Pre-defined sequence synchronization control method based on event triggering mechanism

Abstract

The invention provides a predefined sequence synchronization control method based on an event trigger mechanism, belongs to the technical field of automatic control and networked control, and solves the problems that the existing control method cannot realize stable convergence of system state components according to a predefined sequence and the communication overhead is relatively large. Comprising the following steps: step 1, defining and describing synchronization stability and dynamic characteristics of a predefined sequence; 2, on the basis of the predefined sequence synchronization stability and the dynamic feature definition, setting sufficient conditions for the system to realize the predefined sequence synchronization stability; 3, designing a predefined sequence synchronization control protocol based on an event trigger mechanism for a second-order continuous system on the basis that the system realizes the predefined sequence synchronization stability; and step 4, applying the designed predefined sequence synchronization control protocol based on the event trigger mechanism to the target system to realize predefined sequence synchronization control of the system.

Description

Technical Field

[0001] The invention relates to a predefined sequence synchronization control method based on an event trigger mechanism, belonging to the technical field of automatic control and network control. Background Art

[0002] In modern complex control systems, achieving stable convergence of system states within a specified time is an important research direction. Finite time control, fixed time control and predefined time control are currently widely used time control technologies, but these methods still have some shortcomings in practical applications.

[0003] Finite time control is a classic method, which is characterized by making the system state converge to the target point within a finite time. Although this method can meet certain engineering needs, its convergence time usually depends on the initial state information. This dependence limits the applicability of finite time control in complex environments or scenarios with unknown initial conditions. In order to overcome this limitation, fixed time control technology came into being. The characteristic of fixed time control is that the convergence time is independent of the initial state, which improves the reliability of control to a certain extent. However, the convergence time of the fixed time control method is still complexly related to multiple system parameters, making the design and adjustment process more difficult. For this reason, predefined time control technology was proposed. This method allows users to pre-set the convergence time according to actual needs without considering the complexity of system parameters too much, which greatly improves the flexibility of the control strategy. However, traditional predefined time control is mostly used for single state convergence problems, and there is still a lack of effective solutions for scenarios where multiple state components need to converge in sequence.

[0004] In practical engineering applications, sequential convergence of system states is a common requirement. For example, during the landing of a drone, the landing operation usually needs to be completed in the order of lowering the altitude, decelerating, hovering, and landing to ensure the safety and reliability of the operation. Similarly, in robot operation tasks, multiple mechanical joints need to be adjusted to the specified positions in sequence to ensure the accuracy of the operation. In these scenarios, the state components not only need to converge within the preset time, but must also be completed strictly in a predefined order. However, most existing time control methods focus on the overall convergence time of the state and cannot meet the needs of sequential control convergence.

[0005] In addition, with the widespread application of networked control systems, the communication efficiency of signal transmission has become a key issue that limits control performance. Traditional continuous sampling or periodic sampling control methods will lead to unnecessary frequent signal transmission, increase the communication burden, and may even cause channel congestion, thus affecting the real-time and stability of the system. In order to improve communication efficiency, event-triggered control technology has received widespread attention in recent years. This method significantly reduces the communication frequency by designing trigger conditions to send control signals only under specific conditions. However, existing event-triggered control methods mostly focus on the control of a single state variable, and lack support for scenarios where multiple states need to converge in sequence. Summary of the invention

[0006] In order to solve the problems that the existing control method cannot achieve stable convergence of system state components in a predefined sequence and the communication overhead is large, the present invention further proposes a predefined sequence synchronization control method based on an event trigger mechanism.

[0007] The technical solution adopted by the present invention to solve the above-mentioned problem is: the present invention comprises the following steps:

[0008] Step 1: Define and describe the synchronization stability and dynamic characteristics of the predefined sequence;

[0009] Step 2: Based on the definition of predefined sequence synchronization stability and dynamic characteristics, set sufficient conditions for the system to achieve predefined sequence synchronization stability;

[0010] Step 3: On the basis of achieving the synchronization stability of the predefined sequence in the system, a predefined sequence synchronization control protocol based on the event trigger mechanism is designed for the second-order continuous system;

[0011] Step 4: Apply the designed predefined sequence synchronization control protocol based on event trigger mechanism to the target system to realize the predefined sequence synchronization control of the system.

