A control method and apparatus adapted for dynamically coupling electronic oscillator networks

Abstract

The application discloses a control method suitable for a dynamic coupling electronic oscillator network, comprising the following steps: S1, constructing a coupling oscillator network model describing the dynamic interaction relationship between electronic oscillators which are coupled with each other; S2, based on the constructed coupling oscillator network model, establishing a coupling oscillator state signal tracking error model of a nonlinear state; S3, constructing a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability; and S4, verifying the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy. The control method suitable for the dynamic coupling electronic oscillator network can significantly improve the operation safety and robustness of the coupling oscillator network system and effectively suppress the fluctuation of the control input. By introducing a non-periodic event triggering mechanism, the triggering frequency of the controller is significantly reduced, and the system resource consumption is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of coupled oscillator network system control, and more particularly, to an event-triggered distributed model predictive control method with input fluctuation suppression function suitable for a dynamic coupled electronic oscillator network, a system, a readable storage medium and a computer device. BACKGROUND

[0002] Coupled oscillator network systems exist widely in nature and engineering, and have wide applications in biology and physics, etc. Typical applications include rhythm regulation of biological neural networks, synchronous operation of power grid generators, and cooperative control of multiple robots, etc.

[0003] The core control difficulty of such systems lies in: on the one hand, the complex interaction between individual dynamics and network coupling effect needs to be coordinated to achieve the desired synchronization or cluster mode; on the other hand, the network topology uncertainty, parameter heterogeneity and environmental noise, etc. must be overcome, and a robust distributed control strategy must be designed. In addition, in large-scale networks, the control accuracy and computational complexity need to be balanced, which puts forward innovation requirements for traditional control methods. The solution to these problems requires the combination of nonlinear dynamics, distributed optimization and intelligent control, etc. multidisciplinary methods.

[0004] In addition, input fluctuations pose challenges to the stability of industrial control systems, where excessive changes can lead to instability of closed-loop systems through cumulative phase-lag effects. In environments where specialized equipment with high performance is required to operate, reducing excessive fluctuations in actuator inputs is crucial to ensuring the stability of safety protection systems, prolonging the service life of equipment, and ensuring the reliability of operations.

[0005] According to the above analysis, the current control method research for coupled oscillator network systems mainly focuses on nonlinear control strategies, heterogeneous parameter regulation, multi-mode coupling and intelligent optimization, etc. For the research on nonlinear control strategies, few consider the impact of excessive fluctuations in actuator inputs on coupled oscillator network systems.

[0006] Therefore, the present application proposes an event-triggered distributed model predictive control method with input fluctuation suppression function suitable for a dynamic coupled electronic oscillator network, which significantly improves the operation safety and robustness of coupled oscillator network systems and effectively suppresses the fluctuations in control inputs. By introducing a non-periodic event triggering mechanism, the triggering frequency of the controller is significantly reduced, the system resource consumption is reduced, and the risk of control input violating the constraint condition is effectively reduced, which has theoretical significance, strong realizability and is conducive to improving economic benefits. SUMMARY

[0007] The purpose of this invention is to provide an event-triggered distributed model predictive control method with input fluctuation suppression function suitable for dynamically coupled electronic oscillator networks, which significantly improves the operational safety and robustness of coupled oscillator network systems and effectively suppresses fluctuations in control input.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A control method suitable for dynamically coupled electronic oscillator networks includes the following steps:

[0010] S1. Construct a coupled oscillator network model to describe the dynamic interaction between electronic oscillators that are mutually coupled with voltage signals;

[0011] S2. Based on the constructed coupled oscillator network model, establish a nonlinear coupled oscillator state signal tracking error model;

[0012] S3. Construct a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability;

[0013] S4. Verify the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy.

[0014] Further, in step S1, a coupled oscillator network model describing the dynamic interaction between electronic oscillators that are mutually coupled with voltage signals is constructed, as follows:

[0015] The coupled oscillator network model consists of multiple electronic oscillators coupled to each other by voltage signals. A coupled oscillator network consisting of four electronic oscillators coupled to each other by voltage signals is established, and the dynamic model of the coupled oscillator network is given as follows:

[0016]

[0017] Where, ω i (t) represents the phase of the i-th oscillator. Let i represent the set of integers i = 1, 2, 3, 4. Let u represent the frequencies of the i-th and j-th oscillators, respectively. i (t) is the control input, γ i k is the damping coefficient. ij This is the coupling weight, meaning that each oscillator i is affected by all the oscillators j connected to it, and the strength of the influence depends on...

