actual controller u i and the adaptation law are

[0070]

[0071] Furthermore, the step S5 specifically includes the following content:

[0072] According to step S3 and combined with step S4, we can calculate and obtain:

[0073]

[0074] where It can be obtained that all states in the random pure feedback multi-agent system under the time-varying constraint are semi-globally uniformly bounded, and the tracking error is driven to a small neighborhood of the preset time T, satisfying ET≤k i,5 .

[0075] Beneficial effects:

[0076] The research object of the present invention is a type of random nonlinear multi-agent system with asymmetric time-varying full-state constraints, pure feedback structure and unknown nonlinear terms. This type of system can describe the actual application system more specifically. The present invention introduces a new type of asymmetric time-varying barrier Lyapunov function to effectively deal with time-varying state constraints. Secondly, the fuzzy logic system is used to accurately estimate the uncertainty in the system. On this basis, the present invention provides a practical preset time consistency control method, which makes the adjustment time of the system arbitrarily adjustable in the mean sense, thereby achieving preset time stability. The method is concise in form, easy to implement, and insensitive to parameter changes. The present invention can ensure that all followers in the system successfully track the output signal of the leader. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the technical solution of the present invention and the effects achieved in the implementation examples, the technical solution and implementation examples of the present invention will be introduced in the form of drawings below. Figure 2 and Figure 3 All results are obtained on system (2.1); Figures 4 - 7 The results obtained on the system (2.2) are shown in the following figures:

[0078] Figure 1 It is a system structure diagram of the present invention;

[0079] Figure 2 The output effect diagram of system (2.1)

[0080] Figure 3 is the tracking error of system (2.1);

[0081] Figure 4 This is the output effect diagram of system (2.2);

[0082] Figure 5 is the trajectory of the state x2 of the system (2.2);

[0083] Figure 6 is the adaptive law θ of system (2.2) i，1 and θ i，2 The change of θ i，1 The following figure shows the change of θ i，2 changes in

[0084] Figure 7 The image of the controller u of the system (2.2). Detailed implementation manners

[0085] In order to more clearly illustrate the technical solutions in the present invention, the following content is described in combination with the attached Figure 1 The present invention is described. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention. Based on the embodiments in the present invention, other cases obtained by other persons without creative labor belong to the scope protected by the present invention.

[0086] According to Figure 1 , the predefined-time consensus control method for a stochastic pure-feedback multi-agent system with time-varying constraints proposed by the present invention mainly includes the following steps:

[0087] S1. Determine the mathematical model of a class of stochastic pure-feedback multi-agent systems with time-varying constraints and design the error variables under multi-agent consensus control;

[0088] S2. Design a fuzzy logic system to accurately estimate and compensate the unknown non-linear terms in the stochastic pure-feedback multi-agent system;

[0089] S3. Select a barrier Lyapunov function and judge the conditions that need to be satisfied to achieve practical predefined-time stability;

[0090] S4. Based on steps S1, S2 and S3, combine the backstepping method, the barrier Lyapunov function and the fuzzy control technology to design the controller;

[0091] S5. Stability analysis is carried out to prove that the stochastic pure-feedback multi-agent system with time-varying constraints satisfies the predefined-time stability conditions.

[0092] Specifically, the step S1 includes the following content:

[0093] (1) For a class of stochastic pure-feedback multi-agent systems with time-varying constraints, the model is selected as

[0094]

[0095] Where

[0096] For a class of robot manipulator systems, under the condition of considering random noise, the obtained dynamic model is:

[0097]

[0098] Where x i,1 and x i,2Represent position and velocity respectively; t represents time variable, ω represents random disturbance, J represents the mass of the object, g represents gravitational acceleration, l represents distance, u represents the control input of the robot manipulator, and D represents the damping coefficient;

[0099] (2) In order to achieve the consistency control problem under multi-agent, consider a leader agent (generating a reference signal y d ) and N follower agents (need to track the leader's state). The error variables of each subsystem of the random pure feedback multi-agent system are designed to be

[0100]

[0101] From a i,j represents the signal edge weight from the i-th subsystem to the j-th subsystem; if the i-th follower obtains the leader's information, then b i >0; otherwise, b i =0;y i and y j Respectively represent the output states of the i-th and j-th followers. Specifically, the step S2 specifically includes the following contents:

