A control method for networked nonlinear systems based on fuzzy adaptive event triggering

Abstract

The present invention relates to a networked nonlinear system control method based on fuzzy adaptive event triggering, including: S1, equivalent T-S fuzzy modeling of networked nonlinear system based on T-S fuzzy theory; S2, constructing fuzzy adaptive event triggering mechanism based on T-S fuzzy model structured characteristics and fuzzy membership function information; S3, constructing T-S fuzzy networked closed-loop system based on fuzzy adaptive event triggering mechanism under sampling input based on fuzzy adaptive event triggering mechanism and sampling control strategy; S4, establishing sufficient conditions for asymptotic stability of T-S fuzzy networked closed-loop system based on fuzzy adaptive event triggering mechanism based on Lyapunov stability theory; S5, calculating state feedback gain matrix of T-S fuzzy networked closed-loop system based on linear matrix inequality theory, and realizing control of networked nonlinear system based on T-S fuzzy model. The method is conducive to reducing unnecessary communication transmission and saving control cost while ensuring system stability.

Description

Technical Field

[0001] The invention belongs to the technical field of networked system control, and in particular relates to a networked nonlinear system control method based on fuzzy adaptive event triggering. Background Art

[0002] In recent years, networked systems have been widely used in intelligent manufacturing, smart transportation, and collaborative control of multiple autonomous unmanned systems due to their many advantages such as high flexibility, strong reliability, easy sharing, and low cost. It should be pointed out that the limited communication bandwidth resources of networked systems are prone to cause communication delays, data packet loss, and information confusion, which further deteriorate system performance. In order to alleviate the above problems, event triggering mechanisms have emerged. By constructing trigger conditions determined by the system change amplitude and threshold functions, the communication frequency is effectively optimized and bandwidth congestion is alleviated. On the other hand, in reality, most networked systems have nonlinear dynamic characteristics. How to simplify the stability analysis and synthesis process of networked nonlinear systems has become one of the research hotspots in academia. As the mainstream method of nonlinear control research, TS fuzzy method has been widely used in the study of networked nonlinear systems and has achieved fruitful theoretical results.

[0003] However, when studying networked nonlinear systems based on TS fuzzy models, the event trigger mechanism is usually designed as a static event trigger mechanism with a constant threshold function, which cannot adapt to the dynamic changes of the system state and the obtained results are somewhat conservative. In addition, existing studies have not fully considered the structural characteristics of the TS fuzzy model and the effective information of the fuzzy membership function in the design of the event trigger mechanism. All fuzzy subsystems share a set of event trigger mechanisms, which leads to a decrease in design freedom and flexibility, and causes unnecessary data transmission and communication. Therefore, exploring new event trigger mechanism design methods with more economical communication costs has an important role in promoting the theoretical research and practical application of networked nonlinear systems. Summary of the invention

[0004] The purpose of the present invention is to provide a networked nonlinear system control method based on fuzzy adaptive event triggering, which is beneficial to reduce unnecessary communication transmission and save control costs while ensuring system stability.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a networked nonlinear system control method based on fuzzy adaptive event triggering, comprising the following steps:

[0006] Step S1: Based on TS fuzzy theory, equivalent TS fuzzy modeling is performed on the networked nonlinear system;

[0007] Step S2: construct a fuzzy adaptive event triggering mechanism based on the structural characteristics of the TS fuzzy model and the fuzzy membership function information;

[0008] Step S3: Based on the fuzzy adaptive event triggering mechanism and the sampling control strategy, a TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism under sampling input is constructed;

[0009] Step S4: Based on the Lyapunov stability theory, establish the sufficient conditions for the asymptotic stability of the TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism;

[0010] Step S5: Based on the linear matrix inequality theory, the state feedback gain matrix of the TS fuzzy networked closed-loop system is calculated to realize the control of the networked nonlinear system based on the TS fuzzy model.