[0018] Define state variables Control input u i (t), then the state equation of the entire system is:

[0019]

[0020] where t∈R [0,∞] , and are the state and control input of the system, respectively, R [0,∞] denotes a set of real numbers greater than 0, are the state and control input of the system, respectively, are the state and control input of the system, respectively, are the state and control input of the system, respectively, k ij is the coupling strength of the oscillator, denotes the set of coupling neighbor systems of subsystem i.

[0021] Further, in step S2, based on the constructed coupling oscillator network model, a nonlinear state coupling oscillator state signal tracking error model is established, specifically as follows:

[0022] Assume that the expected phase trajectory and frequency trajectory are ω i,ref (t)=0 and Define the tracking error as:

[0023]

[0024] Define the tracking error system state variable and control input v i (t), the nonlinear state coupling oscillator state signal tracking error model is expressed as:

[0025]

[0026] where the i-th electronic oscillator has input constraints and input fluctuation constraints where, and are the input constraint set and the input fluctuation constraint set, respectively, and, and are both compact sets containing , and is a k -dimensional real number space, and Δ is the unit time; in addition, the function is twice differentiable, and where z i and v i are the actual coupling oscillator system state and control input state, respectively, is a k -dimensional real number space, and satisfies where, and respectively are the error predicted state and input of the nominal electronic oscillator, and respectively are the error assumed state and assumed input of the electronic oscillator, constant is the Lipschitz constant;

[0027] According to the above tracking error model, the global tracking error model is obtained, denoted as:

[0028]

[0029] where is the lumped error state vector, which is stacked by the phase error and frequency error variables of each electronic coupler, and its corresponding dimension is: Similarly, is the lumped control input vector, which is also stacked by the control input of each electronic coupler, and its corresponding dimension is: is the lumped local nonlinear dynamic vector, which is stacked by the nonlinear dynamic coupling part of each electronic coupler, is the equivalent dynamic after linearization of the nonlinear coupling dynamic; is an n z dimensional real number space;

[0030] The linearized expressions of the tracking error model and the global tracking error model near the origin are denoted as:

[0031]

[0032] where, respectively are the system matrix, input matrix, global system matrix, global input matrix of the electronic coupler system after linearization near its equilibrium point, and there exists a state feedback matrix K i such that the matrix further makes the closed-loop electronic coupler system stable.

[0033] Further, a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability is constructed, which is as follows:

[0034] S3.1, construct a global terminal invariant domain and its terminal stable controller:

[0035] For the i-th nominal electronic coupler system Given two performance weight matrices Q i , R i > 0, there exists a matrix Ki a set of terminal constraints where, is the ith electronic coupler nominal system error dynamics, is the nominal error phase state, is the nominal input state; there exists ε i > 0 and a unique matrix P i > 0 satisfying conditions (i) (ii) (iii) for the closed loop system Ω i (ε i ) is positive invariant; and (iv) for there exists where

[0036] for the system given matrices P, and K, there exists a constant satisfying conditions (i) (ii) (iii) for the closed loop system is positive invariant; and (iv) for there exists

[0037] S3.2, Optimal Control Problem Description Model:

[0038] Define a sequence of triggering instants as where t0= 0; the local optimal problem of subsystem i at triggering instant t k can be expressed as:

[0039]

[0040] where and denote the feasible input trajectory and the corresponding predicted state trajectory, respectively, with superscript * optimal case; T is the prediction horizon; is the triggering parameter; ε i ∈ R (0,∞) and describes the size of the terminal invariant domain of decoupled subsystem α i ∈ R (0,1) is the designed contraction rate; the cost function is expressed as where Q i , R i , P i > 0 are weight matrices;

[0041] The control input of subsystem i is obtained by solving an optimization problem. The design is as follows:

[0042]

[0043] S3.3, Constructing event triggering conditions:

[0044] For those starting from the same initial state at trigger time t k Below, at the optimal input The system under action (1) and for The range of state prediction bias is limited to:

[0045]

[0046] in, as well as

[0047] By monitoring the above state prediction deviations, the conditions for triggering the next event are established:

[0048]

[0049] in As the trigger threshold, and Ensure that the Zeno phenomenon does not occur.

