A high-precision specified time consistency control method based on dynamic event triggering

Abstract

The application discloses a high-precision specified time consistency control method based on dynamic event triggering, and comprises the following steps: step 1, designing a full-distributed observer based on time-varying gain; step 2, designing a control rate of a first follower based on a parameter Lyapunov equation; step 3, selecting a controller update time of the first follower based on a dynamic event triggering or self-triggering mechanism of an internal dynamic variable according to requirements; and step 4, calculating the expression of the minimum triggering time interval according to the dynamic event triggering or self-triggering mechanism designed in step 3. The method can not only realize the consistency of a multi-agent system within a specified time set by any user, but also introduces a dynamic variable to adjust the triggering mechanism, thereby significantly reducing the communication and control update times on the premise of ensuring no Zeno phenomenon, and has important engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control and relates to an event-triggered control method, specifically a time-consistent control method based on dynamic event triggering. Background Technology

[0002] As typical representatives of multi-agent cooperative control systems, unmanned vehicle fleets, drone swarms, and networked unmanned surface vessels must balance complex nonlinear dynamic characteristics with dynamically changing environmental constraints to meet the requirements of high coordination, high real-time performance, and high safety in mission execution. Meanwhile, with the development and cross-penetration of artificial intelligence and network communication technologies, single-agent intelligent operation modes are becoming less common, replaced by complex network systems with multi-agent cooperative operations. The introduction of wireless communication networks and sensor networks has significantly enhanced the interconnectivity between agents and led to more frequent information exchange. However, network characteristics also bring challenges related to limited communication resources; continuous communication and control not only consume significant amounts of energy and bandwidth but can also lead to channel congestion. Therefore, the specified-time consistency control method based on fully distributed dynamic event triggering, with its advantages such as pre-set convergence time independent of the initial state, saving communication resources, no need for continuous state monitoring (for self-triggered systems), and strong anti-interference capabilities, perfectly aligns with the increasingly complex real-time cooperative performance requirements of nonlinear multi-agent systems. Therefore, conducting related algorithm research is of significant application value. Summary of the Invention

[0003] To further improve the cooperative control performance of nonlinear multi-agent systems in network environments, this invention provides a high-precision, time-specified consistency control method based on dynamic event triggering. This method not only achieves consistency within any user-defined timeframe but also introduces dynamic variables to adjust the triggering mechanism. While ensuring the absence of the Zeno phenomenon, it significantly reduces the number of communication and control updates, possessing significant engineering application value.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A high-precision time-specified consistency control method based on dynamic event triggering includes the following steps:

[0006] Step 1: Design a fully distributed observer based on time-varying gain:

[0007]

[0008] in, For the first , A distributed observer state designed by followers, For the number of followers, For followers To followers The communication weight or connection status, Specify the time adjustment function;

[0009] Step 2: Design the first Control law of a follower based on the parametric Lyapunov equation:

[0010] ;

[0011] in, For the first The first follower in the The system state at the moment of the next trigger. For the first The first follower in the The state of the distributed observer at the next trigger moment. For the first Solutions to Lyapunov equations with follower parameters In time The value at time, ;

[0012] Step 3: Select the appropriate option based on your needs. The controller update time for each follower based on a dynamic event-triggered or self-triggered mechanism using internal dynamic variables. :

[0013] Dynamic event triggering mechanism:

[0014]

[0015] in:

[0016] ,

[0017] , Internal dynamic variables Its initial value , , where n is the state dimension of a single follower, and the nth... Consistency tracking error between followers and leaders ;

[0018] Dynamic self-triggering mechanism:

[0019]

[0020] in:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Step 4: Based on the dynamic event triggering or self-triggering mechanism designed in Step 3, calculate the following expression for the minimum triggering time interval:

[0030] Dynamic event triggering mechanism:

[0031]

[0032] Dynamic self-triggering mechanism:

[0033]

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] 1. The method proposed in this invention utilizes time-varying gain. The design reduces the uniform convergence time of nonlinear multi-agent systems. It can be preset arbitrarily by the user and is completely independent of the initial state of the system, which solves the limitation of traditional finite-time control that depends on the initial value.

[0036] 2. The method proposed in this invention introduces internal dynamic variables. Compared to static triggering mechanisms, the design of the triggering mechanism significantly reduces unnecessary communication transmissions and controller updates. It also ensures that the minimum triggering time interval is positive and designable, theoretically eliminating the Zeno phenomenon of infinitely rapid triggering and guaranteeing the feasibility of physical implementation.

[0037] 3. The dynamic self-triggering protocol proposed in this invention only needs to use the information of the most recent triggering time to determine the next triggering time, avoiding the high-frequency sampling burden and computational consumption of sensors caused by real-time continuous state monitoring, and is suitable for practical engineering applications with limited sensor resources.

