A multi-agent cooperative control method based on event-triggered unknown non-autonomous leader-follower

Abstract

The application discloses a kind of unknown non-autonomous follower under event-triggered multi-agent cooperative control method based on, construct state-based time-varying topology graph, follower and its tracking navigator are based on the time-varying topology graph communication;Utilize distributed hybrid adaptive observer to estimate navigator state;Combined with distributed hybrid adaptive observer and unbounded potential energy function, design event-triggered controller with distance weight, so that the multi-agent closed-loop system formed by the navigator and each follower keeps communication topology sustainedly connected, the tracking error of each follower relative to the navigator asymptotically converges, and excludes Zeno behavior in event-triggered process.The application solves the problem of multi-agent connectivity maintenance cooperative tracking only relying on local neighborhood information, and can effectively adapt to network communication constraints.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control technology, specifically relating to a multi-agent cooperative control method under an unknown non-autonomous navigator based on event triggering. Background Technology

[0002] In resource-constrained multi-agent practical engineering scenarios, the limited wireless transmission bandwidth and node endurance are prominent issues. Continuous periodic communication results in a large amount of invalid data interaction, making event-triggered communication mechanisms the mainstream solution for alleviating communication pressure and reducing node energy consumption. In recent years, a large number of research results have emerged around event-triggered cooperative control, but most solutions only design trigger rules for the control loop, without adapting the event-triggered mechanism at the observation level, and lack a dedicated distributed observation architecture that can synchronously identify the unknown frequency of the leader and compensate for the unknown external input of the leader. Most existing adaptive distributed observation solutions can only cope with single uncertainties: some studies can achieve online identification of harmonic frequencies, but cannot resist the influence of external disturbances to the leader; some solutions have anti-interference compensation capabilities, but require all leader trajectory frequencies to be known, making it difficult to adapt to the complex working conditions where the leader trajectory frequency is unknown and superimposed with external disturbances. At the same time, traditional distributed observers generally rely on continuous-time communication modes, which cannot be deeply integrated with event-triggered mechanisms, continuously occupying communication resources during operation, making it difficult to directly apply to resource-constrained cluster platforms such as UAVs and small mobile robots. In the paper “Event-triggered coordination control for multi-agent systems with connectivitypreservation” (Fan Y, Chen J, Song C, et al. International Journal of Control, Automation and Systems, 2020, 18(4): 966-979), connectivity triggers and convergence triggers were designed to realize network connectivity maintenance and agent aggregation, respectively, and constraint functions were introduced to ensure that the control input is bounded. However, this method has the following shortcomings: First, its research object is limited to multi-agent aggregation problems without a leader, and it does not consider cooperative tracking control in the presence of a dynamic leader. In practical engineering applications such as UAV swarms and mobile robot formations, followers usually need to track a given leader or desired trajectory. Second, this method assumes that the system has no unknown parameters or external disturbances, and does not design a state observer. Each agent needs to directly obtain the state information of its neighbors, which is difficult to apply directly when there are external inputs and parameter uncertainties in the system. Third, this method uses a constraint function to make the control quantity tend to zero when the communication distance is close to the sensor range to maintain the connection. Although this ensures the boundedness of the control input, it sacrifices the convergence speed and makes it difficult to achieve a good balance between maintaining the connection and fast convergence. In addition, the event triggering function of this scheme still needs to continuously monitor the state information of neighbors, and the communication burden is not fundamentally alleviated. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a multi-agent cooperative control method based on event triggering under an unknown non-autonomous navigator.

[0004] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0005] A multi-agent cooperative control method based on event-triggered unknown non-autonomous navigators:

[0006] A state-based time-varying topology graph is constructed, and followers and their tracking leaders communicate based on the time-varying topology graph;

[0007] The leader state is estimated using a distributed hybrid adaptive observer.

[0008] By combining a distributed hybrid adaptive observer and an unbounded potential function, an event-triggered controller with distance weights is designed to maintain continuous communication topology between the navigator and the multi-agent closed-loop system composed of followers. The tracking errors of each follower relative to the navigator asymptotically converge, and Zeno behavior during the event triggering process is eliminated.