[0102] The fuzzy logic system's ability to approximate unknown functions is used to handle nonlinear terms in random pure feedback multi-agent systems, and the Gaussian function is selected as the basis function of the fuzzy logic system:

[0103]

[0104] Where χ is the basis vector, c j is the center of the receptive field, w j is the width of the basis function;

[0105] Specifically, step S3 includes the following contents:

[0106] (1) Considering the existence of time-varying state constraints in the random pure feedback multi-agent system, it is necessary to design a barrier Lyapunov function to restrict the state of the random pure feedback multi-agent system. The form used here is:

[0107]

[0108] in z i,1 =x i,1 -y d , is θ i,1 The estimated value of θ i,1 represents the adaptive parameter, γ i,1is a positive constant used to adjust the weight of the error term in the Lyapunov function; L1 and H1 are time-varying bounds of the states, defined as L1 = y d + H1 and

[0109] After obtaining the virtual controller, it is necessary to impose constraints on the controller to satisfy the constraint conditions, and the specific form is shown in Equation (2.6)

[0110]

[0111] where α represents the virtual controller before constraint;

[0112] For an nth-order stochastic nonlinear system, the final Lyapunov function is obtained as shown in Equation (2.7):

[0113]

[0114] where V i,j represents the local Lyapunov function of the ith agent in the jth-order subsystem;

[0115] (2) Consider a general stochastic nonlinear system If there exists a positive definite and continuous function V(x) such that

[0116] 1. Satisfy

[0117]

[0118] 2. There exists max‖x‖ p = ∈, satisfying

[0119]

[0120] where 0 < k2 < 1, k4 > 1, ε > 1, η > 0, k5 > 0, then the stochastic nonlinear system is actually pre-defined time stable and satisfies where T(x0) represents the time when the stochastic nonlinear system first converges to the desired output. The differential operator is defined as

[0121] Specifically, the step S4 specifically includes the following contents:

[0122] (1) For N nth-order stochastic nonlinear systems of a class of stochastic pure-feedback type, use the backstepping method to design the control law and the adaptation law to obtain the general model of the stochastic pure-feedback multi-agent system:

[0123]

[0124] where \(k = 1, 2, \ldots, n - 1\), \(i = 1, 2, \ldots, N\). The state vector of the stochastic pure-feedback multi-agent system. \(\omega\) is a standard Wiener process. The drift term \(f\) i,k (·) and the diffusion term \(\psi\) i,k (·) are both assumed to be unknown smooth functions. \(y\) i and \(u\) i represent the output and input of the \(i\)-th subsystem, respectively.

[0125] Considering the mutual influence among agents, in the design of the controller, the first step in the backstepping method is completed first, and then the remaining \(n - 2\) steps are completed, and finally the design of the \(n\)-th step is completed.

[0126] (2) Design of the virtual control law and the adaptation law. The first step:

[0127] For the general model (2.10) discussed in this method, considering the fuzzy system involved in step S2 and the stability criterion involved in step S3, design the virtual control law and the adaptation law.

[0128] By using the mean value theorem, the unknown smooth function can be expressed as:

[0129]

[0130] where and \(0 < \alpha < 1\).

[0131] The original general model (2.10) is rewritten as:

[0132]

[0133] According to the design process of the backstepping method, through calculation, we get:

[0134]

[0135] After further calculation, we get

[0136]

[0137] where

[0138] Using the fuzzy logic system to handle the nonlinear term, we can get:

[0139]

[0140] where Further calculations yield:

[0141]

[0142] Virtual Controller α i,1 and adaptive rate for:

[0143]

[0144] Its parameters satisfy b i,1 >0,γ i,1 >0,g i,1 >0.

[0145] (3) Design of virtual control rate and adaptive rate, step k:

[0146] Using an operation similar to the first step, after constructing the barrier Lyapunov function, calculate

[0147] It is worth noting that at step k, It has the following forms:

[0148]

[0149] Further calculations yield

[0150]

[0151] The virtual controller and the adaptive rate are:

[0152]

[0153]

[0154] The parameters satisfy b i,k >0,γ i,k >0,g i,k >0.

[0155] (4) Design of actual control rate and adaptive rate, step n:

[0156] After constructing the barrier Lyapunov function, calculate

[0157]

[0158] in

[0159] Actual controller u i and adaptive law for

[0160]

[0161] Specifically, step S5 includes the following contents:

[0162] According to the content involved in step S3 of claim 1, combined with the content of step S4 of claim 1, it can be calculated that:

[0163]

[0164] in It can be obtained that all states in the random pure feedback multi-agent system are semi-globally uniformly bounded (SGUUB), and the tracking error is driven to a small neighborhood of the preset time T, satisfying ET≤k i,5 .