[0012] Preferably, the definition and description of the synchronization stability of the predefined sequence in step 1 specifically includes:

[0013] For the system Where f(0) = 0, x(0) = x 0 , function f: is a nonlinear function. If the predefined sequence synchronization stability condition 1 and the predefined sequence synchronization stability condition 2 are satisfied, and the convergence time of all state components in the system meets the predefined time System Synchronous stability with predefined sequences.

[0014] Preferably, the first predefined sequence synchronization stability condition is: In a finite time, the system state vector x(t) converges to the origin;

[0015] The second predefined sequence synchronization stability condition is: the system state component x = [x 1 ,x 2 ,…,x n ] T According to the predefined convergence sequence S = [s 1 ,s 2 ,…,s n ] converges to the origin, where s i ∈{1,2,…,m},m≤n;

[0016] system The expression of the convergence time relationship of each state component is:

[0017]

[0018] In formula (1), T i (x 0 ) is the system state component x i The time required to converge from the initial state to the origin, T j (x 0 ) is the system state component x j The time required to converge from the initial state to the origin.

[0019] Preferably, the definition and description of the dynamic features in step 1 specifically includes:

[0020] For the system Where f(0) = 0, x(0) = x 0 , if the dynamic characteristic conditions are met, the system It has dynamic characteristics;

[0021] The expression of dynamic characteristic condition is:

[0022]

[0023] In formula (2), is the weight matrix, for i,j∈{1,2,…,n}, when i > j When , the ratio of the corresponding state components It decreases monotonically with time; when i = j When , the ratio of the corresponding state components is a constant value, x(t) is the state value of the system at time t, is the derivative of x(t) with respect to the time variable t.

[0024] Preferably, step 2 specifically includes:

[0025] For the system Where f(0) = 0, x(0) = x 0 , if the implementation conditions 1 and 2 are met, the system Able to c >0 according to the sequence S = [s 1 ,s 2 ,…,s n ] The state components specified by the convergence order achieve predefined time synchronization stability;

[0026] The first condition is that there exists a Lyapunov function V(x(t)) such that the system satisfies in, is the derivative of the Lyapunov function V(x(t)) with respect to the time variable t, α 1 is the first parameter, α 1 >0,α 2 is the second parameter, α 2 <0, p is the third parameter, p>1, q is the fourth parameter, 0<q<1, and

[0027] The second condition is: system With dynamic characteristics and weight matrix ε=diag{ε 1 ,ε 2 ,…,ε n}satisfy Among them, i,j∈{1,2,…,n}.

[0028] Preferably, step 3 specifically includes:

[0029] Step 3.1: According to the control requirements, determine the predefined convergence sequence S = [s 1 ,s 2 ,…,s n ] and the total convergence time T c , establish a second-order system dynamics model Where p(t) is the position of the system,

[0030] is the derivative of p(t) with respect to the time variable t, v(t) is the velocity of the system,

[0031] is the derivative of v(t) with respect to the time variable t, u(t) is the control input of the system,

[0032] Step 3.2: Design the sliding mode variable of the system dynamics model as s(t)=v(t)+ss (t);

[0033] Step 3.3: Design a predefined sequence synchronization control protocol u(t)=w(t k ), where u(t) represents the actual control signal acting on the system at time t, t k Indicates the time when the event is triggered;

[0034] Step 3.4: Define the event trigger error value as e(t)=w(t)-u(t), and design the event trigger protocol in the predefined sequence synchronization control protocol;

[0035] s s (t) The expression of the switching law is:

[0036]

[0037] In formula (3), r 2 is the first constant, r 2 >1,g 2 is the second constant, l 1 is the fifth parameter,

[0038] l 2 is the sixth parameter,

[0039] l 1 and l 2 The value of ensures that s s and The continuity of T c2 <T c is the predefined convergence time, ∈ is the weight matrix, The weight matrix ∈ satisfies when s i <s j hour

[0040] i > j , when s i =s j hour i = j , i,j∈{1,2,…,n},

[0041] ∈ m is the smallest diagonal element of the weight matrix ∈, triggering the sliding mode vector σ is a constant;

[0042] The expression of w(t) is:

[0043]

[0044] In formula (4), T c1 is the predefined convergence time, r 1 is the third constant, r 1 >1,g 1 is the fourth constant, 0<g 1 <1, c 1 is the fifth constant, c 1 >0,c 2 is the sixth constant, c 2 >0, for The derivative with respect to the time variable t;

[0045] The expression of the event triggering protocol is:

[0046]

[0047] In formula (5), is the seventh constant, is the eighth constant.

