Multi-unmanned vehicle fixed time and scheduled time distributed optimization method and system

Abstract

This invention discloses a distributed optimization method and system for multiple unmanned vehicles at fixed and predetermined times. The method includes: establishing a dynamic model and communication topology diagram of the multiple unmanned vehicle system; constructing a global objective function; designing centralized optimization algorithms for fixed and predetermined times based on the communication topology diagram and the global objective function; designing distributed gradient estimators for fixed and predetermined times; designing gradient-based distributed optimization algorithms for fixed and predetermined times based on the distributed gradient estimators and the centralized optimization algorithms; and using the gradient-based distributed optimization algorithms to control the multiple unmanned vehicles, thereby obtaining the optimal solution of the global objective function. This invention ensures that the state of the multiple unmanned vehicle system reaches the optimal solution of the global objective function within a fixed or predetermined time period.

Description

Technical Field

[0001] This invention relates to the field of unmanned vehicles, specifically to a distributed optimization method and system for multiple unmanned vehicles at fixed and predetermined times. Background Technology

[0002] Multi-agent systems are an important research direction in the field of artificial intelligence. The agents comprising these systems possess autonomy, sociality, responsiveness, and proactiveness, enabling them to perceive their environment, make decisions, and execute actions. In multi-agent systems, each agent can utilize limited local information to collaboratively complete tasks through communication and cooperation. This unique advantage, coupled with the development of computer network technology, has sparked a surge of research into the cooperative control of multi-agent systems. Distributed optimization problems, as one of the key issues in the cooperative control of multi-agent systems, have wide applications in resource allocation, source localization in sensor networks, and other fields. By cleverly decomposing complex global optimization problems into multiple sub-problems handled by different agents, distributed optimization algorithms can significantly reduce problem complexity, improve solution efficiency, and make the entire system more flexible and scalable. Multi-unmanned vehicle systems, as a typical application example of multi-agent systems, have demonstrated enormous potential and value in recent years in various fields such as logistics distribution, intelligent transportation, and agricultural operations. In unmanned vehicle systems, distributed optimization algorithms can be applied to problems such as collaborative operation and resource allocation among multiple unmanned vehicles. Each unmanned vehicle has a local objective function, and the global objective function to be optimized is the sum of all local objective functions. The goal of distributed optimization is to converge the state of each autonomous vehicle to the optimal point of the system's global objective function through local information exchange, with only the local objective functions of neighboring autonomous vehicles known.

[0003] In existing centralized optimization algorithms, the central node needs to process a large amount of data, which increases the network's operational burden and leads to poor scalability and weak anti-interference capabilities. Distributed optimization algorithms have significant advantages in reducing network communication burden and improving the system's robustness to node failures. However, the objective function in optimization problems is often a global function, making it challenging to design distributed optimization algorithms without using global information. Furthermore, most existing distributed optimization algorithms can only solve optimization problems in infinite time, theoretically reaching only suboptimal solutions. In practical applications, it is often necessary to bring the autonomous vehicle's state towards the optimal point of the global objective function within a finite time. Although finite-time distributed optimization algorithms have solved the problem of infinite convergence time to some extent, they require the initial state of the autonomous vehicle when estimating the convergence time, and different initial states correspond to different convergence times, undoubtedly increasing the system's computational burden. More importantly, this method cannot pre-set the system's solution time according to actual needs. In addition, the design of most existing distributed optimization algorithms includes many adjustable parameters and requires the autonomous vehicle's local objective function to be convex or strongly convex, which limits the applicability of these algorithms. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention aims to provide a distributed optimization method and system for multiple unmanned vehicles at fixed or predetermined times. Under conditions of unknown initial state and non-convex local objective function, this method ensures that the state of the multiple unmanned vehicle system reaches the optimal solution of the global objective function within a fixed or predetermined time.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A distributed optimization method for multiple unmanned vehicles at fixed and scheduled times includes:

[0007] Establish a dynamic model and communication topology diagram for a multi-unmanned vehicle system;

[0008] Based on the dynamic model, a global objective function is constructed;

[0009] Based on the communication topology graph and the global objective function, centralized optimization algorithms with fixed time and predetermined time are designed respectively;

[0010] Design distributed gradient estimators for fixed time and predetermined time respectively;

[0011] Based on distributed gradient estimators and centralized optimization algorithms, fixed-time and predetermined-time distributed optimization algorithms based on gradient estimation are designed respectively.