[0009] Furthermore, the distributed hybrid adaptive observer is:

[0010]

[0011] in, For the observer state, For follower i, the online estimate of the unknown parameters of the leader. It depends on The system matrix, For distributed cooperative error, To adaptively compensate for gain, For robust adaptive gain, Let i be the set of neighboring nodes of agent i. It is a nonlinear gain function. For distributed consensus collaborative feedback gain, For the online estimates of the unknown parameters of the leader by the follower j, , , This is the gain coefficient. For time-varying regularization functions, This is the time-varying forgetting decay function.

[0012] Furthermore, the event triggering controller is:

[0013]

[0014] in, For the first iThe state of a follower For the first j The state of a follower For the number of followers, For the system matrix, The moment the event is triggered. It is a positive number. This is a weighting function related to the distance between agents.

[0015] Furthermore, the event triggering time Generated by the following trigger function: ,in, , For trigger threshold parameters, measurement error , For the triggering error of the control item, This represents the triggering error of the state.

[0016] Furthermore, the triggering error of the control item State triggering error .

[0017] Furthermore, the weighting function related to the distance between agents , The relative distance between the two followers Let be the edge set in the time-varying topological graph. For the initial edge set, This represents the unbounded potential energy function.

[0018] Furthermore, the time-varying topology graph contains a directed spanning tree rooted at the leader node, and the sub-communication graph formed by the follower nodes is an undirected graph; communication edges are generated only when the real-time relative distance between two followers is less than the sensor's sensing radius.

[0019] Furthermore, the follower is a single-integrator multi-agent system, including an aerial drone and a ground-based following vehicle.

[0020] The beneficial effects of this invention are as follows: This invention addresses practical engineering scenarios such as collaborative inspections in drone swarms and unmanned vehicle swarms. By relying on a distributed observation architecture, it breaks the swarm's dependence on global communication and a central controller. Each agent can complete state estimation solely based on its own local interaction information with neighboring nodes, effectively solving the collaborative communication problem in scenarios with no base station coverage and limited wireless channel bandwidth. All observer gains do not require engineers to repeatedly debug and adjust them offline in advance. Adaptive parameters such as frequency estimation and disturbance compensation can be updated online in real time according to the swarm's operating status, without being affected by changes in the leader's maneuvering frequency or external wind disturbances / load. The control structure is redesigned to adapt to changes in field conditions such as fluctuations. The observer's adaptive update law and event-triggered communication rules can autonomously adapt to various dynamic conditions. It can identify the non-preset sinusoidal maneuver frequency of the navigator online and continuously offset the influence of external environmental disturbances and unknown inputs of the navigator. At the same time, the event-triggered mechanism triggers data interaction on demand, eliminating the redundant transmission of traditional periodic communication, greatly reducing the frequency of wireless communication and equipment energy consumption. Ultimately, while saving communication and computing resources, it ensures that the tracking error of all following agents towards the navigator asymptotically converges to zero, meeting the accuracy requirements of actual operations such as swarm formation and target tracking. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the design of multi-agent cooperative control based on an event-triggered unknown non-autonomous navigator, as per the present invention.

[0022] Figure 2 This is a communication diagram between the leader and followers of this invention.

[0023] Figure 3(a) shows the observation error diagram of the first component state of the observer.

[0024] Figure 3(b) shows the observation error diagram of the second component state of the observer.

[0025] Figure 4 This is a diagram of the observer state observation error L2.

[0026] Figure 5(a) shows the frequency estimate of the first path of the observer.

[0027] Figure 5(b) shows the frequency estimates for the second path of the observer.

[0028] Figure 6 An adaptive compensation gain map for unknown inputs to the observer.

[0029] Figure 7 This is the robust adaptive gain plot for the observer.

[0030] Figure 8(a) shows the distance between follower 1 and navigator.

[0031] Figure 8(b) shows the distance between follower 2 and navigator.