[0050] Furthermore, in S4, the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy are verified, as follows:

[0051] S4.1 Recursive Feasibility Analysis:

[0052] Assume that at initial time t0, there exists a set of initial state trajectories such that the optimization problem has a solution; for the global tracking error system, the recursive feasibility of the algorithm is guaranteed when the triggering condition of the next event is met:

[0053] (i):

[0054] (ii):

[0055] (iii):

[0056] Based on the following control inputs:

[0057]

[0058] for By applying the Gronwall-Bellman inequality, we obtain:

[0059]

[0060] Substitute s = t k into the above equation and use condition (i) to obtain

[0061]

[0062] According to the terminal invariant and comparison principle, we have

[0063]

[0064] Using condition (ii), we have

[0065]

[0066] Next, when , since the optimization problem is feasible at t k , we can derive that the control input k+1 at t satisfies the input and input variation constraints; for the case of , the satisfaction of the input and input variation constraints is guaranteed by the terminal invariant and terminal stable controller;

[0067] According to the control input at t k+1 , we have

[0068]

[0069] To prove , we only need to prove

[0070]

[0071] For , we can observe that

[0072]

[0073] Since F i (w) is monotonically increasing with respect to w ∈ R (0,∞) , using t k - t k-1 ≥ hT, we have

[0074]

[0075] According to condition (i), we have

[0076] ​​

[0077] For It can be obtained that

[0078]

[0079] To prove It suffices to prove

[0080]

[0081] It can be simplified to prove

[0082]

[0083] By condition (iii), it can be obtained that Since H i (0) = 0, it follows that Next, it can be obtained that

[0084]

[0085] Thus, the control input At the triggering time, it is a feasible solution, and the recursive feasibility verification is completed. k+1

[0086] S4.2, Stability analysis of closed-loop system:

[0087] In the case that the recursive feasibility is satisfied, the following conditions are satisfied:

[0088]

[0089] It can be obtained that the state of the system will converge to the terminal invariant domain in finite time; subsequently, in the terminal invariant domain , the closed-loop tracking error system is asymptotically stable.

[0090] When , define a non-negative function as:

[0091]

[0092] Next, according to the suboptimality of , it can be derived that:

[0093]

[0094] where

[0095]

[0096] For By Holder's inequality and​ It can be obtained that:

[0097]

[0098] For According to and It can be obtained that:

[0099]

[0100] For According to inequality and terminal domain inequality It can be obtained that:

[0101]

[0102] The addition can obtain V(x(t k+1 ))-V(x(t k ))<0, so that the state z(t) of the system enters the terminal domain in a finite time; on the other hand, when is selected as a Lyapunov function, it can be obtained that Therefore, the state of the system gradually converges to zero, and the stability of the closed-loop system is verified.

[0103] The technical scheme of the second aspect of the application provides a control system suitable for a dynamically coupled electronic oscillator network, comprising:

[0104] A coupled oscillator model construction module is configured to construct a coupled oscillator network model describing the dynamic interaction relationship between electronic oscillators in which voltage signals are coupled to each other.

[0105] A tracking error model construction module is configured to establish a coupled oscillator state signal tracking error model of a nonlinear state based on the constructed coupled oscillator network model.

[0106] A control strategy construction module is configured to construct a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability.

[0107] A control strategy feasibility analysis module is configured to verify the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy.

[0108] The technical scheme of the third aspect of the application provides a readable storage medium having a computer program stored thereon, and the program is executed by a processor to implement the steps of the control method suitable for a dynamically coupled electronic oscillator network provided by the technical scheme of the first aspect.

[0109] The technical solution of the fourth aspect of the present application provides a computer device, comprising a storage medium and a processor; the storage medium is used for storing a computer program; and the processor is used for executing the computer program to realize the steps of the control method suitable for dynamically coupling an electronic oscillator network provided by the technical solution of the first aspect.

[0110] The beneficial effects of the present application are as follows:

[0111] 1. Significantly improve the operation safety and robustness of the coupled oscillator network system.

[0112] 2. Effectively suppress the fluctuation of the control input.

[0113] 3. Effectively and significantly reduce the triggering frequency of the controller and reduce the consumption of system resources.