[0048] The beneficial effects of the present invention are:

[0049] (1) The present invention designs a control protocol that can make the system dynamically conform to this characteristic, so that the system state can converge in sequence according to a predefined order. With the help of this characteristic, the various state components of the system can gradually reach the target value within a predefined time and with a predefined priority according to the task requirements, thereby solving the problem that traditional control methods cannot meet the requirements of sequential convergence.

[0050] (2) The present invention effectively reduces unnecessary signal transmission in the control process by introducing an event trigger mechanism into the design of the control protocol, thereby optimizing the communication efficiency of the system. Compared with the traditional continuous sampling or periodic sampling method, this mechanism triggers the signal only when the system status meets certain conditions. This design significantly reduces the communication burden, making the present invention suitable for application scenarios with limited communication resources.

[0051] (3) The present invention effectively avoids the occurrence of Zeno (continuous triggering of the event triggering mechanism) behavior by reasonably setting the event triggering conditions and thresholds. Thanks to this design, the system can maintain stable operation while ensuring communication efficiency and ensure the accuracy of the sequential convergence process, thereby improving the reliability of system operation.

[0052] (4) The control theorem proposed in the present invention has wide applicability and is not limited to the designed and verified second-order systems, but can be extended to general nonlinear systems. This scalability enables the present invention to be flexibly adjusted according to specific needs and adapt to more complex scenarios, showing strong practical value and versatility. At the same time, the present invention provides a new solution to the problems of sequential convergence of multi-state components and optimization of communication efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A flowchart of a predefined sequence synchronization control method based on an event trigger mechanism provided by the present invention;

[0054] Figure 2 A curve diagram of the position component change of the system provided by the present invention;

[0055] Figure 3 A curve diagram showing the change in ratio of position components of the system provided by the present invention;

[0056] Figure 4 A schematic diagram of the triggering interval of the event triggering mechanism provided by the present invention. DETAILED DESCRIPTION

[0057] Specific implementation method 1: Combination Figure 1-4 To illustrate this embodiment, Figure 1 As shown, the steps of a predefined sequence synchronization control method based on an event trigger mechanism described in this embodiment include:

[0058] S1: Define and describe the synchronization stability and dynamic characteristics of the predefined sequence;

[0059] S101: This embodiment proposes a definition of predefined sequence synchronization stability, which is used to describe the stability characteristics of a dynamic system. Where f(0) = 0, x(0) = x 0 , function f: is a nonlinear function that may be discontinuous. When the following conditions are met, the system is defined as having sequential synchronization stability:

[0060] S10101: The system has finite-time stability, that is, within a finite time, the system state vector x(t) converges to the origin;

[0061] S10102: System state component x=[x 1 ,x 2 ,…,x n ] T According to the predefined convergence sequence S = [s 1 ,s 2 ,…,s n] converges to the origin, where s i ∈{1,2,…,m},m≤n. Under this condition, the convergence time of each state component of the system satisfies the following relationship:

[0062]

[0063] T i (x 0 ) is the system state component x i The time required to converge from the initial state to the origin, T j (x 0 ) is the system state component x j The time required to converge from the initial state to the origin; in addition, when the system satisfies the sequence synchronization stability and the convergence time of all state components meets the predefined time T c >0, that is The system is said to have predefined sequence synchronization stability.

[0064] S102: This embodiment proposes a definition of a weighted ratio preservation characteristic to describe the dynamic characteristics of the system. Where f(0) = 0, x(0) = x 0 , if it meets the following conditions:

[0065]

[0066] Then the system is said to have a weighted ratio preservation characteristic. In formula (2), is the weight matrix, for i,j∈{1,2,…,n}, when i > j When , the ratio of the corresponding state components It decreases monotonically with time; i = j When , the ratio of the corresponding state components is a constant value, x(t) is the state value of the system at time t, is the derivative of x(t) with respect to the time variable t.

[0067] S2: Based on the definition of synchronization stability and dynamic characteristics of the predefined sequence, sufficient conditions for the system to achieve synchronization stability of the predefined sequence are set;

[0068] For the system When the following conditions are met, c >0 according to the sequence S = [s 1 ,s 2 ,…,s n ] The state components converge in the order specified by the predefined time synchronization stability:

[0069] S201: There exists a Lyapunov function V(x(t)) such that the system satisfies Among them, α 1 is the first parameter, α 1 >0,α 2 is the second parameter, α 2 <0, p is the third parameter, p>1, q is the fourth parameter, 0<q<1, and

[0070]

[0071] S202: The system has a weighted ratio preservation characteristic and the weight matrix ε=diag{ε 1 ,ε 2 ,…,ε n}satisfy:

[0072]

[0073] In formula (3), i,j∈{1,2,…,n}.

