Distributed optimization method for high-order heterogeneous multi-agent system based on disturbance observer

Abstract

The application provides a high-order heterogeneous multi-agent system distributed optimization method based on an interference observer, and relates to the technical field of control and information. The application designs a limited-time interference observer to estimate disturbance for a high-order heterogeneous multi-agent system with matched and unmatched disturbance, adopts a proportional-integral distributed optimizer in an interconnection system to estimate an optimal value, designs a tracking controller to compensate for disturbance and track the optimal value, and realizes an optimization target. Through the research on the distributed optimization method of the high-order heterogeneous multi-agent system with unmatched disturbance, the application solves a distributed optimization problem applied to practical scenes such as multi-robot source positioning, solves an anti-interference problem in practical application, and brings convenience to people's daily life. Therefore, the research on the multi-agent distributed optimization method has not only a profound theoretical value, but also a rich practical value.

Description

Technical Field

[0001] This invention relates to the field of control and information technology, and in particular to a distributed optimization method for high-order heterogeneous multi-agent systems based on interference observers. Background Technology

[0002] An intelligent agent is an individual possessing autonomy, storage, computation, and communication capabilities. A multi-agent system (MAS) is a system comprising multiple intelligent agents that collaborate to achieve a specific goal through information exchange with their neighbors. MAS employs a distributed control approach, eliminating the need for a central node (central controller). Each agent makes decisions using only its own and its neighbors' information, resulting in advantages such as low communication costs, high scalability, and strong robustness. In practical applications of distributed coordinated control, many control tasks require MAS to meet certain optimization indices, leading to distributed optimization problems for MAS, such as the sensor network source point cooperative localization problem, the multi-robot system optimization aggregation and formation problem, and the smart grid economic dispatch problem. In distributed optimization problems, each agent has a local cost function, and the global cost function to be optimized is the sum of all local cost functions. The goal of distributed optimization is to converge the states of each agent to the optimal point of the global cost function of the MAS through distributed algorithms, given only the local cost functions are known, via local information exchange.

[0003] In the field of multi-agent distributed optimization, existing research mainly focuses on distributed control of first-order systems to achieve optimization objectives, with little attention paid to multi-agent systems with mismatched disturbances and higher-order dynamics. Most real-world control objects can be modeled as nonlinear systems, and in practical optimization tasks, these systems typically exhibit second-order or higher-order dynamics. Therefore, research on nonlinear higher-order systems is more prevalent. On the other hand, real-world systems are inevitably affected by various disturbances and uncertainties, such as external environmental disturbances, input channel disturbances, and parameter perturbations. In higher-order systems, disturbances may enter the system through channels different from the control input, i.e., mismatched disturbances. Active anti-disturbance control methods based on disturbance observers have been proposed to address mismatched disturbances within the system. This invention considers a scenario present in practical applications, such as the multi-robot source search problem, where multiple agents are placed in an unknown field and search for source points using a distributed algorithm. In this type of situation, the agent cannot obtain field strength information for all locations in the entire field. Therefore, its optimizer cannot use the global gradient information of the local cost function, but can only calculate the gradient of the local cost function at the current real-time location by measuring the field strength. This creates a feedback loop between the optimizer and the tracking controller, and the resulting interconnected system poses some challenges to the analysis. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a distributed optimization method for high-order heterogeneous multi-agent systems based on interference observers. Compared to previous research, this invention can be applied to more practical multi-agent systems facing such problems, broadening the application field of distributed control and optimization, and has significant practical application value.

[0005] A distributed optimization method for high-order heterogeneous multi-agent systems based on interference observers includes the following steps:

[0006] Step 1: Construct the network topology graph of the multi-agent system, which is an undirected connected graph. in, Represents a set of N nodes. Describe the set of edges. Represents the adjacency matrix. Let a represent the set of N×N dimensional real matrices; in the adjacency matrix, if there is an edge connecting nodes i and j, then a ij =a ji =1, otherwise a ij =a ji =0. Define the set of neighboring nodes of node i as...