[0011] Furthermore, the specific implementation method of step S1 is:

[0012] First, consider a general networked nonlinear system as shown below:

[0013] (1)

[0014] in, x ( t ), u ( t ) are the state variables and control inputs of the networked nonlinear system at time t, represents the nonlinear dynamic characteristics of the networked nonlinear system at time t;

[0015] Using fuzzy theory, the equivalent TS fuzzy modeling is performed on the networked nonlinear system of formula (1). The process is as follows:

[0016] like for , for , …, for , then the networked nonlinear system of equation (1) is described by the following equation:

[0017] (2)

[0018] in, A i and B i is the known system parameter matrix; i Indicates i Fuzzy rules, i =1,2,…, r ,r represents the number of fuzzy rules; is the antecedent variable, represents the corresponding fuzzy set, where Antecedent variable ; Through single-point fuzzification and defuzzification, equation (2) is transformed into the TS fuzzy model as shown below:

[0019] (3)

[0020] in, represents the normalized fuzzy membership function, through Calculated; at the same time, for any t>0, the following constraints are satisfied:

[0021] (4).

[0022] Furthermore, the specific implementation steps of step S2 include:

[0023] Step S2-1: In combination with the structured characteristics of the TS fuzzy model, the following fuzzy rules are used in the non-periodic sampling mode to construct a fuzzy adaptive event triggering mechanism:

[0024] like for , for , …, for , then the fuzzy adaptive event triggering condition is as follows:

[0025] (5)

[0026] in, is the difference in system state change between the current sampling time and the last event triggering time of the jth fuzzy subsystem, x ( p K ) is the system state of the jth fuzzy subsystem at the current sampling time, is the current non-periodic sampling time shared by each fuzzy subsystem, is the cumulative sum of K non-periodic sampling intervals, K is the number of non-periodic sampling intervals, d μ is the μth non-periodic sampling interval, is the system state of the jth fuzzy subsystem at the time of the last event triggering, t k j is the kth triggering moment of the jth fuzzy subsystem; represents the event trigger weight matrix of the jth fuzzy subsystem, Trigger the threshold function for events greater than zero;

[0027] Step S2-2: Constructing a fuzzy adaptive event trigger threshold function based on the fuzzy membership function information as follows:

[0028] (6)

[0029] in, is an update function containing fuzzy membership function information, and its structure is as follows:

[0030] (7)

[0031] Among them are:

[0032] (8)

[0033] Among them, L j (t k j )、N1(t k j )、N2(t k j )、N3(t k j ) are all intermediate calculations; and satisfy:

[0034] (9)

[0035] in, α j , β is a parameter to be determined, α To set parameters;

[0036] Combining the results of step S2-1 and step S2-2, the fuzzy adaptive event triggering time is obtained as follows:

[0037] (10)

[0038] Among them, N + Is a positive integer.

[0039] Furthermore, the specific implementation steps of step S3 include:

[0040] Step S3-1: Based on the fuzzy adaptive event triggering mechanism and sampling control strategy, the event triggering time series and the non-periodic sampling time series analysis are performed; the networked TS fuzzy system is defined to be in the non-periodic sampling mode, and its non-periodic sampling interval d μ is always positive and satisfies the boundedness condition , where d m and Mare the lower and upper bounds of the sampling period respectively; when designing the controller, the sampler and the non-periodic sampling interval d μ It is shared by all fuzzy subsystems, and the fuzzy adaptive event triggering mechanism is designed specifically; therefore, the event triggering time series of each fuzzy subsystem is a subset of the non-periodic sampling time series, that is, it satisfies the following conditions:

[0041] (11)

[0042] Among them, p μ The μth non-periodic sampling moment;

[0043] Furthermore, the interval between two adjacent event triggers According to the non-periodic sampling time interval Divide, that is And there is ;

[0044] Step S3-2: Construct the TS fuzzy controller under non-periodic sampling input as follows:

[0045] (12)

[0046] Where K j represents the jth fuzzy subsystem controller gain to be calculated; based on the time interval division result in step S3-1, Substituting into equation (12), the TS fuzzy networked closed-loop system based on fuzzy adaptive event triggering mechanism under sampling input is further obtained as follows:

[0047] (13).