[0012] A distributed optimization algorithm based on gradient estimation with fixed and predetermined times is used to control multiple unmanned vehicles and obtain the optimal solution of the global objective function.

[0013] A distributed optimization system for multiple unmanned vehicles with fixed and scheduled times includes:

[0014] The model building unit is used to establish the dynamic model and communication topology of a multi-unmanned vehicle system.

[0015] The global objective function construction unit constructs the global objective function based on the dynamic model;

[0016] The centralized optimization algorithm design unit designs centralized optimization algorithms for fixed time and predetermined time based on the communication topology graph and the global objective function.

[0017] A distributed gradient estimator design unit is used to design fixed-time and predetermined-time distributed gradient estimators.

[0018] The distributed optimization algorithm design unit designs fixed-time and predetermined-time distributed optimization algorithms based on gradient estimation, respectively, based on distributed gradient estimators and centralized optimization algorithms.

[0019] The control unit uses a fixed-time and predetermined-time distributed optimization algorithm based on gradient estimation to control multiple unmanned vehicles and obtain the optimal solution of the global objective function.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0021] (1) This patented technology designs a fixed-time and predetermined-time distributed optimization method based on a distributed gradient estimator. The distributed gradient estimator can be used to estimate the required global objective function gradient information within a fixed time or a predetermined time. The resulting distributed optimization method is suitable for large-scale systems and has advantages such as privacy protection, robustness to node failures, and strong scalability.

[0022] (2) The proposed distributed optimization method solves the optimization problem of multi-unmanned vehicle system under arbitrary initial state and non-convex local objective function; the method removes the restriction that the local objective function of the system is a convex function or a strongly convex function, and does not require prior knowledge of the initial state of the unmanned vehicle, and its application range is wider.

[0023] (3) Under the fixed-time optimization algorithm, the time estimate for the system to solve the optimization problem is given, which does not depend on the initial state of the system; under the predetermined-time optimization algorithm, the time for solving the optimization problem can be preset according to actual needs within the range allowed by physical conditions, and the preset time does not depend on the initial state and system parameters.

[0024] (4) Compared with existing optimization algorithms based on traditional fixed-time stability methods, the fixed-time and predetermined-time distributed optimization method based on exponential functions proposed in this patent has fewer parameters, a simpler structure, and is easier to estimate time. Attached Figure Description

[0025] Figure 1 Flowchart of a distributed optimization method for multiple unmanned vehicles with fixed and scheduled times.

[0026] Figure 2 This is a communication topology diagram between autonomous vehicles.

[0027] Figure 3 A distributed optimization algorithm for the position state (x-axis component) of each autonomous vehicle over a fixed time period is used. i The curve showing the change under the action of (t).

[0028] Figure 4 A distributed optimization algorithm for the position state (y-axis component) of each autonomous vehicle over a fixed time period is used. i The curve showing the change under the action of (t).

[0029] Figure 5 The graph shows the change curves of the position state (x-axis component) of each unmanned vehicle under the action of a distributed optimization algorithm over a predetermined time.

[0030] Figure 6 The graph shows the change curves of the position state (y-axis component) of each unmanned vehicle under the action of a distributed optimization algorithm over a predetermined time. Detailed Implementation

[0031] The current technical problem to be solved is: in a multi-autonomous vehicle system with arbitrary initial states and non-convex local objective functions, how to design a distributed fixed-time and predetermined-time optimization algorithm and apply it to the autonomous vehicles using only information from neighboring autonomous vehicles, so that the states of each autonomous vehicle converge to the optimal point of the system's global objective function, and how to estimate the upper bound of the convergence time of the distributed fixed-time optimization algorithm. Based on the proposed technical problem, this embodiment fully considers practical applications and proposes a fixed-time and predetermined-time distributed optimization method that is effective for arbitrary initial states and non-convex local objective functions. The time to solve the optimization problem is independent of the system's initial state and can be preset according to actual needs. The proposed method has advantages such as strong scalability, fast convergence speed, and wide applicability. It includes the following steps:

[0032] I. Establishing the dynamic model and communication topology of the multi-unmanned vehicle system

[0033] Consider a system consisting of N Mecanum wheel autonomous vehicles, where the dynamic model of the i-th autonomous vehicle is as follows:

[0034]

[0035] In the formula, x i1 x i2 v i1 v i2 Let θ represent the position and linear velocity of the i-th unmanned vehicle on the two-dimensional plane, respectively; i This represents the orientation angle of the i-th unmanned vehicle, which is the angle with the x-axis; Let represent the angular velocity of the i-th autonomous vehicle. Since the Mecanum wheel autonomous vehicle can achieve translational motion at any angle, the dynamic model of the i-th autonomous vehicle can be simplified to the following dynamic model:

[0036]

[0037] Let x i (t)=[x i1 ,x i2 ] T u i (t)=[v i1 ,v i2 ] T The general form of the dynamic equation of the i-th unmanned vehicle is:

[0038]

[0039] The communication topology of a multi-autonomous vehicle system is an undirected connected graph. Where ν = {ν1,…,ν} N} represents the set of autonomous vehicles, N is the number of autonomous vehicles, and ε∈ν×ν represents the set of edges; (ν i ,ν j )∈ε represents an unmanned vehicle ν i and ν j Information can be transmitted between them; A = a ij ∈R N×N Representation diagram The adjacency matrix of the autonomous vehicle ν i and ν j There is information exchange between them, namely (ν i ,ν j If )∈ε, then the element a of the adjacency matrix is... ij >0, otherwise a ij =0, assume a ii =0; For driverless cars v i Neighbor set; diagram The corresponding Laplace matrix Among them l ij =-a ij ,

[0040] II. Constructing the global objective function and describing the optimization problem

[0041] The local objective function of the i-th autonomous vehicle is f i (x i The global objective function of the system is the sum of all local objective functions, and its expression is:

[0042]

[0043] The global objective function f(x) satisfies strong convexity φ, where φ is the convex parameter of the function f(x).

[0044] The main objective of this invention is to minimize the global objective function f(x) of the system by designing a distributed optimization algorithm. The equivalent distributed optimization problem with consistency constraints can be described as follows:

[0045]

[0046] In the formula x i (t), x j (t) represents the position states of the i-th and j-th autonomous vehicles, respectively, and x = (x1, ..., xj) N ) T ; Expressing the search function The minimum point x; i (t)=x j (t), i = 1, 2, ..., N, i ≠ j indicates that N unmanned vehicles have the same position and state.

[0047] III. Design of Fixed-Time and Predetermined-Time Centralized Optimization Algorithms Based on the Global Objective Function of Autonomous Vehicles

[0048] 3.1 Design a fixed-time centralized optimization algorithm

[0049] The algorithm is designed to solve the above distributed optimization problem within a fixed time or a predetermined time. The fixed-time centralized optimization algorithm based on the agent's global objective function is as follows:

[0050]

[0051] Where u i (t) represents the control input for the i-th unmanned vehicle, with parameter λ. 11 and λ 12 It is a positive number; And q are positive constants and satisfy 0 < q < 1 / 2; ||x i (t)-x j (t)|| represents x i (t)-x jThe Euclidean norm of (t); Represents the function f(x) i The gradient of f(x) with respect to time t, f(x) i (t) is x i (t) is the system global objective function with independent variables; express The Euclidean norm; a ij The adjacency matrix A = (a ij ) N×N The elements, where a ij >0 indicates that the i-th autonomous vehicle can obtain status information from the j-th autonomous vehicle; otherwise, a ij =0; T1 is the fixed-time estimate for all autonomous vehicles to achieve consensus. The fixed-time estimate for the system to solve the optimization problem under the fixed-time centralized optimization algorithm is T = T1 + T2, where T2 is the estimated time for the autonomous vehicles to converge from the consensus state to the optimal solution of the global objective function after time t > T1, and its expression is: φ is a convex parameter of the global objective function.

[0052] 3.2 Design a centralized optimization algorithm for predetermined time.