[0114] 4. Effectively reduce the risk of violation of the constraint condition of the control input. BRIEF DESCRIPTION OF DRAWINGS

[0115] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings:

[0116] Figure 1 A flowchart of the control method suitable for dynamically coupling an electronic oscillator network of the present application is shown;

[0117] Figure 2 A schematic diagram of a double-mode event-triggered distributed model predictive control block diagram of the present application is shown;

[0118] Figure 3 A schematic diagram of the state trajectory of four oscillators under the double-mode event-triggered distributed model predictive control method in the embodiment of the present application is shown;

[0119] Figure 4 A schematic diagram of the control input trajectory of four oscillators under the double-mode event-triggered distributed model predictive control method in the embodiment of the present application is shown;

[0120] Figure 5 A schematic diagram of the input fluctuation trajectory of four oscillators under the double-mode event-triggered distributed model predictive control method in the embodiment of the present application is shown;

[0121] Figure 6 A structural block diagram of the control system suitable for dynamically coupling an electronic oscillator network of the present application is shown. DETAILED DESCRIPTION

[0122] In order to more clearly illustrate the present application, the present application will be further described below in conjunction with the preferred embodiments and the accompanying drawings. Those skilled in the art should understand that the specific descriptions below are illustrative rather than limiting, and should not limit the protection scope of the present application.

[0123] The control method provided by the embodiment is suitable for dynamically coupling an electronic oscillator network, has an event-triggered distributed model prediction function with input fluctuation suppression function, and has the following steps as shown in the figure: Figure 1

[0124] S1, a coupled oscillator network model describing the dynamic interaction relationship between electronic oscillators coupled by voltage signals is constructed.

[0125] Specifically, in step S1, the coupled oscillator network model is composed of a plurality of electronic oscillators coupled by voltage signals, a coupled oscillator network composed of four electronic oscillators coupled by voltage signals is established, and the dynamic model of the coupled oscillator network is as follows:

[0126]

[0127] Where ω i (t) represents the phase of the i-th oscillator, represents an integer set of i = 1, 2, 3, 4, respectively represent the frequency of the i-th and j-th oscillators, u i (t) is the control input, γ i is the damping coefficient, k ij is the coupling weight, that is, each oscillator i is affected by all oscillators j connected to it, and the influence strength depends on The control target is to stabilize the interacting oscillators;

[0128] For ease of analysis, define the state variable and the control input u i (t), then the state equation of the entire system is:

[0129]

[0130] Where t ∈ R [0,∞] , and are the state and control input of the system, respectively, R [0,∞] represents a set of real numbers greater than 0, are real number spaces of dimension n , respectively, n ij is the dimension of the system state and control input, and k is the coupling strength of the oscillator, represents the coupled neighbor system set of subsystem i.

[0131] S2, based on the constructed coupled oscillator network model, a coupled oscillator state signal tracking error model of nonlinear state is established;

[0132] In particular, in step S2, the nonlinear state-coupled oscillator state signal tracking error model is as follows:

[0133] Let the desired phase trajectory and frequency trajectory be ω i,ref (t) = 0 and Define the tracking error as:

[0134] Define the tracking error system state variables and control input v i (t), the nonlinear state-coupled oscillator state signal tracking error model is expressed as:

[0135]

[0136] where the i-th electronic oscillator has input constraints and input fluctuation constraints where, and are the input constraint set and the input fluctuation constraint set, respectively, and and are compact sets containing , and is a -dimensional real number space, and Δ is the unit time; in addition, the function is twice differentiable, and where z i and v i are the actual coupled oscillator system state and control input state, respectively, is a -dimensional real number space, and satisfies where, and are the error prediction state and input of the nominal electronic oscillator, respectively, and are the error assumed state and assumed input of the electronic oscillator, respectively, and the constant is the Lipschitz constant;

[0137] According to the tracking error model (5), the global tracking error model is obtained, which is expressed as:

[0138]

[0139] where is the lumped error state vector, which is stacked by the phase error and frequency error variables of each electronic coupler, and the corresponding dimension is: Similarly, It is the lumped control input vector, which is also composed of the control inputs of each electronic coupler. Its corresponding dimension is: It is a lumped local nonlinear dynamic vector, formed by the accumulation of the nonlinear dynamic coupling parts of each electronic coupler. It is the equivalent dynamic after linearization of nonlinear coupled dynamics; For n z 3D real space;

[0140] The linearized expressions of the tracking error model (5) and the global tracking error model (7) near the origin are respectively:

[0141]

[0142] in, These are the system matrix, input matrix, global system matrix, and global input matrix of the electronic coupler system after linearization near its equilibrium point, respectively, and there exists a state feedback matrix K. i , making the matrix This makes the closed-loop electronic coupler system stable.