[0048] Furthermore, the specific implementation method of step S4 is:

[0049] First, given the following symbol set:

[0050]

[0051] Among them, h1(t), h2(t), φ1, φ2, , are all intermediate variables. o 1. o 2 are all unknown parameters, s is a differential variable, N, N1, N2, N3 are all unknown matrices, * represents a main diagonal symmetric matrix block, l m is the matrix to be determined, is a zero matrix with n rows and (m-1) n columns, is a zero matrix with n rows and n columns, is a zero matrix with n rows and (11-m)n columns, where m and n are matrix dimension parameters, determined by the system state dimension and the form given by the subsequent Lyapunov function;

[0052] Furthermore, the Lyapunov-Krasovskii function is constructed, and the sufficient conditions for the asymptotic stability of the TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism are obtained by combining the free weight matrix method, the fuzzy adaptive event triggering condition and the Schur complement lemma as follows:

[0053] for , given the parameters that satisfy the conditions , , , And parameters , if there exists a positive definite matrix , a matrix of suitable dimension and a non-singular matrix U such that the following inequality holds:

[0054] (14)

[0055] (15)

[0056] Among them are:

[0057]

[0058] in, , , , , , , These are all intermediate calculations. is a parameter to be determined, sym[ ] represents a sym operation, sym[X]=X T +X means calculating the sum of the matrix X itself and its transposed state.

[0059] Furthermore, the specific implementation method of step S5 is:

[0060] Based on the matrix contract transformation method and linear matrix inequality theory, the state feedback gain matrix K of the TS fuzzy networked closed-loop system is calculated. j , as follows:

[0061] for Given parameters that meet the conditions , , , And parameters , if there exists a positive definite matrix , a matrix of suitable dimension And non-singular matrices So that the following inequality holds:

[0062] (16)

[0063] (17)

[0064] And the fuzzy controller gain is given by Calculated;

[0065] Among them are:

[0066]

[0067] in, , , , , , , These are all intermediate calculations. To be determined parameter.

[0068] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a networked nonlinear system control method based on fuzzy adaptive event triggering. Taking into account the structural characteristics of the fuzzy model, a targeted adaptive event triggering mechanism is designed for different fuzzy subsystems, giving the event triggering mechanism more design flexibility. A TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism is further constructed, and the sufficient conditions for the asymptotic stability of the system and the control method are derived by using the Lyapunov stability theory and the linear matrix inequality theory. The fuzzy adaptive event triggering condition of the present invention depends on the system sampling time state, the previous trigger time state and the fuzzy membership function information, and the triggering threshold can also be adjusted according to the actual situation of different fuzzy subsystems, so as to more accurately, effectively and targetedly alleviate network bandwidth congestion, optimize communication and computing resources, and save the control cost of the networked nonlinear system based on the TS fuzzy model. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flow chart of a method implementation of an embodiment of the present invention;

[0070] Figure 2 It is a TS fuzzy networked closed-loop system structure based on a fuzzy adaptive event triggering mechanism in an embodiment of the present invention;

[0071] Figure 3 is a state trajectory diagram of a TS fuzzy networked closed-loop permanent magnet synchronous motor system in an embodiment of the present invention;

[0072] Figure 4 is a sampling control input trajectory diagram based on a fuzzy adaptive event trigger mechanism in an embodiment of the present invention;

[0073] Figure 5 is a triggering time and triggering interval diagram corresponding to the first fuzzy subsystem in an embodiment of the present invention;

[0074] Figure 6 is a triggering time and triggering interval diagram corresponding to the second fuzzy subsystem in an embodiment of the present invention;

[0075] Figure 7 It is a fuzzy adaptive trigger threshold trajectory diagram in an embodiment of the present invention. DETAILED DESCRIPTION

[0076] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0077] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0078] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0079] like Figure 1 As shown, this embodiment provides a networked nonlinear system control method based on fuzzy adaptive event triggering, comprising the following steps:

[0080] Step S1: Perform equivalent fuzzy modeling for a general networked nonlinear system based on TS fuzzy theory.