[0053] The predetermined time centralized optimization algorithm based on the agent's global objective function is as follows:

[0054]

[0055] Where u i (t) represents the control input of the i-th unmanned vehicle, q, And η are positive constants and satisfy 0 < q < 1 / 2, 0 < η < 1; Undirected connected communication topology diagram of a multi-driver autonomous vehicle system Algebraic connectivity; parameters Indicates base e The logarithm of T; p ηT is the pre-defined time for a multi-unmanned vehicle system to solve an optimization problem. p The time for achieving consistency for the pre-set autonomous vehicles is the same as in step 3.1, with other parameters remaining the same.

[0056] IV. Designing a Fixed-Time and Predetermined-Time Distributed Gradient Estimator

[0057] The fixed-time and predetermined-time centralized optimization algorithm described in step three requires the gradient information of the system's global objective function, which is not suitable for large systems or systems requiring privacy protection. To avoid using global information and solve the optimization problem in a distributed manner, fixed-time and predetermined-time distributed gradient estimators are designed respectively, so that each autonomous vehicle estimates the gradient information of the system's global objective function in a distributed manner within a fixed time and a predetermined time.

[0058] 4.1 Design a fixed-time distributed gradient estimator

[0059] The fixed-time distributed gradient estimator designed based on information interaction between autonomous vehicles is as follows:

[0060]

[0061] In the formula, the parameter θ 11 ,θ 12 It is a positive number, and in ‖ρ i (t)-ρ j (t)‖ ∞ Represents ρ i (t)-ρ j The infinite norm of (t), This indicates that within the time interval [t0, T] e ]Above ||ρ i (t)-ρ j (t)‖ ∞ Take the maximum value, T e For ω i (t) converges to the average gradient of the global objective function. The required fixed time; ω i (t) represents the estimate of the average gradient of the global objective function for the i-th autonomous vehicle, ν i (t) is an intermediate variable; defined ω i The update rate of (t) is shown below:

[0062]

[0063] Under the aforementioned fixed-time distributed gradient estimator, each autonomous vehicle only needs to communicate with its neighboring autonomous vehicles to achieve the desired result within a fixed time T. e The average gradient of the global objective function is estimated internally. Time T e The expression is

[0064]

[0065] 4.2 Design a pre-defined time distributed gradient estimator

[0066] The predetermined time distributed gradient estimator designed based on information interaction between autonomous vehicles is as follows:

[0067]

[0068] Parameters in the formula in ‖ρ i (t)-ρ j (t)‖ ∞ Represents ρ i (t)-ρ j The infinite norm of (t), This indicates that within the time interval [t0, ηT] p ]Above ||ρ i (t)-ρ j (t)‖ ∞ Take the maximum value; 0 < η < 1, ηT p ω is preset i (t) converges to the average gradient of the global objective function. Time; ω i (t), ν i (t), ρ i The definition of (t) and ω i The update rate of (t) is the same as in step 4.1.

[0069] Under the aforementioned time-determined distributed gradient estimator, each autonomous vehicle only needs to communicate with its neighboring autonomous vehicles to achieve the desired result within the predetermined time ηT. p The average gradient of the global objective function is estimated internally.

[0070] V. Determine a distributed optimization algorithm based on a gradient estimator, so that multiple unmanned vehicle systems can solve optimization problems in a distributed manner within a fixed time and a predetermined time.

[0071] When the estimation error of the i-th autonomous vehicle on the average gradient of the global objective function is... After converging to 0, the following distributed optimization algorithm based on gradient estimation can be obtained based on the gradient mean estimation of the global objective function and the centralized optimization algorithm.

[0072] 5.1 Determine a distributed optimization algorithm for the system to solve the optimization problem within a fixed time.

[0073] The fixed-time distributed optimization algorithm based on gradient estimation is as follows:

[0074]

[0075] Where Nω i(t) represents the gradient of the i-th autonomous vehicle with respect to the global objective function of the system at time t, where T1' = max{T1,T e}, T1 is the fixed time estimate for all autonomous vehicles to achieve consistency, T e For ω i (t) converges to the average gradient of the global objective function. The required fixed time, with other parameters being the same as in the centralized optimization algorithm in step 4.1, is used. The fixed time estimate for the system to solve the optimization problem under the fixed-time distributed optimization algorithm is T = T' + T2, where T2 is the estimated time for the autonomous vehicle to converge from the consistent state to the optimal solution of the global objective function after time t > T1', and its expression is: φ is a convex parameter of the global objective function.