[0074] S3: On the basis of achieving the synchronization stability of predefined sequences in the system, a synchronization control protocol for predefined sequences based on event triggering mechanism is designed;

[0075] S301: Determine the predefined convergence sequence S of the system according to the control requirements = [s 1 ,s 2 ,…,s n ] and the total convergence time T c .

[0076] Building a system dynamics model in and Represent the position, velocity and control input of the system respectively, is the derivative of p(t) with respect to the time variable t, is the derivative of v(t) with respect to the time variable t.

[0077] S302: Design the sliding surface to be s(t)=v(t)+s s (t), where s s (t) is the switching law defined as follows:

[0078]

[0079] In formula (4), r 2 is the first constant, r 2 >1,g 2 is the second constant, l1 is the fifth parameter,

[0080] l 2 is the sixth parameter,

[0081] l 1 and l 2 The value of ensures that s s and The continuity of T c2 <T c is the predefined convergence time, ∈ is the weight matrix, The weight matrix ∈ satisfies when s i <s j hour

[0082] i > j , when s i =s j hour i = j , i,j∈{1,2,…,n},

[0083] ∈ m is the smallest diagonal element of the weight matrix ∈, triggering the sliding mode vector σ is a constant;

[0084] S303: Design a predefined sequence synchronization control protocol u(t)=w(t k ), where u(t) represents the actual control signal acting on the system at time t, t k represents the time when the event is triggered, w(t) is defined as

[0085]

[0086] In formula (5), T c1 is the predefined convergence time, r 1 is the third constant, r 1 >1,g 1 is the fourth constant, 0<g 1 <1, c 1 is the fifth constant, c 1 >0,c 2 is the sixth constant, c 2 >0, for The derivative with respect to the time variable t;

[0087] S304: Define the event trigger error value as e(t)=w(t)-u(t), and design the event trigger protocol in the predefined sequence synchronization control protocol:

[0088]

[0089] In formula (6), is the seventh constant, is the eighth constant.

[0090] S4: Apply the designed predefined sequence synchronization control protocol based on event trigger mechanism to the target system to realize the predefined sequence synchronization control of the system.

[0091] In this embodiment, the parameters are specifically set as follows: 1 =1.4, σ=0.1,c 1 =1, c 2 =0.3, And ∈=diag{1.5,0.6,0.6,0.3}, the simulation step is set to 0.0001s, and the motion process of the system within 4s is obtained through simulation. Figure 2 As shown, it can be seen that p 1 First, it converges to 0, p 2 and p 3 Next, they converge to 0, p 4 Finally, it converges to 0, which is the same as the convergence order specified in the predefined convergence sequence S = [1, 2, 2, 3]. In addition, all state components of the system converged before 4s, which is less than the predefined convergence time T c1 +T c2 ;like Figure 3 As shown, it can be seen is a constant value, and the absolute values ​​of the ratios between the other state components converge to 0 monotonically decreasing, which is consistent with the conclusion that the system has the weighted ratio preservation characteristic mentioned above; Figure 4 As shown, it can be seen that the event trigger mechanism is not triggered continuously, and compared with the simulation step size of 0.0001s, the communication frequency of the system is significantly reduced.

[0092] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. A predefined sequence synchronization control method based on an event trigger mechanism, characterized in that: The steps of the predefined sequence synchronization control method based on the event trigger mechanism include: Step 1: Define and describe the synchronization stability and dynamic characteristics of the predefined sequence; Step 2: Based on the definition of predefined sequence synchronization stability and dynamic characteristics, set sufficient conditions for the system to achieve predefined sequence synchronization stability; Step 3: On the basis of achieving the synchronization stability of the predefined sequence in the system, a predefined sequence synchronization control protocol based on the event trigger mechanism is designed for the second-order continuous system; Step 4: Apply the designed predefined sequence synchronization control protocol based on event trigger mechanism to the target system to realize the predefined sequence synchronization control of the system.

