Event-triggered fixed-time consensus control method for multi-unmanned aerial vehicle system

Abstract

The application provides an event-triggered multi-unmanned aerial vehicle system fixed time synchronization consistency control method, comprising the following steps: establishing a multi-unmanned aerial vehicle system model and a state equation under a fixed topology structure; designing a fixed time synchronization consistency control strategy based on an event trigger mechanism; segmentally designing an event trigger mechanism in the fixed time synchronization consistency control strategy, designing a trigger condition based on speed information when each unmanned aerial vehicle tracks a virtual speed state, and switching to a trigger condition based on position information when the speed of each unmanned aerial vehicle is consistent with the virtual speed; designing a constraint condition of the fixed time synchronization consistency control strategy and estimating the stop time of the unmanned aerial vehicle, so that all states of the multi-unmanned aerial vehicle system are simultaneously consistent within a fixed time. The application meets the urgent demand of system state synchronization convergence in different dimensions, and can effectively reduce the update frequency of the controller and the energy consumption of the system.

Description

Technical Field

[0001] This invention relates to a control method for multi-UAV systems, and more particularly to a fixed-time synchronization and consistency control method for multi-UAV systems based on event triggering. Background Technology

[0002] Unmanned aerial vehicles (UAVs) are powered, unmanned, controllable, and reusable aircraft capable of performing specific tasks. UAVs have enormous development potential in smart cities, the national economy, and the military. Compared to single UAVs, multiple UAVs can achieve a leap in mission execution capabilities through close collaboration among themselves. Consistency, as a fundamental research topic in multi-UAV systems, has attracted considerable interest from scholars. In the study of UAV consistency problems, convergence speed is widely recognized as an important performance indicator for evaluating consistency protocols. In addition, control cost is also a key factor in designing control protocols. Therefore, the consistency problem of multi-UAV systems has become a hot research topic in academia.

[0003] It should be noted that there are different types of consistency, such as exponential consistency, finite-time consistency, and fixed-time consistency. Compared with exponential and finite-time consistency, although the convergence time of fixed-time consistency does not depend on the initial state of the system, it cannot meet the urgent need for synchronous convergence of different dimensions of the system's states. For example, in a swarm system of drones, if they can reach the designated position and form the designated posture at the same time through information exchange to carry out a saturation attack on the target, efficiency can be effectively improved, thereby avoiding the time lag problem of individual drones far from the target reaching the equilibrium point.

[0004] In existing research on the consistency problem of multi-UAV systems, although all states of the UAV system can achieve consistency within a fixed time and are independent of the initial state of the system, this cannot meet the urgent need for simultaneous consistency across different dimensions of the system, and is subject to corresponding limitations in practical applications. Furthermore, in the consistency problem of multi-UAV systems, the controller design mostly considers continuous control, which is usually quite complex. This leads to high controller update frequency, high communication resource consumption, and high control costs. To date, most studies have only considered event triggering conditions in fixed-time consistency problems to save system energy. To further reduce the controller update frequency and system energy consumption, segmented design of event triggering mechanisms is of greater significance for achieving fixed-time synchronous consistency. Summary of the Invention

[0005] The purpose of this invention is to provide a fixed-time synchronization and consistency control method for multi-UAV systems based on event triggering. All states of the multi-UAV system achieve consistency simultaneously within a fixed time, meeting the urgent need for synchronous convergence of different dimensions of system states, while effectively reducing the update frequency of the controller and system energy consumption.

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] A method for fixed-time synchronization and consistency control of a multi-UAV system based on event triggering, comprising the following steps:

[0008] Step 1: Establish a multi-UAV system model and state equations under a fixed topology;

[0009] Step 2: Based on the multi-UAV system model and state equations, design a fixed-time synchronization and consistency control strategy based on an event-triggered mechanism;

[0010] Step 3: Design the event triggering mechanism in the fixed-time synchronization consistency control strategy in segments. When each UAV tracks its virtual speed state, design the triggering condition based on speed information; when the speed of each UAV reaches the same as its virtual speed, switch to the triggering condition based on position information.

[0011] Step 4: Design the constraints of the fixed-time synchronization and consistency control strategy and estimate the UAV rest time. The fixed-time synchronization and consistency control strategy is adopted to make all states of the multi-UAV system achieve consistency simultaneously within a fixed time.

[0012] Furthermore, the multi-UAV system model is as follows:

[0013] ;

[0014] in, and These represent the position and velocity state vectors of the unmanned aerial vehicle (UAV) system, respectively. It is the next displacement. It is span displacement. It is the altitude of the drone. For the control protocol to be designed, External interference to the system and These are the damping constants for position and velocity states, respectively. , This refers to the number of drones.