[0007] Step 2: Establish a dynamic model of a high-order heterogeneous multi-agent system, where the dynamic equation of the i-th agent is as follows:

[0008]

[0009]

[0010] y i =x i1

[0011] Among them, M i ≥1 is the order of the i-th agent. It is the system's state variable, u i It is a control input. If the input is not on the same channel, it is considered a mismatch disturbance. It is a matching perturbation, y i It is the output; each order of interference d ik k = 1, ..., M i It is γ ik Differentiable to order -1, and Satisfied Lipschitz constant

[0012] Step 3: Design the following finite-time disturbance observer for the i-th agent:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] Among them, h ik =x i(k+1) k = 1, ..., M i -1, It is the observer gain with a positive value. l = 1, ..., γ ik They are x ik and (d) ik ) (l-1) The estimate, It is an intermediate variable, sgn(x) is a sign function, when x>0 sgn(x)=1, when x<0 sgn(x)=-1, when x=0 sgn(x)=0, sig a (x)=|x| a sgn(x), where 0 < a < 1;

[0020] Step 4: Apply the following proportional-integral distributed optimizer to the interconnected system:

[0021]

[0022]

[0023] in, p is the local cost function that the i-th agent needs to optimize. i and q i These are dummy variables; δ1, δ2, δ3, and δ4 are positive constants. The optimizer achieves the goal of distributed optimization, that is... Represents a set of N nodes;

[0024] Step 5: Based on the dynamic model of a high-order heterogeneous multi-agent system, establish the following error system model:

[0025] e i1 =x i1 -p i

[0026] e ik =xik -α i(k-1) k = 2, ..., M i

[0027] Where, α ik Yes, x i The virtual control law of the subsystem

[0028] Step 6: Based on the disturbance estimated by the finite-time disturbance observer and the optimized value generated by the optimizer, design the following tracking controller for the interconnected system:

[0029]

[0030]

[0031]

[0032] Among them, b ik and m ik k = 1, ..., M i It is a constant with a positive value;

[0033] Step 7: Select a suitable composite Lyapunov function for the distributed optimizer-tracking controller interconnect system, choosing a value that satisfies the stability condition to achieve the target optimization.

[0034] The beneficial effects of adopting the above technical solution are as follows:

[0035] This invention provides a distributed optimization method for high-order heterogeneous multi-agent systems based on a disturbance observer. This method can eliminate the influence of mismatched perturbations in high-order heterogeneous multi-agent systems, achieving the distributed optimization objective without global gradient information, and thus has greater feasibility in applications.

[0036] Compared with the prior art, the specific beneficial technical effects of the present invention are as follows: (1) The research object is a high-order system, which is more in line with the characteristics of actual systems and has a wider range of applications. (2) By using a disturbance observer to compensate for disturbances in the system in a feedforward manner, especially mismatched disturbances, the speed of disturbance suppression is faster and has higher application value. (3) The method is applied to a class of real-world scenarios, that is, the agent does not need to obtain the global gradient information of the cost function in advance, and can complete the optimization objective only by using the measured gradient output in real time. Attached Figure Description

[0037] Figure 1 A flowchart of a distributed optimization method provided in an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram of the network topology established in an embodiment of the present invention;

[0039] Figure 3 This is a state trajectory diagram of each intelligent agent in the embodiments of the present invention under the action of the controller to achieve optimization. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and examples. The following embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0041] Distributed optimization methods for high-order heterogeneous multi-agent systems based on interference observers, such as Figure 1 As shown, it includes the following steps:

[0042] Step 1: Construct the network topology graph of the multi-agent system, which is an undirected connected graph. in, Represents a set of N nodes. Describe the set of edges. Represents the adjacency matrix. Let represent the set of N×N dimensional real matrices. In the adjacency matrix, if nodes i and j are connected by an edge, then a ij =a ji =1, otherwise a ij =a ji =0. Define the set of neighboring nodes of node i as...

[0043] In this embodiment, an undirected connected topological graph is constructed, with the structure as follows: Figure 2 As shown in the diagram. Nodes numbered 1, 2, 3, and 4 represent intelligent agents.

[0044] Step 2: Establish a dynamic model of a high-order heterogeneous multi-agent system, where the dynamic equation of the i-th agent is as follows:

[0045]

[0046]

[0047] y i =x i1

[0048] Among them, M i ≥1 is the order of the i-th agent. Different agents can have different orders, meaning that multi-agent systems are heterogeneous. It is the system's state variable, u i It is a control input. If the input is not on the same channel, it is considered a mismatch disturbance. It is a matching perturbation, y i This is the output. Each order of interference d ikk = 1, ..., M i It is γ ik Differentiable to order -1, and Satisfied Lipschitz constant

[0049] Step 3: Design the following finite-time disturbance observer for the i-th agent:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] Among them, h ik =x i(k+1) k = 1, ..., M i -1, It is the observer gain with a positive value. l = 1, ..., γ ik They are x ik and (d) ik ) (l-1) The estimate, It is an intermediate variable. sgn(x) is a sign function; when x > 0, sgn(x) = 1; when x < 0, sgn(x) = -1; and when x = 0, sgn(x) = 0. a (x)=|x| a sgn(x), where 0 < a < 1.