[0081] The specific implementation method of step S1 is:

[0082] First, consider a general class of networked nonlinear systems, as shown below:

[0083] (18)

[0084] in, , are the state variables and control inputs of the networked nonlinear system at time t, represents the nonlinear dynamic characteristics of the networked nonlinear system at time t, which is assumed to be a general type of continuous nonlinear function.

[0085] Furthermore, using fuzzy theory, the networked nonlinear system of equation (18) is modeled equivalently using TS fuzzy modeling. The process is as follows:

[0086] like for , for , …, for , then the networked nonlinear system of equation (18) can be described by the following equation:

[0087] (19)

[0088] in, A i and B i is a system parameter matrix of suitable and known dimension; i Indicates i Fuzzy rules, i =1,2,…, r , r represents the number of fuzzy rules; is the antecedent variable, represents the corresponding fuzzy set, where Antecedent variable Dimension. Further, through single-point fuzzification and defuzzification, Equation (19) is transformed into the global TS fuzzy system as shown below:

[0089] (20)

[0090] in, represents the normalized fuzzy membership function, through Calculated; at the same time, for any t>0, the following constraints are satisfied:

[0091] (twenty one)

[0092] Step S2: construct a fuzzy adaptive event triggering mechanism based on the structural characteristics of the TS fuzzy model and the fuzzy membership function information, increase the design freedom and flexibility, and specifically improve the utilization of computing resources and network bandwidth resources.

[0093] The specific implementation steps of step S2 include:

[0094] Step S2-1: First, combining the structural characteristics of the TS fuzzy model, in the non-periodic sampling mode, based on the parallel distributed compensation method, the present invention adopts the following fuzzy rules to construct a fuzzy adaptive event triggering mechanism:

[0095] like for , for , …, for , then the fuzzy adaptive event triggering condition is as follows:

[0096] (twenty two)

[0097] in, is the difference in system state change between the current sampling time and the last event triggering time of the jth fuzzy subsystem, x ( p K ) is the system state of the jth fuzzy subsystem at the current sampling time, is the current non-periodic sampling time shared by each fuzzy subsystem, is the cumulative sum of K non-periodic sampling intervals, K is the number of non-periodic sampling intervals, d μ is the μth non-periodic sampling interval, is the system state of the jth fuzzy subsystem at the time of the last event triggering, t k j is the kth triggering moment of the jth fuzzy subsystem; at this time, considering the different situations of the last triggering moment of each fuzzy subsystem, the difference of system state change is defined as the variable associated with j; represents the event trigger weight matrix of the jth fuzzy subsystem, Trigger the threshold function for events greater than zero, while satisfying the boundedness condition From formula (22), it can be obtained that the fuzzy adaptive event triggering rule provided by the present invention depends on the difference in system state change between the current sampling time of the fuzzy subsystem and the previous event triggering time, which can effectively optimize the communication and calculation frequency.

[0098] Step S2-2: Further, based on the fuzzy membership function information, a fuzzy adaptive event trigger threshold function is constructed to increase the design freedom and flexibility and optimize the communication frequency in a targeted manner. The following fuzzy adaptive event trigger threshold function is constructed: :

[0099] (twenty three)

[0100] in, is an update function containing fuzzy membership function information, and its structure is as follows:

[0101] (twenty four)

[0102] Among them are:

[0103] (25)

[0104] Among them, L j (t k j )、N1(t k j )、N2(t k j )、N3(t k j ) are all intermediate calculations; and satisfy:

[0105] (26)

[0106] in, α j , β is a parameter to be determined, α To set parameters.