[0032] Figure 8(c) shows the distance between follower 1 and follower 2.

[0033] Figure 8(d) shows the distance between follower 1 and follower 3.

[0034] Figure 8(e) shows the distance between follower 2 and follower 4.

[0035] Figure 8(f) shows the distance between follower 3 and follower 5.

[0036] Figure 8(g) shows the distance between follower 4 and follower 6.

[0037] Figure 9(a) shows the distance change between follower 1 and navigator.

[0038] Figure 9(b) shows the distance change between follower 2 and navigator.

[0039] Figure 9(c) shows the distance change between follower 3 and navigator.

[0040] Figure 9(d) shows the distance change between follower 4 and navigator.

[0041] Figure 9(e) shows the distance change between follower 5 and navigator.

[0042] Figure 9(f) shows the distance change between follower 6 and navigator. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention; the scope of protection of this invention is not limited thereto.

[0044] like Figure 1 As shown, the design process of a multi-agent cooperative control method based on event triggering under an unknown non-autonomous navigator is as follows:

[0045] Step 1: Establish the system dynamic equations.

[0046] Specifically, it involves establishing a set of single-integrator multi-agent systems (including aerial drones and ground-following vehicles) and their dynamic equations for tracking the leader.

[0047] In this embodiment, the control object to be studied is first determined. The followers are a group of single-integrator multi-agent systems, and the state-space equation is:

[0048] ,

[0049] The state-space equation of the navigator is:

[0050]

[0051] in, Let i be the state of the i-th follower. For the control input of the i-th follower, For the number of followers, For the navigator's external input, It is the state of a leader. It depends on some unknown parameter vector The system matrix, It is a known constant matrix. It is the expected trajectory.

[0052] Step 2: Construct a state-based time-varying topology graph.

[0053] The node set contains the leader and all followers. Edges are determined by the relative distance between followers being less than the sensor range. An undirected communication edge is generated between two followers only when the real-time relative distance between them is less than their own sensor's sensing radius.

[0054] Define a state-based time-varying topology graph The node set is 0 represents the navigator. express One follower Let be the edge set. The connectivity of a graph changes with the relative positions of two followers, defined as the relative distance between two followers. , , Therefore, edge set Defined as: for a given sensor range r and the follower's motion time , If and only if That is, when the relative distance between two followers is less than the sensor range, then the edge formed by the two followers has an edge set. middle.

[0055] Step 3: Design a distributed adaptive observer for the unknown non-autonomous navigator from Step 1.

[0056] The observer for the navigator state is designed as follows:

[0057]

[0058] in, It is the observer state. For follower i, the online estimate of the unknown intrinsic frequency of the leader. To adaptively compensate for gain, For robust adaptive gain; It is a distributed cooperative error, generated by the communication topology, and relies only on local information from itself and its neighbors; Let i be the set of neighboring nodes of agent i. It is a nonlinear gain function; For distributed consensus collaborative feedback gain, gain For frequency estimation consistency cooperative gain, gain , is the update adjustment coefficient for adaptive compensation gain, gain , is the update adjustment coefficient for robust adaptive gain; It is a time-varying regularization function, used as a regularization term in the denominator to avoid the denominator becoming singular when the error approaches 0; This is a time-varying forgetting decay function that acts on the adaptive gain update law to prevent forgetting. , Unlimited expansion ensures that the gain is globally bounded.

[0059] Step 4: Observer convergence analysis.

[0060] Define state observation error Gain estimation error System matrix parameter error , ,in, In navigator mode, , For the unknown constant parameters of the system that are greater than 0, the dynamic equations for the state observation error, gain estimation error, and parameter error are obtained by rearranging them. , , , , construct containing , , and Lyapunov energy function:

[0061]

[0062] in, This is the weighted Laplace matrix corresponding to the communication topology of a multi-agent system, used to characterize the weighted relationship of communication connections between agents; Let m be an m-order identity matrix, where m is the dimension of the navigator's state vector; This represents the Kronecker product operation of matrices.