[0038] 4. This invention provides a designable minimum trigger time interval parsing expression, allowing engineers to directly select the minimum trigger time interval based on hardware bandwidth limitations. Attached Figure Description

[0039] Figure 1 A flowchart illustrating a high-precision time consistency control method based on dynamic event triggering.

[0040] Figure 2 The state trajectory of the system in Case 1.

[0041] Figure 3 This is the state trajectory of the system in Case 2.

[0042] Figure 4 These are the control signals for the systems in Case 1 and Case 2.

[0043] Figure 5 For the system of Case 1 in different The state trajectory below. Detailed Implementation

[0044] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0045] This invention provides a high-precision time-specified consistency control method based on dynamic event triggering, such as... Figure 1 As shown, the method includes the following steps:

[0046] Step 1: Design a fully distributed observer based on time-varying gain. The specific steps are as follows:

[0047] Step 11: Consider having a leader and A nonlinear multi-agent system consisting of several followers.

[0048] The dynamics of the leader system can be expressed as:

[0049] (1);

[0050] in, The derivative of the leader system variable. Represents the nonlinear term of the leader system. Dimensions representing the system state Represents time, For the state variables of the leader system.

[0051] The dynamics of each follower system can be expressed as:

[0052] (2);

[0053] in, Let i be the state variable of the i-th follower system. Let be the derivative of the i-th follower system variable. Let represent the nonlinear term of the i-th follower system, and satisfy . ,here It is a constant, where , Represents time, Dimensions representing the system state As the control input of the system, matrix and The specific form of the system's state matrix is ​​shown below:

[0054] ,

[0055] Step 12: Design a fully distributed observer based on time-varying gain:

[0056] (3);

[0057] in, For the first , A distributed observer state designed by followers, For the number of followers, As a representative of the followers To followers The communication weight or connection status, For the specified time adjustment function:

[0058] (4);

[0059] It is a time-varying parameter, here For any specified time and Its initial value for:

[0060]

[0061] in, The convergence time preset for the user. , , Dimensions representing the system state , , , For when Solution of time-parametric Lyapunov equation The value, These represent the largest eigenvalue, the largest value, and the diagonal matrix, respectively.

[0062] Step 13: Repeat step 12 until all follower distributed observer designs are complete;

[0063] Step 2: Design the first The control law of a follower based on the parametric Lyapunov equation is as follows:

[0064] Step 21: Design the control law based on the parametric Lyapunov equation, specifically expressed as:

[0065] (5);

[0066] Among them, the superscript mark For matrix transpose, for example represent transpose, For the first The first follower in the The system state at the moment of the next trigger. For the first The first follower in the The state of the distributed observer at the next trigger moment. For the first Solutions to Lyapunov equations with follower parameters In time The value at time,

[0067] (6);

[0068] Step 22: Repeat step 21 until all follower control rates are designed.

[0069] observe From the definition (that is, formula (4)), we can see that, At any time It tends towards positive infinity. That is... It tends towards positive infinity; therefore, the feedback controller based on the event-triggered mechanism of equations (2), (3), and (5) is physically unrealizable. Furthermore, In time zone The inner region is not defined, causing the controller (5) to be in the time region. The internal structure is also not defined. To design a physically realizable controller, a... Design methodology:

[0070]

[0071] in, It is a sufficiently large constant, and is sufficiently close to Time time The value of .

[0072] Step 3: Select the appropriate option based on your needs. The controller update time for each follower based on a dynamic event-triggered or self-triggered mechanism using internal dynamic variables. The specific steps are as follows:

[0073] Step 31: The dynamic event-triggered mechanism is suitable for networked multi-agent systems with abundant sensing capabilities but strictly limited communication bandwidth. The dynamic self-triggered mechanism is suitable for practical engineering deployments with highly limited hardware resources; the triggering mechanism should be selected according to requirements.

[0074] Step 32: Construct internal dynamic variables:

[0075] (7);

[0076] in , , , , , where n is the state dimension of a single follower, and the nth... Consistency tracking error between followers and leaders ;

[0077] Step 33: Design the event triggering mechanism:

[0078] 1. Dynamic event triggering mechanism:

[0079] (8);

[0080] 2. Dynamic self-triggering mechanism

[0081] (9);

[0082] in:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] Step 34: Repeat step 33 until all follower controller update time designs are complete.

[0092] Step 4: Based on the event triggering mechanism designed in Step 3, calculate the expression for the minimum triggering time interval. The specific steps are as follows:

[0093] Step 41: Calculate the expression for the minimum trigger time interval based on the selected triggering mechanism:

[0094] 1. Minimum triggering interval for dynamic event triggering mechanism The expression is:

[0095] (10);

[0096] 2. Minimum triggering interval for dynamic self-triggering mechanism The expression is:

[0097] (11);

[0098] Step 42: Repeat step 41 until the minimum trigger interval for all followers has been calculated.