[0107] Based on the above results, it can be seen that the present invention designs corresponding fuzzy adaptive event triggering mechanisms for different fuzzy subsystems, which are jointly determined by the fuzzy membership function information, the system state of the fuzzy subsystem at the current sampling moment, the current sampling moment, and the difference in system state change between the current sampling moment and the last event triggering moment. The transmission and update frequency of system information is adaptively adjusted to alleviate the calculation and communication burden.

[0108] Combining the results of step S2-1 and step S2-2, the triggering time of the fuzzy adaptive event is derived as follows:

[0109] (27)

[0110] Among them, N + Is a positive integer.

[0111] Step S3: Based on the fuzzy adaptive event triggering mechanism and the sampling control strategy, a TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism under sampling input is constructed.

[0112] The specific implementation steps of step S3 include:

[0113] Step S3-1: First, based on the fuzzy adaptive event triggering mechanism and sampling control strategy, the event triggering time series and the non-periodic sampling time series analysis are performed. Define the networked TS fuzzy system to be in the non-periodic sampling mode, and its non-periodic sampling interval d μ is always positive and satisfies the boundedness condition , where d m and M are the lower and upper bounds of the sampling period, respectively. When designing a controller, the sampler and the non-periodic sampling interval d μ It is shared by all fuzzy subsystems, and the fuzzy adaptive event triggering mechanism is designed specifically. Therefore, the event triggering time series of each fuzzy subsystem is a subset of the non-periodic sampling time series, that is, it satisfies the following conditions:

[0114] (28)

[0115] Among them, p μ The μth non-periodic sampling moment.

[0116] Furthermore, the interval between two adjacent event triggers According to the non-periodic sampling time interval Divide, that is And there is Since the minimum event triggering interval is a non-periodic sampling time interval, the fuzzy adaptive event triggering mechanism provided by the present invention does not have the Zeno phenomenon.

[0117] Step S3-2: First, construct the TS fuzzy controller under non-periodic sampling input as follows:

[0118] (29)

[0119] Among them, K j represents the jth fuzzy subsystem controller gain to be calculated. Based on the time interval division result in step S3-1, Substituting into equation (29), the TS fuzzy networked closed-loop system based on fuzzy adaptive event triggering mechanism under sampling input is further obtained as follows:

[0120] (30)

[0121] From the results of step S2 and step S3, it can be seen that based on the fuzzy adaptive event trigger mechanism provided by the present invention, the control input update of the above closed-loop system (13) depends on the fuzzy membership function information, the system state at the last trigger time and the system state at the current sampling time, and can be adaptively adjusted according to the change of the system state. In summary, the structure of the TS fuzzy networked closed-loop system based on the fuzzy adaptive event trigger mechanism is as follows: Figure 2 shown.

[0122] Step S4: Based on the Lyapunov stability theory, sufficient conditions for the asymptotic stability of the TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism are established.

[0123] The specific implementation method of step S4 is:

[0124] First, to simplify the expression and facilitate calculation, the following symbol set is given:

[0125]

[0126] Among them, h1(t), h2(t), φ1, φ2, , are all intermediate variables. o 1. o 2 are all unknown parameters, s is a differential variable, N, N1, N2, N3 are all unknown matrices, * represents a main diagonal symmetric matrix block, l m is the matrix to be determined, is a zero matrix with n rows and (m-1) n columns, is a zero matrix with n rows and n columns, It is a zero matrix with n rows and (11-m)n columns. m and n are both matrix dimension parameters, which are determined by the system state dimension and the form given by the subsequent Lyapunov function.

[0127] Furthermore, by constructing the Lyapunov-Krasovskii function and combining the free weight matrix method, fuzzy adaptive event triggering conditions and Schur complement lemma, the sufficient conditions for the asymptotic stability of the TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism are obtained as follows:

[0128] for , given the parameters that satisfy the conditions , , , And parameters , if there exists a positive definite matrix , a matrix of suitable dimension and a non-singular matrix U such that the following inequality holds:

[0129] (31)

[0130] (32)

[0131] Among them are:

[0132]

[0133] in, , , , , , , These are all intermediate calculations. is a parameter to be determined, sym[ ] represents a sym operation, sym[X]=X T +X means calculating the sum of the matrix X itself and its transposed state.