[0076] 5.2 Determine the distributed optimization algorithm that enables the system to solve the optimization problem within a predetermined time.

[0077] The predetermined time distributed optimization algorithm based on gradient estimation is as follows:

[0078]

[0079] in Nω i (t) represents the gradient of the global objective function estimated by the i-th autonomous vehicle at time t; ηT p To achieve consistency and ω for all pre-set autonomous vehicles i (t) converges to the average gradient of the global objective function. Time, T p The time it takes for the preset autonomous vehicle state to converge to the optimal solution of the global objective function; other parameters are the same as those in the centralized optimization algorithm in step 4.2.

[0080] The present invention also provides a distributed optimization system for multiple unmanned vehicles with fixed time and predetermined time, comprising:

[0081] The model building unit is used to establish the dynamic model and communication topology of a multi-unmanned vehicle system.

[0082] The global objective function construction unit constructs the global objective function based on the dynamic model;

[0083] The centralized optimization algorithm design unit designs centralized optimization algorithms for fixed time and predetermined time based on the communication topology graph and the global objective function.

[0084] A distributed gradient estimator design unit is used to design fixed-time and predetermined-time distributed gradient estimators.

[0085] The distributed optimization algorithm design unit designs fixed-time and predetermined-time distributed optimization algorithms based on gradient estimation, respectively, based on distributed gradient estimators and centralized optimization algorithms.

[0086] The control unit uses a fixed-time and predetermined-time distributed optimization algorithm based on gradient estimation to control multiple unmanned vehicles and obtain the optimal solution of the global objective function.

[0087] Example 1

[0088] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0089] like Figure 1 As shown, the specific steps of the distributed optimization method for multiple unmanned vehicles at fixed and predetermined times according to the present invention are as follows:

[0090] 1. Establish the dynamic model and communication topology of the multi-unmanned vehicle system. The multi-unmanned vehicle system includes 6 unmanned vehicles. The dynamic model of the i-th unmanned vehicle is shown below:

[0091]

[0092] Where x i (t), u i (t) represents the position state and control input of the i-th unmanned vehicle, respectively. x represents i (t) derivative with respect to time t, x i (t) is usually obtained from the sensors and inertial measurement units equipped by the autonomous vehicle, and is used to describe the motion of the autonomous vehicle under control input. x1(0) = (0, 0.5) is selected. T x2(0) = (-1, 1.6) T x3(0) = (1.2, -0.5) T x4(0) = (-1, 1) T x5(0) = (0.2, 1.5) T x6(0) = (3,2) T The communication topology between autonomous vehicles is as follows: Figure 2 As shown.

[0093] 2. Construct the global objective function and describe the optimization problem. The local objective functions for the six autonomous vehicles are f1(x1) = sin(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14 ...3, x14, x1 11 )+sin(x 12 ),f2(x2)=2(x 21 +0.7) 2 +2(x 22 +2) 2 f3(x3)=2(x 31 +1.5)2 +(x 32 +1) 2 f4(x4)=2(x 41 +0.2) 2 +2(x 42 +0.1) 2 f5(x5)=(x 51 +2) 2 +2(x 52 +0.4) 2 f6(x6) = 1.5(x 61 +0.8) 2 +1.5(x 62 +1) 2 The global objective function is the sum of all local objective functions, and its expression is: The distributed optimization problem can be described as follows:

[0094]

[0095] The optimal solution x of the global objective function was calculated. * = (-0.9742, -0.9171), the convex parameter φ of the global objective function is 16. The goal of this example is to design distributed optimization algorithms for fixed and predetermined times, respectively, so that all six autonomous vehicles can solve the above optimization problem within a fixed or predetermined time, that is, all six autonomous vehicles can converge to the optimal solution x of the global objective function within a fixed or predetermined time. * =(-0.9742,-0.9171).