2. A method for synchronous control of a predefined sequence based on an event trigger mechanism according to claim 1, characterized in that: The definition and description of the synchronization stability of the predefined sequence in step 1 specifically include: For the system Where f(0)=0,x(0)=x0, function f: is a nonlinear function. If the predefined sequence synchronization stability condition 1 and the predefined sequence synchronization stability condition 2 are satisfied, and the convergence time of all state components in the system meets the predefined time System Synchronous stability with predefined sequences.

3. The method for synchronous control of a predefined sequence based on an event trigger mechanism according to claim 2, characterized in that: The first condition for the stability of predefined sequence synchronization is: In a finite time, the system state vector x(t) converges to the origin; The second predefined sequence synchronization stability condition is: the system state component x = [x1, x2, ..., x n ] T According to the predefined convergence sequence S = [s1, s2, ..., s n ] converges to the origin, where s i ∈{1,2,…,m},m≤n; system The expression of the convergence time relationship of each state component is: In formula (1), T i (x0) is the system state component x i The time required to converge from the initial state to the origin, T j (x0) is the system state component x j The time required to converge from the initial state to the origin.

4. The method for synchronous control of a predefined sequence based on an event trigger mechanism according to claim 1, characterized in that: The definition and description of dynamic features in step 1 specifically include: For the system Where f(0) = 0, x(0) = x0, if the dynamic characteristic conditions are met, then the system It has dynamic characteristics; The expression of dynamic characteristic condition is: In formula (2), is the weight matrix, for i,j∈{1,2,…,n}, when i > j When , the ratio of the corresponding state components It decreases monotonically with time; when i = j When , the ratio of the corresponding state components is a constant value, x(t) is the state value of the system at time t, is the derivative of x(t) with respect to the time variable t.

5. The method for synchronous control of a predefined sequence based on an event trigger mechanism according to claim 1, characterized in that: Step 2 specifically includes: For the system Where f(0) = 0, x(0) = x0. If the implementation conditions 1 and 2 are met, then the system Able to c > 0 according to the sequence S = [s1, s2, ..., s n ] The state components specified by the convergence order achieve predefined time synchronization stability; The first condition is that there exists a Lyapunov function V(x(t)) such that the system satisfies in, is the derivative of the Lyapunov function V(x(t)) with respect to the time variable t, α1 is the first parameter, α1>0, α2 is the second parameter, α2<0, p is the third parameter, p>1, q is the fourth parameter, 0<q<1, and The second condition is: system With dynamic characteristics and weight matrix ε=diag{ε1,ε2,…,ε n }satisfy Among them, i,j∈{1,2,…,n}.

6. The method for synchronous control of a predefined sequence based on an event trigger mechanism according to claim 1, characterized in that: Step 3 specifically includes: Step 3.1: According to the control requirements, determine the predefined convergence sequence S = [s1, s2, …, s n ] and the total convergence time T c , establish a second-order system dynamics model Where p(t) is the position of the system, is the derivative of p(t) with respect to the time variable t, v(t) is the velocity of the system, is the derivative of v(t) with respect to the time variable t, u(t) is the control input of the system, Step 3.2: Design the sliding mode variable of the system dynamics model as s(t)=v(t)+s s (t); Step 3.3: Design a predefined sequence synchronization control protocol u(t)=w(t k ), where u(t) represents the actual control signal acting on the system at time t, t k Indicates the time when the event is triggered; Step 3.4: Define the event trigger error value as e(t)=w(t)-u(t), and design the event trigger protocol in the predefined sequence synchronization control protocol; s s (t) The expression of the switching law is: In formula (3), r2 is the first constant, r2>1, g2 is the second constant, l1 is the fifth parameter, l2 is the sixth parameter, The values ​​of l1 and l2 ensure that s s and The continuity of T c2 <T c is the predefined convergence time, ∈ is the weight matrix, The weight matrix ∈ satisfies when s i <s j hour i > j , when s i =s j hour i = j , i,j∈{1,2,…,n}, ∈ m is the smallest diagonal element of the weight matrix ∈, triggering the sliding mode vector σ is a constant; The expression of w(t) is: In formula (4), T c1 is the predefined convergence time, r1 is the third constant, r1>1, g1 is the fourth constant, 0<g1<1, c1 is the fifth constant, c1>0, c2 is the sixth constant, c2>0, for The derivative with respect to the time variable t; The expression of the event triggering protocol is: In formula (5), is the seventh constant, is the eighth constant.

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