[0134] In this step, the constructed Lyapunov-Krasovskii function is: , among which are:

[0135] (33)

[0136] (34)

[0137] (35)

[0138] (36)

[0139] (37)

[0140] (38)

[0141] The Lyapunov-Krasovskii function Taking the first-order derivative, we get the following result:

[0142] (39)

[0143] (40)

[0144] (41)

[0145] (42)

[0146] (43)

[0147] Furthermore, the following lemma is used to scale the inequality for the integral term in the obtained derivative:

[0148] Lemma 1: Given a matrix M of suitable dimension, a positive definite matrix N, and a vector , if in the interval Inside, is a continuous and differentiable function, then the following inequality holds:

[0149] (44)

[0150] The following results are obtained:

[0151] (45)

[0152] Furthermore, consider the fuzzy adaptive event triggering constraints:

[0153] (46)

[0154] And the following identities are introduced based on the free weight matrix method:

[0155] (47)

[0156] Based on the above analysis, based on the Schur complement lemma and the constraints of Equations (31) and (32), the sufficient conditions for the asymptotic stability of the TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism are proved.

[0157] Step S5: Based on the linear matrix inequality theory, the state feedback gain matrix K of the TS fuzzy networked closed-loop system is calculated: j , realizing the control of networked nonlinear systems based on TS fuzzy model.

[0158] The specific implementation method of step S5 is:

[0159] Based on the matrix contract transformation method and linear matrix inequality theory, the state feedback gain matrix K of the TS fuzzy networked closed-loop system can be calculated using the Matlab LMI toolbox. j , as follows:

[0160] for Given parameters that meet the conditions , , , And parameters , if there exists a positive definite matrix , a matrix of suitable dimension And non-singular matrices So that the following inequality holds:

[0161] (48)

[0162] (49)

[0163] And the fuzzy controller gain can be given by Calculated.

[0164] Among them are:

[0165]

[0166] in, , , , , , , These are all intermediate calculations. To be determined parameter.

[0167] First, define the symbol set as follows:

[0168]

[0169] Then, equation (48) and equation (49) can be calculated from equation (31) and equation (32) respectively by the method of contract transformation, and the above theorem is proved.

[0170] Furthermore, a nonlinear networked permanent magnet synchronous motor system is used to verify the effectiveness of the networked system control strategy based on fuzzy adaptive event triggering proposed in the present invention and its superiority in saving communication resources.

[0171] First, the nonlinear networked permanent magnet synchronous motor system is as follows:

[0172] (50)

[0173] in, , , For nonlinear networked permanent magnet synchronous motor systems The corresponding current, voltage and stator inductance on the axis; The motor rotor angular velocity, stator resistance, pole pair number, viscous friction coefficient, load torque and magnetic flux linkage are expressed in this way. Definition , and assuming that the conditions are met: , as well as Based on the relevant theory of TS fuzzy system, the above nonlinear networked permanent magnet synchronous motor system can be equivalently expressed by the following TS fuzzy system:

[0174] (51)

[0175] in , is the non-periodic sampling control input based on the fuzzy adaptive event trigger mechanism. The fuzzy membership functions are as well as The system parameter matrix is ​​as follows:

[0176]

[0177] The remaining parameters are as follows: as well as By solving equations (48) and (49) using the Matlab LMI toolbox, the state feedback control gain matrix of the networked permanent magnet synchronous motor system based on the TS fuzzy model is obtained as follows:

[0178]

[0179] And there are:

[0180]

[0181] The relevant parameters of the fuzzy adaptive event triggering mechanism are: . Under the initial condition And fixed sampling period The simulation results of this example can be obtained by using Matlab software. Figure 3 It is the state trajectory diagram of TS fuzzy networked closed-loop permanent magnet synchronous motor system. Figure 4 is the sampling control input trajectory diagram based on the fuzzy adaptive event trigger mechanism, Figure 5 , Figure 6 They are the triggering time and triggering interval diagrams corresponding to the first fuzzy subsystem and the second fuzzy subsystem, Figure 7 It is the trajectory diagram of adaptive trigger threshold.