[0096] 3. Design of a centralized optimization algorithm with fixed time and predetermined time based on the global objective function of autonomous vehicles.

[0097] The fixed-time centralized optimization algorithm is designed as follows:

[0098]

[0099] Where the parameter λ 11 =2,λ 12 =1, q=0.25, a ii =0, a ij =1, i,j=1,…,6.

[0100] The predetermined time centralized optimization algorithm is designed as follows:

[0101]

[0102] Where the parameter λ 21 =5.6257, λ 22=0.1541, q=0.25, η = 0.5, T p =4.

[0103] 4. Design a fixed-time and predetermined-time distributed gradient estimator

[0104] The fixed-time distributed gradient estimator is designed as follows:

[0105]

[0106] Where the parameter θ 11 =2,θ 12 =130, q=0.25, Using the designed distributed gradient estimator, ω i (t) can be achieved in a fixed time T e =5.6247 converged to

[0107] The predetermined time distributed gradient estimator is designed as follows:

[0108]

[0109] Where the parameter θ 21 =5.6256, θ 22 =130, q=0.25, a ii =0, a ij =1. Choose η = 0.5, T p =4 Using the designed distributed gradient estimator, ω i (t) can be completed at the scheduled time Convergence to

[0110] 5. Based on the gradient estimator, determine the distributed optimization algorithm so that multiple unmanned vehicle systems can solve the optimization problem in a distributed manner within a fixed time and a predetermined time.

[0111] The fixed-time distributed optimization algorithm based on gradient estimation is as follows:

[0112]

[0113] Where the parameter λ 11 =2,λ 12 =1, q=0.25, a ii =0, a ij =1,T1'=max{T1,T e}=5.6257,ω iThe value of (t) can be obtained from the calculation process in the previous step. The position state of each unmanned vehicle is in the above u i The curve of change under the action of (t) is as follows: Figure 3 and Figure 4 As shown, each unmanned vehicle can reach the optimal solution x of the global objective function within a fixed time T = 5.934. * =(-0.9742,-0.9171).

[0114] The predetermined time distributed optimization algorithm based on gradient estimation is as follows:

[0115]

[0116] Where λ 21 =5.6257, λ 22 =0.1541; q=0.25, a ii =0, a ij =1, ω i The value of (t) can be obtained from the calculation process in the previous step. Choosing η = 0.5, T... p =4, the position status of each unmanned vehicle is as described above u i The curve of change under the action of (t) is as follows: Figure 5 and Figure 6 As shown, each unmanned vehicle can be deployed at the predetermined time T. p =The optimal solution x of the global objective function within 4. * =(-0.9742,-0.9171).