[0099] This invention overcomes the limitations of traditional finite-time control that relies on initial values, achieving consistent convergence within a specified time. At the control level, it not only avoids the high-frequency sampling and computational burden of real-time state monitoring and significantly reduces unnecessary communication interactions, but also provides a designable analytical expression for the minimum trigger time interval, theoretically circumventing the Zeno phenomenon and possessing significant engineering application value.

[0100] Example:

[0101] This embodiment uses a single-link robotic arm system control as a specific implementation method, and designs its control gain using the method of this invention. Specifically, it includes the following steps:

[0102] Step 1: Using definition transformation, the single-link manipulator system is converted into a general nonlinear system model. The specific process is as follows:

[0103] Consider the following relative dynamics model of a single-link manipulator system:

[0104]

[0105] in, It is an angular position. and It is the moment of inertia. It is the spring constant. It is the total mass. It's distance. It is the torque input, which is the control input.

[0106] definition , and select and Then, the single-link manipulator system can be written in the following form:

[0107] .

[0108] Define afterwards This system can be written in the form of system (12) (13), that is:

[0109] (12);

[0110] (13);

[0111] matrix and The specific form of the system's state matrix is ​​shown below:

[0112] ;

[0113] The nonlinear term satisfies here ,in , Dimensions representing the system state.

[0114] Step 12: Design a fully distributed observer based on time-varying gain:

[0115] (14);

[0116] in, For the first , The state of a distributed observer designed with N followers, where N is the number of followers. As a representative of the followers To followers The communication weight or connection status, For the specified time adjustment function:

[0117] (15);

[0118] It is a time-varying parameter, here For any specified time and Its initial value for:

[0119]

[0120] in, The convergence time preset for the user, It is close enough to Time time The value, , , Dimensions representing the system state , , , For when Solution of time-parametric Lyapunov equation The value, These represent the largest eigenvalue, the largest value, and the diagonal matrix, respectively.

[0121] Step 13: Repeat step 12 until all follower distributed observer designs are complete;

[0122] Step 2: Design the first The control law of a follower based on the parametric Lyapunov equation is as follows:

[0123] Step 21: Design the control law based on the parametric Lyapunov equation, specifically expressed as:

[0124] (16);

[0125] Among them, the superscript mark For matrix transpose, for example represent The transpose of, where, For the first The first follower in the The system state at the moment of the next trigger. For the first The first follower in the The state of the distributed observer at the next trigger moment. For the first Solutions to Lyapunov equations with follower parameters In time The value at time,

[0126] (17);

[0127] Step 22: Repeat step 21 until all follower control rates are designed.

[0128] Step 3: Select the appropriate option based on your needs. The controller update time for each follower based on a dynamic event-triggered or self-triggered mechanism using internal dynamic variables. The specific steps are as follows:

[0129] Step 31: The dynamic event-triggered mechanism is suitable for networked multi-agent systems with abundant sensing capabilities but strictly limited communication bandwidth. The dynamic self-triggered mechanism is suitable for practical engineering deployments with highly limited hardware resources; the triggering mechanism should be selected according to requirements.

[0130] Step 32: Construct internal dynamic variables and:

[0131] (18);

[0132] in , , , , , where n is the state dimension of a single follower, and the nth... Consistency tracking error between followers and leaders ;

[0133] Step 32: Design the event triggering mechanism:

[0134] 1. Dynamic event triggering mechanism:

[0135] (19);

[0136] 2. Dynamic self-triggering mechanism

[0137] (20);

[0138] in:

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] Step 32: Repeat step 32 until all follower controller update time designs are complete.

[0148] Step 4: Based on the event triggering mechanism designed in Step 3, calculate the expression for the minimum triggering time interval as follows. The specific steps are as follows:

[0149] Step 41: Calculate the expression for the minimum trigger time interval based on the selected triggering mechanism:

[0150] 1. Dynamic event triggering mechanism:

[0151] (twenty one);

[0152] 2. Dynamic self-triggering mechanism:

[0153] (twenty two);

[0154] Step 42: Repeat step 41 until the minimum trigger time interval for all followers is calculated; then perform simulation verification.

[0155] In the simulation, the initial state is chosen as... , , , , The initial values ​​for the distributed observers are randomly selected as follows: , , Sampling interval 0.0001s, selected convergence time Consider two different cases: Case 1: Constructing the dynamic event-triggered controller in this invention; Case 2: Constructing the dynamic self-triggered controller in this invention.