[0182] from Figure 3 It can be clearly seen from the simulation results that under the action of the fuzzy adaptive event trigger mechanism designed in the present invention, the state of the networked permanent magnet synchronous motor system based on the TS fuzzy model It can effectively tend to be stable, which verifies the effectiveness of the theoretical results of the present invention.

[0183] In this simulation verification, by involving appropriate sampling cycles, the number of data to be transmitted for each fuzzy subsystem is 100. Based on the fuzzy adaptive event triggering mechanism, the first fuzzy subsystem and the second fuzzy subsystem have 31 and 27 sampling data respectively to participate in the actual information transmission to update the control input signal, and the average data transmission rate is 29%. Figure 5 and Figure 6 It can be seen from the results that under the condition of ensuring system stability, the networked system control method based on fuzzy adaptive event triggering provided by the present invention can effectively optimize the information transmission efficiency and achieve the control goal of alleviating the communication and computing burden.

[0184] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0185] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0186] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0187] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0188] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A networked nonlinear system control method based on fuzzy adaptive event triggering, characterized in that: The following steps are involved: Step S1: Based on TS fuzzy theory, equivalent TS fuzzy modeling is performed on the networked nonlinear system; Step S2: construct a fuzzy adaptive event triggering mechanism based on the structural characteristics of the TS fuzzy model and the fuzzy membership function information; Step S3: Based on the fuzzy adaptive event triggering mechanism and the sampling control strategy, a TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism under sampling input is constructed; Step S4: Based on the Lyapunov stability theory, establish the sufficient conditions for the asymptotic stability of the TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism; Step S5: Based on the linear matrix inequality theory, the state feedback gain matrix of the TS fuzzy networked closed-loop system is calculated to realize the control of the networked nonlinear system based on the TS fuzzy model; The specific implementation method of step S1 is: First, consider a general networked nonlinear system as shown below: （1） in, x ( t ), u ( t ) are the state variables and control inputs of the networked nonlinear system at time t, represents the nonlinear dynamic characteristics of the networked nonlinear system at time t; Using fuzzy theory, the equivalent TS fuzzy modeling is performed on the networked nonlinear system of formula (1). The process is as follows: like for , for , …, for , then the networked nonlinear system of equation (1) is described by the following equation: （2） in, A i and B i is the known system parameter matrix; i Indicates i Fuzzy rules, i =1,2,…, r , r represents the number of fuzzy rules; is the antecedent variable, represents the corresponding fuzzy set, where Antecedent variable Dimension; Through single-point fuzzification and defuzzification, equation (2) is transformed into the TS fuzzy model as shown below: （3） in, represents the normalized fuzzy membership function, through Calculated; at the same time, for any t>0, the following constraints are satisfied: （4） The specific implementation steps of step S2 include: Step S2-1: In combination with the structured characteristics of the TS fuzzy model, the following fuzzy rules are used in the non-periodic sampling mode to construct a fuzzy adaptive event triggering mechanism: like for , for , …, for , then the fuzzy adaptive event triggering condition is as follows: （5） in, is the difference in system state change between the current sampling time and the last event triggering time of the jth fuzzy subsystem, x ( p K ) is the system state of the jth fuzzy subsystem at the current sampling time, is the current non-periodic sampling time shared by each fuzzy subsystem, is the cumulative sum of K non-periodic sampling intervals, K is the number of non-periodic sampling intervals, d μ is the μth non-periodic sampling interval, is the system state of the jth fuzzy subsystem at the time of the last event triggering, t k j is the kth triggering moment of the jth fuzzy subsystem; represents the event trigger