[0015] Furthermore, if let Then the state equation is:

[0016] ;

[0017] Wherein, parameter matrix , , , express The identity matrix.

[0018] Furthermore, a fixed-time synchronization consistency control strategy based on an event-triggered mechanism is designed, specifically including:

[0019] For any given moment, a virtual velocity is introduced:

[0020] ;

[0021] in , Indicates with drones A collection of drones with communication connections Indicates drone From drones Obtain information, For norm sign functions, and These are respectively norm sign functions and Power of 1 , ;

[0022] Design the speed tracking error at any given moment ;

[0023] Design an event-triggered fixed-time synchronization and consistency control protocol based on speed tracking error.

[0024] Furthermore, for the event trigger moment, a virtual velocity is introduced, and the velocity tracking error at any given time is designed, specifically including:

[0025] For each drone ,definition , ,in Indicates drone The When the secondary event is triggered, At that time, define a new virtual velocity:

[0026] ;

[0027] in , Indicates with drones A collection of drones with communication connections Indicates drone From drones Obtain information;

[0028] The velocity tracking error at the moment the event was triggered is: .

[0029] Furthermore, an event-triggered, fixed-time synchronization consistency control protocol is designed, specifically as follows:

[0030] ;

[0031] in For norm sign functions, , , It is a 2-norm. The derivative of the virtual velocity at the moment the event is triggered. The derivative at the moment the event is triggered. express transpose, , Control gain , , , , ,parameter , ,parameter , .

[0032] Furthermore, when each drone tracks its virtual speed state, triggering conditions based on speed information are designed, specifically including:

[0033] In drones Before the speed catches up with its virtual speed, the speed measurement error is defined as follows:

[0034] ,

[0035] in Indicates virtual speed The derivative;

[0036] The trigger function is constructed as follows:

[0037] ;

[0038] Among them, parameters The triggering parameter can be selected according to actual needs; Let be a known positive constant, and let its value be related to external disturbances to the system. satisfy , , , .

[0039] Furthermore, when the speed of each drone matches its virtual speed, the system switches to a location-based trigger condition, specifically including:

[0040] In drones Once the speed reaches its virtual speed, the position measurement error is defined as follows:

[0041] ;

[0042] The trigger function is constructed as follows:

[0043] ;

[0044] Where parameters For trigger parameters, , , .

[0045] Furthermore, the constraints for designing a fixed-time synchronous consistency control strategy include: the control gain must satisfy two conditions: (1) (2) And there exists a constant. , making the inequality Established, among which ,constant , It is the positive definite and unbounded Lyapunov function to be constructed.

[0046] Furthermore, the estimated drone downtime is:

[0047] .

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] (1) This invention introduces a norm sign function and uses the reverse calculation method to design a fixed-time synchronization consistency control strategy with a segmented event triggering mechanism. When each UAV tracks its virtual speed state, a triggering condition based on speed information is designed. When each UAV catches up with its virtual speed, the triggering condition is switched to a position information-based triggering condition. In practical applications, for a multi-UAV system with any initial state, the calculation method for achieving fixed-time synchronization consistency of multiple UAVs proposed in this invention can accurately calculate the resting time required to achieve synchronization consistency, and it is independent of the initial state of the UAV system.

[0050] (2) In practical applications, for multi-UAV systems, the control strategy based on the segmented event triggering mechanism proposed in this invention can effectively reduce the update frequency of the controller and the energy consumption of the system. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the complete technical solution of the present invention.

[0052] Figure 2 A diagram of the communication network of a drone.

[0053] Figure 3 Simulation diagram of the position trajectory of the UAV under the action of the controller.

[0054] Figure 4 Simulation diagram of the speed trajectory of the UAV under the action of the controller.

[0055] Figure 5 Speed ​​tracking error curve under the action of the controller.

[0056] Figure 6 Simulation diagram of event triggering intervals for each UAV under the control of the controller. Detailed Implementation

[0057] This invention innovatively proposes a fixed-time synchronization and consistency control method for multi-UAV systems based on event triggering. By introducing a norm sign function, a fixed-time synchronization and consistency control strategy with a segmented event triggering mechanism is designed using a back-calculation method. When each UAV tracks its virtual speed state, a triggering condition based on speed information is designed; when each UAV catches up with its virtual speed, the triggering condition switches to one based on position information. This method can effectively reduce the update frequency of the controller and the system energy consumption. Based on the above control strategy, a simple and lower-energy-consumption controller is designed to ensure the fixed-time synchronization and consistency of the multi-UAV system, so that the resting time of the control target can be accurately calculated and is independent of the initial state of the UAV system. Figure 1 As shown, the method specifically includes:

[0058] Step 1: Establish a multi-UAV system model with a fixed topology.