[0057] Step 4: The interconnected system adopts the following proportional-integral distributed optimizer:

[0058]

[0059]

[0060] in, p is the local cost function that the i-th agent needs to optimize. i and q i These are dummy variables, and δ1, δ2, δ3, and δ4 are constants with positive values.

[0061] Step 5: Based on the dynamic model of a high-order heterogeneous multi-agent system, establish the following error system model:

[0062] e i1 =x i1 -p i

[0063] e ik =x ik -α i(k-1) k = 2, ..., M i

[0064] Where, α ik Yes, x i The virtual control law of the subsystem

[0065] Step 6: Based on the disturbance estimated by the finite-time disturbance observer and the optimized value generated by the optimizer, design the following tracking controller for the interconnected system:

[0066]

[0067]

[0068]

[0069] Among them, b ik and m ik k = 1, ..., M i It is a constant with a positive value.

[0070] Step 7: Select a suitable composite Lyapunov function for the distributed optimizer-tracking controller interconnect system, and select values ​​for the above parameters that satisfy the stability conditions.

[0071] The parameters used in this embodiment are as follows:

[0072] The dynamic model of the multi-agent system is as follows: y i =x i1 , i = 1, ..., 4;

[0073] The system interference is: d i1 =0.4sin(1.4t), d i2 =0.4sin(t+2), i=1,...,4;

[0074] The parameters of the distributed optimizer are: δ1 = 5, δ2 = 10, δ3 = 3, δ4 = 3;

[0075] The cost function to be optimized is: f i =0.0042(y i -3)2 , i = 1, ..., 4;

[0076] The interference observer parameters are: λ i1，0 =11.388, λ i1，1 =14.6, λ i1，2 =28.7, λ i2，0 =11.4, λ i2，1 =14.6,

[0077] The tracking controller parameters are: b i1 =9.5, b i2 =5.8, m i1 =10.7, i=1,...,4.

[0078] from Figure 3 It can be seen that the global optimal value is y. i =3, i=1,...,4. Under the conditions considered in this invention, the designed distributed optimization method based on interference observers can effectively suppress mismatch interference and asymptotically achieve the optimization objective.

[0079] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A distributed optimization method for high-order heterogeneous multi-agent systems based on interference observers, characterized in that, Includes the following steps: Step 1: Construct the network topology of the multi-agent system; The network topology graph is an undirected connected graph. ,in, express A set of nodes, Describe the set of edges. Represents the adjacency matrix. express A set of dimensional real matrices; in the adjacency matrix, if the node If there is an edge connecting them, then ,otherwise Define nodes The set of neighbor nodes is ; Step 2: Establish a dynamic model of a high-order heterogeneous multi-agent system; In the dynamic model, the first The dynamic equations of an agent are as follows: ； ； ； in, It is the first The order of an agent, It is the system's state variable. It is a control input. If the input is not on the same channel, it is considered a mismatch disturbance. It is a matching perturbation. It is the output; interference of various orders yes Differentiable of order, and Satisfied Lipschitz constant ; Step 3: For the first An intelligent agent designs a finite-time disturbance observer. The finite-time disturbance observer is as follows: ； ； ； ； ； ； in, , , It is the observer gain with a positive value. , They are and The estimate, It is an intermediate variable. It is a sign function, when hour ,when hour ,when hour , ,in ; Step 4: Apply a proportional-integral distributed optimizer to the interconnected system; The proportional-integral distributed optimizer: ； ； in, It is the first The local cost function that an agent needs to optimize. and It is a dummy variable. , , and It is a positive constant; the optimizer achieves the goal of distributed optimization, that is... , Represents a set of N nodes; Step 5: Establish an error system model based on the dynamic model of a high-order heterogeneous multi-agent system; Step 6: Design a tracking controller for the interconnected system based on the disturbance estimated by the finite-time disturbance observer and the optimized value generated by the optimizer; Step 7: Select a suitable composite Lyapunov function for the distributed optimizer-tracking controller interconnect system, choosing a value that satisfies the stability condition to achieve the target optimization.

2. The distributed optimization method for a high-order heterogeneous multi-agent system based on an interference observer according to claim 1, characterized in that, The error system model described in step 5 is as follows: ； ； in, Yes The virtual control law of the subsystem .

3. The distributed optimization method for a high-order heterogeneous multi-agent system based on an interference observer according to claim 2, characterized in that, The tracking controller described in step 6: ； ； ； in, and It is a constant with a positive value.

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