[0063] Calculate the derivative of the energy function along the error system. Proof by inequality scaling Since the global equations are bounded above, it can be proven that the solutions to the dynamic equations of observation error, gain estimation error, and parameter error exist and are bounded; combined with Barbalat's lemma, it can be proved that... Finally, the conclusion was reached , This means that each agent's observer can achieve asymptotic estimation of the navigator's state and unknown parameters. Among these, Let be the online estimate of the unknown parameters contained in the leader system matrix by the i-th follower agent. This is the vector of true unknown parameters corresponding to the navigator system matrix.

[0064] Step 5: Preliminary design of the event trigger controller.

[0065] According to step three, based on the observer state The navigator output obtained for Design an event-triggered controller based on a distributed observer to enable followers to track the leader's trajectory and maintain initial connection. The preliminary design of the event-triggered controller is as follows:

[0066]

[0067] in, Given a sufficiently smooth function to be determined, The sequence of event trigger times is generated by the following formula:

[0068]

[0069] in, This is for measurement error.

[0070] Step six: System control performance objectives.

[0071] Given a leader-follower system, the designed event-triggered controller must satisfy the following: for any initial conditions ( Make the initial topology graph This gives the following properties to the closed-loop system consisting of a navigator and a follower:

[0072] 1) Continuous topological connectivity: For all Maintain connection;

[0073] 2) Asymptotic tracking: , ;

[0074] 3) No Zeno behavior: The number of times an event is triggered within a finite time is limited, ensuring that the controller is physically feasible.

[0075] Step 7: Basic Assumptions.

[0076] Assumption 1: For the topology graph in step three, assume that the topology graph contains a directed spanning tree rooted at the leader node, and that the sub-communication graphs formed by the follower nodes are undirected graphs, such as... Figure 2 As shown, assuming the topology graph in this embodiment contains a directed spanning tree rooted at leader node 0, and follower nodes... The resulting sub-topological graph is an undirected graph. Assumption 2, for any Navigator external input in step one It is bounded and the boundary is unknown; a solution exists and is bounded.

[0077] Step 8: Improved event-triggered controller based on potential energy function.

[0078] An unbounded potential function is introduced to optimize the controller design in order to maintain the communication connection.

[0079] Define an unbounded potential energy function ,in For a sufficiently smooth function:

[0080] 1) For ;

[0081] 2) Negatively bounded;

[0082] 3) .

[0083] Based on the potential energy function, a weighting function related to the distance between agents is defined:

[0084]

[0085] Improve the distributed event triggering controller in step five:

[0086]

[0087] in, The value should be a sufficiently large positive number, and its specific value can be tuned according to the communication topology, the norm of the system matrix S, and the sensing radius parameter. In the simulation verification condition corresponding to this embodiment, the following is selected: This ensures both continuous connectivity of the communication topology and asymptotic convergence of the tracking error.

[0088] Event triggering time Generated by the following trigger function;

[0089]

[0090] Among them, the trigger threshold parameter Measurement error , For the triggering error of the control item, Let be the triggering error of the state, and:

[0091]

[0092]

[0093] Step nine: System coordinate transformation and closed-loop matrix form.

[0094] By performing a coordinate transformation on the system, the tracking problem is transformed into a stability problem, facilitating unified analysis. The tracking error is defined. , Then the closed-loop dynamics of the tracking error are:

[0095]

[0096] Define a global stacked vector , , , and weighted matrix ,in , The closed-loop system can be rewritten in a unified matrix form:

[0097]

[0098] in, It is an N-order identity matrix, the order of which corresponds to the number of follower agents; It is an n-order identity matrix, the order of which corresponds to the dimension of the state vector of a single agent.

[0099] Step 10: Theoretical analysis of controller performance.

[0100] Assuming an initial topology graph The effectiveness of the controller is demonstrated through three aspects: topology connectivity preservation, trajectory tracking convergence, and Zeno-free behavior.