[0059] No. The unmanned model is described as follows:

[0060]

[0061] in It is the next displacement. It is span displacement. It is the altitude of the drone. It is ground speed. It is the angle of the flight path. It is the azimuth of the flight path. It is engine thrust. It is resistance. It's about quality. It is gravitational acceleration. It's lift. It is the track inclination angle. Using the feedback linearization method, the above UAV mathematical model can be rewritten as follows:

[0062]

[0063] in and These represent the position and velocity state vectors of the unmanned aerial vehicle (UAV) system, respectively. and These are the damping constants for position and velocity, respectively. Furthermore, if external disturbances are considered in a multi-UAV system, the above model can also be expressed as:

[0064]

[0065] in This is an external disturbance to the system. Let... , , , Then its state space can be represented as:

[0066]

[0067] Step 2: Design an event-triggered fixed-time synchronization consistency control strategy.

[0068] To ensure that the various states of multiple unmanned aerial vehicle systems achieve synchronization and consistency within a fixed time period, ,in yes The elements of the adjacency matrix of each drone. , Indicates drone From drones Obtain information; otherwise .make Indicates with drones A set of drones with communication connections is defined by the Laplace matrix. ,satisfy , ; .

[0069] For any given moment, introduce a virtual velocity:

[0070]

[0071] in For norm sign functions, and These are respectively norm sign functions and Power of 1 Define the velocity tracking error at any given time. .

[0072] For each drone ,definition , ,in Indicates drone The When the secondary event is triggered, When, defined:

[0073]

[0074] in The speed tracking error at the moment the event is triggered is .

[0075] Therefore, the following event-triggered, fixed-time synchronization consistency control protocol is designed:

[0076]

[0077] in , , It is a 2-norm. The derivative of the virtual velocity at the moment the event is triggered. The derivative at the moment the event is triggered. express transpose, , , To control the gain, , .

[0078] Step 3: Design the event triggering mechanism in segments.

[0079] To address the issues of high update frequency and high communication resource consumption of the system controller, a segmented event triggering mechanism was designed. When each UAV tracks its virtual speed state, a trigger condition based on speed information is implemented; when the speed of each UAV matches its virtual speed, the trigger condition switches to one based on position information. Details are as follows:

[0080] (1) In drones Before the speed catches up with its virtual speed, define the speed measurement error:

[0081]

[0082] in Indicates virtual speed The derivative;

[0083] Construct the trigger function:

[0084]

[0085] in For trigger parameters, You can choose according to your actual needs; Let be a known positive constant, and let its value be related to external disturbances to the system. satisfy , , , .

[0086] (2) In drones Once the speed reaches its virtual speed, the position measurement error is defined as follows:

[0087]

[0088] Construct the trigger function:

[0089]

[0090] in For trigger parameters, , , .

[0091] Step 4: Propose a method for achieving consistency of all states of a multi-UAV system within a fixed time.

[0092] Under the event-triggered fixed-time synchronization and consistency control strategy designed in step 2, if the control gain satisfies two conditions: (1) (2) And there exists a constant. , making the inequality Established, among which , If the Lyapunov function to be constructed is positive definite and unbounded, then the UAV system can achieve fixed-time synchronization consistency. The estimation method for the pause time is as follows:

[0093]

[0094] Step 5: Verify the effectiveness of the fixed-time synchronization consistency control protocol.

[0095] (1) Proof tending to within a fixed time period Construct the following Lyapunov function:

[0096]

[0097] Calculate the Lyapunov function The derivative of is obtained as follows:

[0098]

[0099] Based on step 4, the pause time for the drone's speed tracking of its virtual speed can be calculated as follows:

[0100]

[0101] Therefore, we can obtain virtual speed Tracking error It converges to 0.

[0102] (2) When When the time comes, construct the following Lyapunov function:

[0103]

[0104] in Represents the Kronecker product;

[0105] Calculate the Lyapunov function The derivative of is obtained as follows:

[0106]

[0107] in It is the smallest non-zero eigenvalue of the Laplacian matrix.

[0108] Based on step 4, the consistent resting time for the drone's position can be calculated as follows:

[0109]

[0110] (3) It has been proven through step (2) that It converges to the equilibrium point within a fixed time; therefore, it is only necessary to prove that... If the ratio of any two elements is a constant, it can be proven that each drone... It can achieve synchronization and consistency at fixed intervals. Differentiating, we get:

[0111]

[0112] Will Substituting into the above equation, we get... ,Right now It is a constant.

[0113] In summary, based on step 4, the effectiveness of the fixed-time synchronization consistency control protocol can be demonstrated. Simultaneously, the rest time required for multiple UAVs to achieve fixed-time synchronization consistency is calculated as follows:

[0114]

[0115] Example

[0116] Consider a multi-UAV system consisting of 5 UAVs to verify the correctness of the theoretical analysis. The dynamic equations of the UAVs are expressed as:

[0117]

[0118] in and They represent the first The position and speed of the drone , It is a control input. It's external interference. The communication network between drones, such as... Figure 2 As shown.