[0165] Simulation experiment:

[0166] In order to verify the effectiveness of the control scheme proposed in this paper, simulation experiments are carried out for systems (2.1) and (2.2). The simulation experiment mainly consists of two parts. The number of agents is set to 5, and their adjacency matrix is set to:

[0167]

[0168] 1. Numerical experiments.

[0169] For system (2.1), the controller and adaptive rate are designed according to formulas (2.20) and (2.22) in the present invention and the predefined time control method, and the simulation results are compared. The system controller parameters are set to k 1,1 =50,k 2,1 =55,k 3,1 =60,k 4,1 =60,k 5,1 =50,k i,2 =7 / 9,k i,3 =0.67,k i,4 =29 / 11,k i,5 =2,γ i,1 =5,γ i,2 =3,τ i,1 =0.5,τ i,2 =0.01,g i,1 0.01,g i,2 =1,ε=1.1,a i,1 =2,a i,2 =2,b i,1 =3,b i,2=1.5. Where i = [1,2,…,5]. The initial value of the system adaptive law is set to zero. The initial value of the system is set to x1(0) = [0.1,0.3,0.4,0.2,0.3] T ,x2(0)=[0,0,0,0,0] T The expected output of the system is y r =0.2sin(t)+0.2sin(0.5t). The state constraint of the system is -0.65+0.1sin(2t) <x i,1 <0.6+0.1sin(2t),-0.5-0.1sin(2t) <x i,2 <0.5+0.1sin(2t). The experimental results are as follows Figure 2 and Figure 3 shown.

[0170] 2. Actual case implementation.

[0171] For system (2.2), the control rate and adaptive rate are designed according to the method of the present invention, and the system controller parameters are set to k 1,1 =30,k 2,1 =40,k 3,1 =40,k 4,1 =35,k 5,1 =35,k i,2 =0.6,k i,3 =0.55,k i,4 =3,k i,5 =

[0172] 1, J = 1, D = 1, M = 0.3, l = 0.3. Other parameters are the same as those in the numerical experiment. Then the system state constraint is selected as -1.5 + 0.1sin (0.5t) <x i,1 <1.2+0.1sin(0.5t),-0.9 <x i,2 <0.9. The experimental results are as follows Figures 4 - 7 shown.

[0173] The present invention not only solves the consistency control problem of random pure feedback multi-agents under the condition of asymmetric time-varying state constraints, but also realizes arbitrary adjustment of the system adjustment time in the mean sense, thereby achieving predefined time stability.

[0174] The above is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited to this. Any other changes or replacements that do not add substantial innovation should be included in the scope of protection of the present invention. Therefore, the specific scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A predefined-time consensus control method for stochastic pure-feedback multi-agent systems with time-varying constraints, characterized in that, It includes the following steps: S1. Determine the mathematical model of a class of stochastic pure-feedback multi-agent systems under time-varying constraints and design the error variables under multi-agent consensus control; S2. Design a fuzzy logic system to accurately estimate and compensate the unknown non-linear terms in the stochastic pure-feedback multi-agent system; S3. Select a barrier Lyapunov function and determine the conditions that need to be satisfied to achieve practical predefined-time stability; S4. Based on steps S1, S2, and S3, combine the backstepping method, barrier Lyapunov function, and fuzzy control technology to design the controller; S5. Conduct stability analysis to prove that the stochastic pure-feedback multi-agent system satisfies the predefined-time stability conditions.

2. According to the predefined-time consensus control method for the stochastic pure-feedback multi-agent system under time-varying constraints described in claim 1, the step S1 includes the following content: (1) For a class of robot manipulator systems, considering random noise, the obtained dynamic model is: where x i,1 and x i,2 represent position and velocity respectively; t represents the time variable, ω represents the random perturbation, J represents the mass of the object, g represents the acceleration due to gravity, l represents the distance, u represents the control input of the robotic arm, and D represents the damping coefficient; (2) To achieve the consensus control problem under multi-agent systems, consider a network consisting of one leader agent and N follower agents, where the leader agent generates a reference signal y d , and the follower agents need to track the leader's state; design the error variables of each subsystem of the stochastic pure-feedback multi-agent system as where a i,j represents the signal edge weight from the i-th subsystem to the j-th subsystem; if the i-th follower obtains the information of the leader, then b i > 0; otherwise, b i = 0; y i and y j represent the output states of the i-th and j-th followers respectively.