weight matrix of the jth fuzzy subsystem, Trigger the threshold function for events greater than zero; Step S2-2: Constructing a fuzzy adaptive event trigger threshold function based on the fuzzy membership function information as follows: （6） in, is an update function containing fuzzy membership function information, and its structure is as follows: （7） Among them are: （8） Among them, L j (t k j )、N1(t k j )、N2(t k j )、N3(t k j ) are all intermediate calculations; and satisfy: （9） in, α j , β is a parameter to be determined, α To set parameters; Combining the results of step S2-1 and step S2-2, the fuzzy adaptive event triggering time is obtained as follows: （10） Among them, N + is a positive integer; The specific implementation steps of step S3 include: Step S3-1: Based on the fuzzy adaptive event triggering mechanism and sampling control strategy, the event triggering time series and the non-periodic sampling time series analysis are performed; the networked TS fuzzy system is defined to be in the non-periodic sampling mode, and its non-periodic sampling interval d μ is always positive and satisfies the boundedness condition , where d m and M are the lower and upper bounds of the sampling period respectively; when designing the controller, the sampler and the non-periodic sampling interval d μ It is shared by all fuzzy subsystems, and the fuzzy adaptive event triggering mechanism is designed specifically; therefore, the event triggering time series of each fuzzy subsystem is a subset of the non-periodic sampling time series, that is, it satisfies the following conditions: （11） Among them, p μ The μth non-periodic sampling moment; Furthermore, the interval between two adjacent event triggers According to the non-periodic sampling time interval Divide, that is And there is ; Step S3-2: Construct the TS fuzzy controller under non-periodic sampling input as follows: （12） Where K j represents the jth fuzzy subsystem controller gain to be calculated; based on the time interval division result in step S3-1, Substituting into equation (12), the TS fuzzy networked closed-loop system based on fuzzy adaptive event triggering mechanism under sampling input is further obtained as follows: （13）。 2. The networked nonlinear system control method based on fuzzy adaptive event triggering according to claim 1 is characterized in that: The specific implementation method of step S4 is: First, given the following symbol set: Among them, h1(t), h2(t), φ1, φ2, , are all intermediate variables. o 1. o 2 are all unknown parameters, s is a differential variable, N, N1, N2, N3 are all unknown matrices, * represents a main diagonal symmetric matrix block, l m is the matrix to be determined, is a zero matrix with n rows and (m-1) n columns, is a zero matrix with n rows and n columns, is a zero matrix with n rows and (11-m)n columns, where m and n are matrix dimension parameters, determined by the system state dimension and the form given by the subsequent Lyapunov function; Furthermore, the Lyapunov-Krasovskii function is constructed, and the sufficient conditions for the asymptotic stability of the TS fuzzy networked closed-loop system based on the fuzzy adaptive event triggering mechanism are obtained by combining the free weight matrix method, the fuzzy adaptive event triggering condition and the Schur complement lemma as follows: for , given the parameters that satisfy the conditions , , , And parameters , if there exists a positive definite matrix , a matrix of suitable dimension and a non-singular matrix U such that the following inequality holds: （14） （15） Among them are: in, , , , , , , These are all intermediate calculations. is a parameter to be determined, sym[ ] represents a sym operation, sym[X]=X T +X means calculating the sum of the matrix X itself and its transposed state.

3. The networked nonlinear system control method based on fuzzy adaptive event triggering according to claim 2 is characterized in that: The specific implementation method of step S5 is: Based on the matrix contract transformation method and linear matrix inequality theory, the state feedback gain matrix K of the TS fuzzy networked closed-loop system is calculated. j , as follows: for Given parameters that meet the conditions , , , And parameters , if there exists a positive definite matrix , a matrix of suitable dimension And non-singular matrices So that the following inequality holds: （16） （17） And the fuzzy controller gain is given by Calculated; Among them are: in, , , , , , , These are all intermediate calculations. To be determined parameter.

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