[0101] (1) Proof of topology connectivity preservation:

[0102] Constructing Lyapunov functions based on unbounded potential functions:

[0103]

[0104] Among them, if , ,otherwise ;

[0105] Calculate the derivative of the energy function along the closed-loop system. By combining the norm scaling with the event triggering conditions, we can obtain ( This is the positive gain coefficient corresponding to the measurement error term during the scaling of the Lyapunov function derivative; its value is determined by the weighting matrix. The upper bound of the largest eigenvalue is determined by the induced norm of the system matrix S, and is used to measure the degree of influence of measurement error on the energy change of the system. Integrating over time, the energy function can be proven. The function is globally bounded. It can be proved by contradiction that if there exists an initial communication edge that breaks at a finite time, the potential energy function will tend to infinity, and... Boundedness is contradictory, therefore for all All The communication topology remains connected at all times.

[0106] (2) Proof of trajectory tracking convergence:

[0107] Choose the Lyapunov energy function based on the Laplace matrix:

[0108]

[0109] in, ,for A special form; in which , , , ,otherwise .

[0110] Calculate the derivative of the energy function along the tracking error system. By scaling the eigenvalues ​​to obtain the differential inequality, and then solving it in conjunction with the event triggering condition, it can be proved that: when Time energy function It asymptotically converges to 0. Since the Laplace matrix is ​​positive definite, the tracking error... Asymptotically converges to 0, that is Followers can achieve asymptotic trajectory tracking of the navigator.

[0111] (3) Proof of no Zeno behavior:

[0112] By taking the derivative of the norm of the measurement error and scaling it using the boundedness of the system state and weighting function, we can find that the error derivative has a bounded upper bound. Integrating the error derivative over a single trigger interval and combining it with the event trigger threshold... It can be deduced that there is a positive lower bound in time between any two event trigger times, and the number of triggers in a finite time is a finite value. Therefore, the system does not exhibit Zeno behavior, and the controller is physically realizable.

[0113] Steps one through ten above are all implemented in the control host, and the control host maintains a communication connection with both the follower and the navigator. Under the control of the event-triggered controller, the follower and the navigator achieve continuous topology connectivity, asymptotic convergence of tracking error, and no Zeno behavior.

[0114] Step 11: Simulation verification.

[0115] The effectiveness of the proposed method was verified by numerical simulation. The simulation settings and results are as follows.

[0116] The simulation object in this step is the multi-agent system composed of the navigator and followers from step one, with dimensions... Number of followers In step one, the state-space equation for the navigator is:

[0117]

[0118] Assuming the sensor's sensing range is And the initial positions of each agent are:

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126] Based on the initial position, we can obtain the initial edge set. for:

[0127]

[0128] like Figure 2 As shown in the diagram, node 0 is the leader, and nodes 1-6 are the followers. Figure 2 The initial topology graph can be seen. It is connected. The unbounded potential energy function is defined as:

[0129]

[0130] Next, select the parameters in the event trigger controller from step eight as follows: , , The effect of the designed controller can be shown below.

[0131] As shown in Figures 3(a) and 3(b), in the initial stage of the simulation, each agent has a large initial error because the initial observation value deviates from the true state of the navigator. As the distributed adaptive observer is updated online, the observation errors of the two components of all agents decay rapidly and eventually converge asymptotically to near zero, which verifies that the observer can achieve effective estimation of the full state of the navigator by relying only on local neighborhood information.

[0132] Depend on Figure 4 It can be seen that the L2 norm of the observation error of all agents continuously decreases and asymptotically converges to zero, without divergence or continuous oscillation, which is consistent with the theoretically derived conclusion of the observer convergence.

[0133] As shown in Figures 5(a) and 5(b), the frequency estimates of each agent at the initial moment deviate from the true values, simulating the actual working condition where the navigator's frequency is unknown. After online iteration using the frequency adaptive law, the frequency estimates of all agents gradually approach and eventually converge to the true frequency, proving that this observer has the ability to identify the unknown inherent parameters of the navigator online without the need for offline tuning in advance.