[0143] S3. Construct a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability, as detailed below:

[0144] S3.1 Constructing a global terminal invariant domain and its terminal stability controller:

[0145] For the i-th nominal electronic coupler system Given two performance weight matrices Q i ,R i If > 0, then there exists a matrix K. i A set of terminal constraints in, Let be the nominal system error dynamic of the i-th electronic coupler. This is the nominal error phase state. It is the nominal input state; ε exists. i >0 and the unique matrix P i >0, condition (i) is satisfied. (ii) (iii) For closed-loop systems Ω i (ε i (iv) is positive and invariant; and for exist in

[0146] For the system Given matrices P, and K, there exist constants satisfying conditions (i) (ii) (iii) for the closed-loop system is positive invariant; and (iv) for there exists

[0147] S3.2, Optimal control problem description model:

[0148] Define a sequence of trigger times as where t0= 0; subsystem i has a local optimal problem at trigger time t k which can be expressed as:

[0149]

[0150]

[0151] where and represent the feasible input trajectory and the corresponding predicted state trajectory, respectively, with superscript * optimal case; T is the prediction horizon; is the trigger parameter; ε i ∈ R (0,∞) and describes the size of the terminal invariant domain of decoupled subsystem α i ∈ R (0,1) is the designed contraction rate; the cost function is expressed as where Q i , R i , P i > 0 are weight matrices;

[0152] The control input of subsystem i is designed as follows by solving the optimal problem

[0153]

[0154] S3.3, Constructing event-triggered conditions:

[0155] For the system (1) and under the optimal input from the same initial state at trigger time t k , the range of state prediction error is limited as: ​​

[0156]

[0157] where, and

[0158] By monitoring the above state prediction bias, the next event triggering condition is established:

[0159]

[0160] where is the triggering threshold, and to ensure that the Zeno phenomenon does not occur.

[0161] S4, verify the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy, as follows:

[0162] S4.1, recursive feasibility analysis:

[0163] Assume that at the initial time t0, there is a set of initial state trajectories such that the optimization problem has a solution; for the global tracking error system (7), when the following event-triggered condition is satisfied, the recursive feasibility of the algorithm is guaranteed:

[0164] (i) (ii) (iii)

[0165] According to the following control input:

[0166]

[0167] For By applying the Gronwall-Bellman inequality, we get:

[0168]

[0169] Bring s = t k + T into the above formula, and use condition (i) to get:

[0170]

[0171] In addition, according to the terminal invariant domain and comparison principle, when , we can get:

[0172]

[0173] Using condition (ii), we get:

[0174]

[0175] Next, when , since the optimization problem is feasible at t k , it can be derived that the control input k+1 at t satisfies the input and input variation constraints; for the case of , the satisfaction of the input and input variation constraints is guaranteed by the terminal invariant and terminal stabilizing controller;

[0176] According to the control input k+1 at t , for , it can be obtained that

[0177]

[0178] To prove , it is only necessary to prove that

[0179]

[0180] For , it can be observed that

[0181]

[0182] Since F i (w) is monotonically increasing with w∈R (0,∞) , using , it can be obtained that

[0183]

[0184] According to condition (i), it can be obtained that

[0185]

[0186] For , it can be obtained that

[0187]

[0188] To prove , it is only necessary to prove that

[0189]

[0190] It can be simplified to prove that

[0191]

[0192] Using condition (iii), it can be obtained that Since H i (0) = 0, therefore Next we can get:

[0193]

[0194] Thus we can get the control input At t k+1 The trigger moment is a feasible solution, and the recursive feasibility is completed.

[0195] S4.2, closed-loop system stability analysis:

[0196] In the case of recursive feasibility, the following conditions are met:

[0197]

[0198] The state of the system can be obtained, which will converge to the terminal invariant domain in finite time; subsequently, in the terminal invariant domain , the global tracking error system (7) is asymptotically stable;

[0199] When , define a non-negative function as:

[0200]

[0201] Next, according to the suboptimality of , we can deduce:

[0202]

[0203] Where,

[0204]

[0205] For By Holder inequality and We can get:

[0206]

[0207] For According to And We get:

[0208]

[0209] For According to the inequality And the terminal domain inequality We can get:

[0210]

[0211] The addition can obtain V(x(t k+1 ))-V(x(t k ))<0, so that the state z(t) of the system enters the terminal domain in a finite time; on the other hand, when is selected as a Lyapunov function, it can be obtained Therefore, the state of the system gradually converges to zero, and the stability of the closed-loop system is verified.