[0117] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A distributed optimization method for multiple unmanned vehicles at fixed and predetermined times, characterized in that, include: Establish a dynamic model and communication topology diagram for a multi-unmanned vehicle system; Based on the dynamic model, a global objective function is constructed; Based on the communication topology graph and the global objective function, centralized optimization algorithms with fixed time and predetermined time are designed respectively; Design distributed gradient estimators for fixed time and predetermined time respectively; Based on distributed gradient estimators and centralized optimization algorithms, fixed-time and predetermined-time distributed optimization algorithms based on gradient estimation are designed respectively. A distributed optimization algorithm based on gradient estimation with fixed and predetermined times is used to control multiple unmanned vehicles and obtain the optimal solution of the global objective function. The fixed-time centralized optimization algorithm is as follows: Among them, u i (t) represents the control input for the i-th unmanned vehicle, with parameter λ. 11 and λ 12 x is a positive constant; i (t), x j (t) represents the positions of the i-th and j-th driverless vehicles. And q are positive constants and satisfy 0 <q<1 / 2;||x i (t)-x j (t)|| represents x i (t)-x j The Euclidean norm of (t); Represents the function f(x) i The gradient of f(x) with respect to time t, f(x) i (t) is x i (t) is the system global objective function with independent variables; express The Euclidean norm; a ij The adjacency matrix A = (a ij ) N×N The elements, where a ij >0 indicates that the i-th autonomous vehicle can obtain status information from the j-th autonomous vehicle; otherwise, a ij =0; T1 is the fixed time estimate for all autonomous vehicles to achieve consensus. The fixed time estimate for the system to solve the optimization problem under the action of the fixed-time centralized optimization algorithm is T = T1 + T2, where T2 is the estimated time for the autonomous vehicle to converge from the consensus state to the optimal solution of the global objective function after time t > T1. The predetermined time centralized optimization algorithm is as follows: Among them, u i (t) represents the control input of the i-th unmanned vehicle, q, And η are positive constants and satisfy 0 < q < 1 / 2, 0 < η < 1; Parameter Undirected connected communication topology diagram of a multi-driver autonomous vehicle system algebraic connectivity; Indicates base e The logarithm of T; p ηT is the pre-defined time for a multi-unmanned vehicle system to solve an optimization problem. p The time required for the autonomous vehicles to achieve consistency is predetermined, and φ is a convex parameter of the global objective function; The fixed-time distributed gradient estimator is: Wherein, parameter θ 11 ,θ 12 It is a positive number, and Where N is the number of driverless cars, ||ρ i (t)-ρ j (t)|| ∞ Represents ρ i (t)-ρ j The infinite norm of (t), This indicates that within the time interval [t0, T] e ]Above ||ρ i (t)-ρ j (t)|| ∞ Take the maximum value, T e For ω i (t) is the fixed time required for convergence to the average gradient of the global objective function; Let f be the local objective function of the i-th autonomous vehicle. i (x i The gradient of ω with respect to time t; i (t) represents the estimate of the average gradient of the global objective function for the i-th autonomous vehicle, v i (t) is an intermediate variable; The predetermined time distributed gradient estimator is: In the formula, the parameters in ||ρ i (t)-ρ j (t)|| ∞ Represents ρ i (t)-ρ j The infinite norm of (t), This indicates that within the time interval [t0, ηT] p ]Above ||ρ i (t)-ρ j (t)|| ∞ Take the maximum value; 0 < η < 1, ηT p ω is preset i (t) is the time it takes to converge to the average gradient of the global objective function; The fixed-time distributed optimization algorithm is as follows: Where, Nω i (t) represents the gradient of the i-th autonomous vehicle at time t with respect to the global objective function of the system, ||Nω i (t)|| is Nω i The Euclidean norm of (t), T1' = max{T1,T e }, T1 is the fixed time estimate for all autonomous vehicles to achieve consistency, T e For ω i (t) The fixed time required for the system to converge to the average gradient of the global objective function is estimated as T = T' + T2, where T2 is the estimated time for the unmanned vehicle to converge from the consistent state to the optimal solution of the global objective function after time t > T1'. The predetermined time distributed optimization algorithm is as follows: Where, Nω i (t) represents the gradient of the global objective function estimated by the i-th autonomous vehicle at time t.

2. The distributed optimization method for multiple unmanned vehicles with fixed time and predetermined time according to claim 1, characterized in that, The fixed time 3. The distributed optimization method for multiple unmanned vehicles with fixed time and predetermined time according to claim 1, characterized in that, The ω i The update rate of (t) is: Where, θ 1* θ 2* For the corresponding θ 11 ,θ 12 Or θ 21 ,θ 22 ,||ω i (t)-ω j (t)|| represents ω i (t)-ω j The Euclidean norm of (t).

4. A distributed optimization system for fixed-time and predetermined-time operation of multiple unmanned vehicles implementing the method of any one of claims 1-3, characterized in that, include: The model building unit is used to establish the dynamic model and communication topology of a multi-unmanned vehicle system. The global objective function construction unit constructs the global objective function based on the dynamic model; The centralized optimization algorithm design unit designs centralized optimization algorithms for fixed time and predetermined time based on the communication topology graph and the global objective function. A distributed gradient estimator design unit is used to design fixed-time and predetermined-time distributed gradient estimators. The distributed optimization algorithm design unit designs fixed-time and predetermined-time distributed optimization algorithms based on gradient estimation, respectively, based on distributed gradient estimators and centralized optimization algorithms. The control unit uses a fixed-time and predetermined-time distributed optimization algorithm based on gradient estimation to control multiple unmanned vehicles and obtain the optimal solution of the global objective function.

Images