[0119] The initial state of the randomly selected drone is... , , , , The initial velocity is , , , , The control gain is set to... , , , , To calculate the upper bound of the pause time, we set... , , , The trigger function parameter is set to , The calculated suspension period is... The position and velocity trajectories of the five drones are as follows: Figure 3 , 4 As shown. The speed tracking error trajectories of the five drones are as follows. Figure 5 As shown. The trigger time interval under the action of the controller is as follows. Figure 6As shown. (Through) Figures 3 to 6 It can be seen that the calculation method for achieving fixed-time synchronization consistency of multiple UAVs proposed in this invention can accurately calculate the rest time required to achieve synchronization consistency.

[0120] The technical solutions of the present invention are not limited to the specific embodiments described above. Any technical modifications made in accordance with the technical solutions of the present invention fall within the protection scope of the present invention.

Claims

1. A fixed-time synchronization and consistency control method for a multi-UAV system based on event triggering, characterized in that, include: Step 1: Establish a multi-UAV system model and state equations under a fixed topology; Step 2: Based on the multi-UAV system model and state equations, design a fixed-time synchronization and consistency control strategy based on an event-triggered mechanism; Step 3: Design the event triggering mechanism in the fixed-time synchronization consistency control strategy in segments. When each UAV tracks its virtual speed state, design the triggering conditions based on speed information. When the speed of each drone matches its virtual speed, switch to a trigger condition based on location information; Step 4: Design the constraints of the fixed-time synchronization and consistency control strategy and estimate the UAV rest time. The fixed-time synchronization and consistency control strategy is adopted to make all states of the multi-UAV system achieve consistency simultaneously within a fixed time.

2. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 1, characterized in that, The multi-UAV system model is as follows: ； in, and These represent the position and velocity state vectors of the unmanned aerial vehicle (UAV) system, respectively. It is the next displacement. It is span displacement. It is the altitude of the drone. For the control protocol to be designed, External interference to the system and These are the damping constants for position and velocity states, respectively. , This refers to the number of drones.

3. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 2, characterized in that, The state equation is: ； in, , parameter matrix , , , express The identity matrix.

4. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 3, characterized in that, Design a fixed-time synchronization consistency control strategy based on an event-triggered mechanism, specifically including: For any given moment, a virtual velocity is introduced: ； in , Indicates with drones A collection of drones with communication connections Indicates drone From drones Obtain information, , For norm sign functions, and These are respectively norm sign functions and Power of 1 ; Design the speed tracking error at any given moment ; Design an event-triggered fixed-time synchronization and consistency control protocol based on speed tracking error.

5. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 4, characterized in that, For the event trigger moment, a virtual velocity is introduced, and the velocity tracking error at any given time is designed, specifically including: For each drone ,definition , ,in Indicates drone The When the secondary event is triggered, At that time, define a new virtual velocity: ； in , Indicates with drones A collection of drones with communication connections Indicates drone From drones Obtain information; The velocity tracking error at the moment the event was triggered is: .

6. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 5, characterized in that, Design an event-triggered, fixed-time synchronization consistency control protocol, specifically as follows: ； in For norm sign functions, , , It is a 2-norm. The derivative of the virtual velocity at the moment the event is triggered. The derivative at the moment the event is triggered. express transpose, , Control gain , , , , ,parameter , ,parameter , .

7. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 6, characterized in that, When each drone tracks its virtual speed state, trigger conditions based on speed information are designed, specifically including: In drones Before the speed catches up with its virtual speed, the speed measurement error is defined as follows: ， in Indicates virtual speed The derivative; The trigger function is constructed as follows: ； Among them, parameters For triggering parameters; Let be a known positive constant, and let its value be related to external disturbances to the system. satisfy , , , .

8. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 7, characterized in that, When the speed of each drone matches its virtual speed, the system switches to a location-based trigger condition, which includes: In drones Once the speed reaches its virtual speed, the position measurement error is defined as follows: ； The trigger function is constructed as follows: ； Where parameters For trigger parameters, , , .

9. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 8, characterized in that, The constraints for designing a fixed-time synchronous consistency control strategy include: the control gain must satisfy two conditions: (1) (2) And there exists a constant. , making the inequality Established, among which ,constant , It is the positive definite and unbounded Lyapunov function to be constructed.

10. The event-triggered fixed-time synchronization and consistency control method for a multi-UAV system according to claim 9, characterized in that, The estimated downtime for the drone is: ； in It is the smallest non-zero eigenvalue of the Laplacian matrix.

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