[0134] Depend on Figure 6 It can be seen that the gain is adaptively and dynamically adjusted with the observation error, and eventually converges to a bounded steady-state value. There will be no unlimited expansion phenomenon. This verifies that the adaptive law with forgetting decay term can not only achieve robust compensation for unknown disturbances, but also ensure that the gain is globally bounded.

[0135] Depend on Figure 7 It can be seen that the robustness gain of all agents is adaptively adjusted according to the system's operating state and eventually remains bounded, thus ensuring system robustness while avoiding state oscillations caused by excessive gain.

[0136] As shown in Figures 8(a) to 8(g), throughout the entire simulation period, the distance between agents corresponding to all initially existing communication edges remained less than the sensing radius of 4 meters, and no edge disconnection occurred. This verifies that the distance weight design based on the unbounded potential function can achieve continuous connectivity of the communication topology and satisfy the closed-loop system requirements. ⊇ The theoretical conclusions.

[0137] As shown in Figures 9(a) to 9(f), as the control action is continuously applied, the distance between all followers and the leader gradually decreases and eventually converges to zero, verifying that the event-triggered controller proposed in this invention can ensure the cooperative tracking accuracy of a multi-agent system while reducing the communication frequency.

[0138] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A multi-agent cooperative control method based on event-triggered unknown non-autonomous navigators, characterized in that: A state-based time-varying topology graph is constructed, and followers and their tracking leaders communicate based on the time-varying topology graph; The leader state is estimated using a distributed hybrid adaptive observer. By combining a distributed hybrid adaptive observer and an unbounded potential function, an event-triggered controller with distance weights is designed to maintain continuous communication topology between the navigator and the multi-agent closed-loop system composed of followers. The tracking errors of each follower relative to the navigator asymptotically converge, and Zeno behavior during the event triggering process is eliminated.

2. The multi-agent cooperative control method under an unknown non-autonomous navigator based on event triggering as described in claim 1, characterized in that, The distributed hybrid adaptive observer is: in, For the observer state, For follower i, the online estimate of the unknown parameters of the leader. It depends on The system matrix, For distributed cooperative error, To adaptively compensate for gain, For robust adaptive gain, Let i be the set of neighboring nodes of agent i. It is a nonlinear gain function. For distributed consensus collaborative feedback gain, For the online estimates of the unknown parameters of the leader by the follower j, , , This is the gain coefficient. For time-varying regularization functions, This is the time-varying forgetting decay function.

3. The multi-agent cooperative control method under an unknown non-autonomous navigator based on event triggering as described in claim 2, characterized in that, The event triggering controller is: in, For the first i The state of a follower For the first j The state of a follower For the number of followers, For the system matrix, The moment the event is triggered. It is a positive number. This is a weighting function related to the distance between agents.

4. The multi-agent cooperative control method under an unknown non-autonomous navigator based on event triggering as described in claim 3, characterized in that, Event triggering time Generated by the following trigger function: ,in, , For trigger threshold parameters, measurement error , For the triggering error of the control item, This represents the triggering error of the state.

5. The multi-agent cooperative control method under an unknown non-autonomous navigator based on event triggering as described in claim 4, characterized in that, Triggering error of control item State triggering error .

6. The multi-agent cooperative control method under an unknown non-autonomous navigator based on event triggering as described in claim 5, characterized in that, Weighting function related to the distance between agents , The relative distance between the two followers Let be the edge set in the time-varying topological graph. For the initial edge set, This represents the unbounded potential energy function.

7. The multi-agent cooperative control method for an unknown non-autonomous navigator based on event triggering according to claim 5, characterized in that, The time-varying topology graph contains a directed spanning tree rooted at the leader node, and the sub-communication graph formed by the follower nodes is an undirected graph; communication edges are generated only when the real-time relative distance between two followers is less than the sensor's sensing radius.

8. The multi-agent cooperative control method under an unknown non-autonomous navigator based on event triggering according to claim 1, characterized in that, The follower is a single-integrator multi-agent system, including an aerial drone and a ground-based following vehicle.

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