[0212] Next, in order to verify the control method suitable for the dynamic coupling oscillator network provided in the embodiment, MATLAB is used for simulation experiment verification, and detailed description is made as follows:

[0213] The coupling oscillator network system mathematical model provided in the embodiment, the double-mode event-triggered distributed model predictive control method with input fluctuation alleviating function is designed, the influence of input fluctuation on system control performance is suppressed, the calculation pressure and communication resource shortage problem caused by distributed control in the control process is alleviated, and the stability of the coupling oscillator is ensured.

[0214] The parameters of the coupling oscillator network system are set as follows, the control input and its fluctuation satisfy |u i (t)|≤8×10 -3 and The damping coefficient γ i =1×10 -2 , the coupling weight k ij =1.25×10 -3 ; in addition, it can be obtained ι z =1.0069, ι v =1, and l=1.25×10 -3 ; the sampling time is δt=0.03s; the control target is to make the coupling interaction oscillator network stable.

[0215] The parameters of the double-mode event-triggered distributed model predictive control method with input fluctuation alleviating function are designed as follows: Q i =[5,0;0,5], R i =0.01, P i =[6.2400,0.6094;0.6094,0.7040], T=50δ, α i =0.6, ε i =3.44×10 -4 , and

[0216] Based on the above parameters, the control method of the present application is simulated and verified, and the corresponding simulation results are shown in Figures 3-5 As shown in the figure, Figure 3 The state trajectory of the four oscillators under the dual-mode event-triggered distributed model predictive control method is shown, which proves that the control method realizes the asymptotic stability of the coupled oscillators; Figure 4 The control input trajectory of the four oscillators under the dual-mode event-triggered distributed model predictive control method is shown, which verifies that the control input constraints are satisfied during the control process; Figure 5 The input fluctuation trajectory of the four oscillators under the dual-mode event-triggered distributed model predictive control method is shown, and the input fluctuation constraint violation only occurs before the switching time, and the event-triggered mechanism effectively reduces the number of input fluctuation constraint violations, only at the trigger times 1.47s, 2.94s and 4.41s, the input fluctuation constraint is violated; The switching time 6.75s corresponds to the first time the state enters the global terminal invariant domain, and since the global terminal stable controller design includes the input fluctuation constraint, the input fluctuation constraint is always satisfied thereafter.

[0217] Through the above analysis, the effectiveness of the event-triggered distributed model predictive control method provided by the embodiment is verified, which is suitable for dynamic coupled electronic oscillator network and has input fluctuation suppression function, significantly improves the operation safety and robustness of the coupled oscillator network system, and effectively suppresses the fluctuation of the control input. By introducing a non-periodic event-triggering mechanism, the triggering frequency of the controller is significantly reduced, the system resource consumption is reduced, and the risk of violating the constraint condition of the control input is effectively reduced.

[0218] As shown in Figure 6 The control system 100 suitable for dynamic coupled electronic oscillator network according to another embodiment of the present application comprises:

[0219] The coupled oscillator model construction module 10 is configured to construct a coupled oscillator network model describing the dynamic interaction relationship between electronic oscillators coupled by voltage signals;

[0220] The tracking error model construction module 20 is configured to establish a nonlinear state coupled oscillator state signal tracking error model based on the constructed coupled oscillator network model;

[0221] The control strategy construction module 30 is configured to construct a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability;

[0222] The control strategy feasibility analysis module 40 is configured to verify the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy.

[0223] Based on the above as Figures 1 to 5Accordingly, embodiments of this application also provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the control method suitable for dynamically coupled electronic oscillator networks of any of the above embodiments.

[0224] Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as CD-ROM, USB flash drive, mobile hard drive, etc.) and includes several instructions to cause a computer device (such as personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of this application.

[0225] Based on the above, Figures 1 to 5 The method shown, and Figure 6 To achieve the above objectives, the present application also provides a computer device, including a storage medium and a processor, as shown in the virtual device embodiment. The storage medium is used to store a computer program, and the processor is used to execute the computer program to implement the steps of the control method suitable for dynamically coupled electronic oscillator networks in any of the above embodiments.