3. According to the predefined-time consensus control method for the stochastic pure-feedback multi-agent system under time-varying constraints described in claim 2, the step S2 includes the following content: Use the approximation ability of the fuzzy logic system to handle the non-linear terms in the stochastic pure-feedback multi-agent system, and select the Gaussian function as the basis function of the fuzzy logic system: where χ is the basis vector, c j is the center of the receptive field, and w j is the width of the basis function.

4. According to the predefined-time consensus control method for the stochastic pure-feedback multi-agent system under time-varying constraints described in claim 3, the step S3 includes the following content: (1) Considering the existence of time-varying state constraints in the stochastic pure-feedback multi-agent system, design a barrier Lyapunov function to limit the states of the stochastic pure-feedback multi-agent system; the form adopted here is: where z i,1 = x i,1 - y d , is the estimated value of θ i,1 , and θ i,1 represents the adaptive parameter, γ i,1 is a positive constant used to adjust the weight of the error term in the Lyapunov function; L1 and H1 are time-varying bounds of the state, defined as L1 = y d + H1 and After obtaining the virtual controller, it is necessary to impose constraints on the controller to meet the constraint conditions, and the specific form is shown in formula (5) where α represents the virtual controller before constraint; For an n-order stochastic non-linear system, the final Lyapunov function is shown in formula (6): where V i,j represents the local Lyapunov function of the i-th agent in the j-th order subsystem; (2) Consider a general stochastic nonlinear system If there exists a positive definite and continuous function V(z) such that 1. Meet 2. There exists max‖x‖ p = ∈, satisfying Among them Then the stochastic nonlinear system is predefined-time stable and satisfies where \(T(x_0)\) represents the time when the stochastic nonlinear system first converges to the desired output, and the differential operator is defined as 5. The predefined-time consensus control method for a stochastic pure-feedback multi-agent system with time-varying constraints according to claim 4, characterized in that, The processing methods included in the step S4 when designing the control law and adaptation rate are as follows: (1) For a class of N n-order stochastic non-linear systems of the stochastic pure-feedback type, use the backstepping method to design the control law and adaptation rate to obtain the general model of the stochastic pure-feedback multi-agent system: where \(k = 1,2,\cdots,n - 1\), \(i = 1,2,\cdots,N\), is the state vector of the stochastic pure-feedback multi-agent system; \(\omega\) is a standard Wiener process; the drift term \(f\) i,k (·) and the diffusion term \(\psi\) i,k (·) are both assumed to be unknown smooth functions; \(y\) i and \(u\) i represent the output and input of the \(i\)-th subsystem, respectively; Considering the mutual influence among agents, when designing the controller, first complete the first step in the backstepping method, then complete the remaining n - 2 steps, and finally complete the design of the nth step; (2) Design of the virtual control law and adaptation rate, the first step: For the general model (9), considering the fuzzy logic system involved in step S2 and the stability conditions involved in step S3, design the virtual control law and adaptation rate; By using the mean value theorem, the original general model (9) can be rewritten as: Using the fuzzy logic system to handle the non-linear terms, we can obtain: Among them Further calculation can obtain: Virtual controller α i,1 and adaptation rate are as follows: where the parameters are respectively b i,1 > 0, γ i,1 > 0, g i,1 > 0; (3) Design of the virtual control law and adaptation rate, the kth step: After constructing the barrier Lyapunov function, calculate The virtual controller and adaptation rate are: Among them, the parameters respectively satisfy b i,k > 0, γ i,k > 0, g i,k > 0; (4) Design of the actual control law and adaptation rate, the nth step After performing the corresponding calculations, the actual controller u i and the adaptation law are 6. The predefined-time consensus control method for the stochastic pure-feedback multi-agent system with time-varying constraints according to claim 5, wherein the step S5 includes the following content: According to step S3 and combined with step S4, it can be calculated that: Among them it can be obtained that all states in the stochastic pure-feedback multi-agent system under time-varying constraints are semi-globally uniformly bounded, and the tracking error is driven into a small neighborhood at the preset time T, satisfying ET ≤ k i,5 .

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