[0156] Table 1

[0157]

[0158] Table 2

[0159]

[0160] Depend on Figures 2-4 It can be seen that the triggering mechanisms designed in Case 1 and Case 2 are able to This achieves system consistency while saving communication resources. Table 1 lists the average event interval and trigger count for Case 1 and Case 2, demonstrating that the dynamic self-triggered mechanism is more conservative than the dynamic event-triggered mechanism. Furthermore, Figure 5Table 2 also shows the differences The simulation results of Case 1, which is related to the value, show that each follower can adapt to different Designed to track leaders, and the time between events will change. It increases with the increase of.

Claims

1. A high-precision time-specified consistency control method based on dynamic event triggering, characterized in that... The method includes the following steps: Step 1: Design a fully distributed observer based on time-varying gain: in, For the first , A distributed observer state designed by followers, For the number of followers, For followers To followers The communication weight or connection status, Specify the time adjustment function; Step 2: Design the first Control law of a follower based on the parametric Lyapunov equation: ； in, For the first The first follower in the The system state at the moment of the next trigger. For the first The first follower in the The state of the distributed observer at the next trigger moment. For the first Solutions to Lyapunov equations with follower parameters In time The value at time, ; Step 3: Select the appropriate option based on your needs. The controller update time for each follower based on a dynamic event-triggered or self-triggered mechanism using internal dynamic variables. : Dynamic event triggering mechanism: in: ， , Internal dynamic variables Its initial value , , where n is the state dimension of a single follower, and the nth... Consistency tracking error between followers and leaders ; Dynamic self-triggering mechanism: in: Step 4: Based on the dynamic event triggering or self-triggering mechanism designed in Step 3, calculate the following expression for the minimum triggering time interval: Dynamic event triggering mechanism: Dynamic self-triggering mechanism: 。 2. The high-precision time-specified consistency control method based on dynamic event triggering according to claim 1, characterized in that... The specific steps of step 1 are as follows: Step 11: Consider having a leader and A nonlinear multi-agent system consisting of several followers, wherein: The dynamics of the leader system are expressed as: ； The dynamics of each follower system are represented as follows: ； in, The derivative of the leader system variable. For the state variables of the leader system, Represents the nonlinear term of the leader system. Let be the derivative of the i-th follower system variable. Let i be the state variable of the i-th follower system. For the system's control input, The matrix represents the nonlinear term of the i-th follower system. and The specific form of the system's state matrix is ​​shown below: ， Step 12: Design a fully distributed observer based on time-varying gain: ； in, For the first , A distributed observer state designed by followers, For the number of followers, As a representative of the followers To followers The communication weight or connection status, Specify the time adjustment function; Step 13: Repeat step 12 until all follower distributed observer designs are complete.

3. The high-precision time-specified consistency control method based on dynamic event triggering according to claim 2, characterized in that... The , Dimensions representing the system state Represents time; And satisfy ,here It is a constant, where .

4. The high-precision time-consistency control method based on dynamic event triggering according to claim 1 or 2, characterized in that... The The specific form is as follows: ， in, The convergence time preset for the user. It is close enough to Time time The value, , , Dimensions representing the system state , , , For when Solution of time-parametric Lyapunov equation The value, These represent the largest eigenvalue, the largest eigenvalue, and the diagonal matrix, respectively. , .

5. The high-precision time-specified consistency control method based on dynamic event triggering according to claim 1, characterized in that... The specific steps of step 2 are as follows: Step 21: Design the control law based on the parametric Lyapunov equation, specifically expressed as: ； Among them, the superscript mark For matrix transpose, For the first The first follower in the The system state at the moment of the next trigger. For the first The first follower in the The state of the distributed observer at the next trigger moment. For the first Solutions to Lyapunov equations with follower parameters In time The value at time, ； Step 22: Repeat step 21 until all follower control rates are designed.

6. The high-precision time-specified consistency control method based on dynamic event triggering according to claim 1, characterized in that... The specific steps of step 3 are as follows: Step 31: Construct internal dynamic variables: ； in , , , , , where n is the state dimension of a single follower, and the nth... Consistency tracking error between followers and leaders ; Step 32: Design the event triggering mechanism: Dynamic event triggering mechanism: ； Dynamic self-triggering mechanism: ； in: Step 33: Repeat step 32 until all follower controller update time designs are complete.

7. The high-precision time-specified consistency control method based on dynamic event triggering according to claim 1, characterized in that... The specific steps of step 4 are as follows: Step 41: Calculate the expression for the minimum trigger time interval based on the selected triggering mechanism: Minimum triggering interval for dynamic event triggering mechanism The expression is: ； Minimum trigger interval for dynamic self-triggering mechanism The expression is: ； Step 42: Repeat step 41 until the minimum trigger interval for all followers has been calculated.

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