[0226] Optionally, the computer device may also include a user interface, a network interface, a camera, radio frequency (RF) circuitry, sensors, audio circuitry, a Wi-Fi module, etc. The user interface may include a display screen, input units such as a keyboard, etc., and optional user interfaces may also include USB interfaces, card reader interfaces, etc. The network interface may optionally include standard wired interfaces, wireless interfaces (such as Bluetooth interfaces, Wi-Fi interfaces), etc.

[0227] Those skilled in the art will understand that the computer device structure provided in this embodiment does not constitute a limitation on the computer device, and may include more or fewer components, or combine certain components, or have different component arrangements.

[0228] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages and stores the hardware and software resources of a computer device, supporting the operation of information processing programs and other software and / or programs. The network communication module is used to enable communication between the various components within the storage medium, as well as communication with other hardware and software within the physical device.

[0229] Obviously, the above embodiments of the present application are merely exemplary and are not intended to limit the embodiments of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art, and it is impossible to enumerate all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present application are still within the protection scope of the present application.

Claims

1. A control method suitable for dynamically coupling a network of electronic oscillators, characterized in that, The method comprises the following steps: S1, constructing a coupled oscillator network model describing the dynamic interaction between electronic oscillators with mutually coupled voltage signals, specifically as follows: The coupled oscillator network model is composed of multiple electronic oscillators with mutually coupled voltage signals, a coupled oscillator network composed of four electronic oscillators with mutually coupled voltage signals is established, and the dynamics model of the coupled oscillator network is given as follows: ； wherein denotes the phase of the th oscillator, denotes a set of integers, , denotes the frequency of the , jth oscillator, is a control input, is a damping coefficient, is a coupling weight, i.e. each oscillator is influenced by all oscillators connected to it, the strength of the influence depending on ; Definition of state variables Control inputs The state equation of the whole system is ； ； wherein, , and are the state and control input of the system, respectively, is a set of real numbers greater than 0, , are , dimensional real number space, , are the dimension of the system state, control input, respectively, is the coupling strength of the oscillator, denotes the set of coupling neighbors of the subsystem . S2, based on the constructed coupled oscillator network model, a coupled oscillator state signal tracking error model of nonlinear state is established; S3, constructing a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability; S4, verifying the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy.

2. The control method suitable for dynamically coupling electronic oscillator networks according to claim 1, characterized in that, In step S2, based on the constructed coupled oscillator network model, a coupled oscillator state signal tracking error model of nonlinear state is established, specifically as follows: Assume the desired phase trajectory and frequency trajectory are and respectively, define the tracking error as: ； Defining a tracking error system state variable and control input The nonlinear state-coupled oscillator state signal tracking error model is then represented as: ； ； Among them, the first Each electronic oscillator has input constraints and input fluctuation constraints ,in, and These are the set of input constraints and the set of input fluctuation constraints, respectively. and All include The compactness, for 3D real space, For unit time; in addition, the function It is twice differentiable, and ,in and These are the actual coupled oscillator system state and the control input state, respectively. for 3D real space, satisfying ,in, and These represent the error prediction state and input of the nominal electronic oscillator, respectively. and These are the error assumption state and the assumption input of the electronic oscillator, respectively, and constants. It is the Lipsis constant; According to the above tracking error model, a global tracking error model is obtained, expressed as: ； where is the lumped error state vector, which is stacked by the phase error and frequency error variables of each electronic coupler, and its corresponding dimension is , is the lumped control input vector, which is also stacked by the control input of each electronic coupler, and its corresponding dimension is , is the lumped local nonlinear dynamic vector, which is stacked by the nonlinear dynamic coupling part of each electronic coupler, is the equivalent dynamic after linearization of the nonlinear coupling dynamic; , is the dimensional real number space; The linearized expressions of the tracking error model and the global tracking error model near the origin are respectively expressed as: ； ； wherein , , , ; , , , are the system matrix, the input matrix, the global system matrix, the global input matrix of the electronic coupler system linearized around its equilibrium point, respectively, and there exists a state feedback matrix such that the matrix , and, in turn, such that the closed-loop electronic coupler system is stable.

3. The control method suitable for dynamically coupling electronic oscillator networks according to claim 2, characterized in that, Constructing a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability, specifically as follows: S3.1, constructing a global terminal invariant domain and its terminal stable controller: For the ith nominal electronic coupler system Given two performance weight matrices there exists a matrix a set of terminal constraints where is the ith electronic coupler nominal system error dynamics, is the nominal error phase state, is the nominal input state; there exists and a unique matrix satisfying conditions (i) (ii) (iii) for closed loop systems , is positive invariant; and (iv) for there exists where ; For the system Given matrices , , , and , there exists a constant satisfying conditions (i) ; (ii) ; (iii) for the closed loop system , is positive invariant; and (iv) for , there exists ; S3.2, optimizing the control problem description model: A sequence of trigger instants is defined as wherein ; subsystem At trigger instants The local optimization problem at trigger instant can be expressed as: ； ； ； ； ； ； wherein and denote feasible input trajectories and corresponding predicted state trajectories, respectively, with the superscript optimal case; is the prediction horizon; is the triggering parameter; and describe the decoupled subsystem the size of the terminal invariant domain; is the designed contraction rate; cost function is represented as wherein is the weight matrix; Subsystems Control inputs by solving an optimization problem The design is as follows: ； S3.3, constructing an event-triggering condition: For the same initial state at the triggering time Next, the optimal input under the subsystem i and , the state prediction bias is limited to: ​ ； wherein , , , , , , , , and ; By monitoring the above state prediction deviation, the next event-triggering condition is established: ； wherein is a triggering threshold, and , ensuring that the Zeno phenomenon does not occur.

4. The control method suitable for dynamically coupling electronic oscillator networks according to claim 3, characterized in that, Verify the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy, specifically as follows: S4.1, recursive feasibility analysis: Assume at the initial time , there exists a set of initial state trajectories such that the optimization problem has a solution; for the global tracking error system, the recursive feasibility of the algorithm is guaranteed when the next event-triggered condition is satisfied: （i）： ； (ii): ; (iii): ; According to the following control input: ； For , by applying the Gronwall-Bellman inequality, we obtain: ； Substituting into the above equation and using condition (i) gives: Substituting into the above equation and using condition (i) gives: ； According to the terminal invariable domain and comparison principle, when the following can be obtained: ； Using condition (ii), we get: ； Next, when the optimization problem is feasible at the time instant, it can be derived that the control input satisfies the input and input variation constraints; for the case, the satisfaction of the input and input variation constraints is guaranteed by the terminal invariant and terminal stabilizing controller; According to Time control input For It can be obtained that: ； To prove It is sufficient to prove that: ； For It can be observed that: ； Due to With Monotonically increasing, using It can be obtained that ； According to condition (i), we can get: ； For It can be obtained that: ； To prove It is sufficient to prove that: ； It can be simplified to prove: ； Using condition (iii), one can obtain ; since , therefore ; one can next obtain: ； From this the control input In The trigger time is a feasible solution, and the recursive feasibility verification is completed. S4.2, closed-loop system stability analysis: In the case of recursive feasibility, the following conditions are met: ； The state of the system will converge to the terminal invariant domain in finite time; Subsequently, in the terminal invariant domain the closed loop tracking error system is asymptotically stable; When a non-negative function is defined as: ； Next, according to suboptimality, it can be derived that: ； Where, ； ； ； For , by Holder's inequality and , we have: ； For , according to and , we get: ； For , from the inequalities and the terminal domain inequality , we have: ； The addition can obtain Therefore, the state of the system In a limited time into the terminal domain On the other hand, when The selection As Lyapunov function, can obtain ; Therefore, the state of the system gradually converges to zero, and the stability of the closed-loop system is verified.

5. A control system implementing the control method of any one of claims 1 to 4, adapted to dynamically couple a network of electronic oscillators, characterized in that, Including: The coupled oscillator model construction module is configured to construct a coupled oscillator network model describing the dynamic interaction between electronic oscillators with mutually coupled voltage signals; The tracking error model construction module is configured to establish a coupled oscillator state signal tracking error model of nonlinear state based on the constructed coupled oscillator network model; The control strategy construction module is configured to construct a dual-mode event-triggered distributed model predictive control strategy with input fluctuation suppression capability; The control strategy feasibility analysis module is configured to verify the recursive feasibility and system stability of the dual-mode event-triggered distributed model predictive control strategy.

6. A readable storage medium characterized by, The computer program is stored on the storage medium and executed by the processor to implement the steps of the control method for dynamically coupled electronic oscillator network according to any one of claims 1 to 4.

7. A computer device, characterized by The storage medium is used to store the computer program, and the processor is used to execute the computer program to implement the steps of the control method for dynamically coupled electronic oscillator network according to any one of claims 1 to 4.

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