Bandwidth limited system T-S fuzzy sliding mode control method based on adaptive WTOD protocol

Abstract

The invention discloses a bandwidth limited system T-S fuzzy sliding mode control method based on an adaptive WTOD protocol, and belongs to the technical field of industrial control and intelligent manufacturing. The method comprises the following steps: establishing a T-S fuzzy networked system model containing time-varying and time-lag; designing a self-adaptive WTOD transmission protocol integrated with a uniform quantization mechanism; constructing a fuzzy sliding mode controller based on the available system state information; giving out discrimination conditions for ensuring that the indexes of the T-S fuzzy networked system are bounded and the sliding mode surface is reachable in an inequality group form; converting an inequality group discrimination condition containing linear coupling into a minimization problem by adopting cone complementary linearization; and optimizing the final upper bound of the closed-loop system state and the upper bound of the sliding mode surface reaching neighborhood based on a particle swarm algorithm. According to the method, the cooperative improvement of the control performance and the communication efficiency is ensured, and a verifiable and easy-to-implement unified analysis and design framework is provided for the bandwidth-limited networked nonlinear system.

Description

Technical Field

[0001] This invention relates to a fuzzy sliding mode control method for bandwidth-constrained systems (TS) based on the adaptive WTOD protocol, belonging to the field of industrial control and intelligent manufacturing technology. Background Technology

[0002] In the increasing complexity and intelligence of industrial control systems, engineering objects generally exhibit significant nonlinear characteristics, making it difficult for traditional linear models to accurately characterize their dynamic behavior. To address this, the TS fuzzy model approximates nonlinear systems through local linear sub-models, effectively improving modeling accuracy and control performance. Sliding mode control, as a robust nonlinear control method, maintains good dynamic performance and stability even under parameter uncertainties and external disturbances. Combining the TS fuzzy model with sliding mode control allows for simplified design using linear control strategies within fuzzy partitions, while the sliding surface switching mechanism suppresses modeling errors and disturbances, achieving accurate and robust control of complex nonlinear systems.

[0003] As engineering practices evolve towards distributed and remote collaborative systems, networked control systems have become a key form of modern industry and intelligent manufacturing. However, under bandwidth-constrained conditions, how to achieve efficient allocation of communication resources while ensuring closed-loop stability has become a core challenge. While existing polling and random access protocols balance fairness and ease of implementation, their allocation of access opportunities according to a preset order or probability makes it difficult to implement differentiated scheduling based on state urgency and information value. In contrast, the WTOD protocol can dynamically adjust priorities based on information importance indicators, allowing critical data to be transmitted preferentially under limited bandwidth. However, existing technical solutions often suffer from the following drawbacks: they rely solely on instantaneous error indicators or historical frequency as a single dimension, lacking a unified and adaptively updatable measurement and scheduling framework, making it difficult to effectively balance instantaneous state changes and long-term communication resource allocation needs.

[0004] Furthermore, existing fuzzy sliding mode control methods in Transmission System (TS) are mostly designed based on the ideal premise of no or negligible time delay, which is incompatible with real-world scenarios where bandwidth is limited and system time delays coexist. In network environments with limited communication and unreliable transmission, existing sliding mode control methods struggle to simultaneously ensure data privacy and control performance. Given that bandwidth-limited scenarios require differentiated scheduling based on information value, and that system time delays alter closed-loop dynamics and affect stability and performance, there is an urgent need to construct a unified analysis and design framework for scenarios with both bandwidth limitations and time delays, proposing verifiable stability criteria and achievable control and scheduling rules. Summary of the Invention

[0005] To address the problems existing in the background technology, the present invention provides a fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol, the method comprising the following steps:

[0007] S1: Establish a fuzzy networked system model of TS with time-varying time delay;

[0008] S2: Design an adaptive WTOD transmission protocol with integrated uniform quantization mechanism;

[0009] S3: Construct a fuzzy sliding mode controller based on available system state information;

[0010] S4: The criteria for ensuring that the exponent of the TS fuzzy network system is bounded and the sliding surface is reachable are given in the form of a system of inequalities.

[0011] S5: Conical complementary linearization is used to transform the discrimination conditions of the system of inequalities with linear coupling into a minimization problem;

[0012] S6: Optimize the final upper bound of the closed-loop system state and the upper bound of the sliding mode surface reaching the neighborhood based on the particle swarm optimization algorithm.

[0013] Furthermore, step S1 includes the following steps:

[0014] S101: If The first antecedent variable of the time system , The second antecedent variable of the time system ... The first time system one preceding variable , Indicates the first A fuzzy rule, It is a fuzzy rule number. It is the first The first fuzzy rule A fuzzy set of variables, where the time-varying, time-delay (TS) fuzzy network system satisfies:

[0015] (1)

[0016] In formula (1):

[0017] express The system state at any given moment; For system state dimensions;

[0018] express The system state at any given moment;

[0019] Represents the time delay term, representing The historical state of a moment It is time-varying and time-delayed, satisfying , and These are the upper and lower bounds of the time delay, respectively;

[0020] express Time-based control input, The dimension of the controller;

[0021] express The external disturbances experienced by the time system satisfy the following conditions: , These are known constants;

[0022] It is the first The known system state transition matrix corresponding to the fuzzy rules;

[0023] It is the first The known time-delay state matrix corresponding to the fuzzy rule;

[0024] It is the first The known input matrix corresponding to the fuzzy rules;

[0025] It is the first The parameters related to the fuzzy rule are uncertain, among which: and The system parameter matrix is ​​known. It is an unknown, uncertain matrix that satisfies , for transpose, It is the identity matrix;

[0026] At the same time, the initial state of the system ;

[0027] S102: Definition of the first Membership function of a fuzzy rule It meets the following two conditions:

[0028] Condition 1: Activation level is bounded:

[0029] (2)

[0030] In formula (2):

[0031] express The first time system one preceding variable In the The first fuzzy rule Fuzzy set of variables Membership degree in;

[0032] Condition 2: Global Normalization:

[0033] (3)

[0034] S103: The system model for defuzzification of the time-varying time-delay (TS) fuzzy network system, obtained based on fuzzy inference, is as follows:

[0035] (4)

[0036] The system state remains initially unchanged. .

[0037] Furthermore, step S2 includes the following steps:

[0038] S201: Set the uniform quantizer independently for each sensor node;

[0039] Given the first The step size of each node is Adjust the real number line according to the step size Divided into countless intervals ( ), The set is an integer set; when the system state is... Each component At that time, the quantized output is defined as The quantization error can be obtained by satisfying the following conditions. ;

[0040] S202: Introduction of Adaptive WTOD Transmission Protocol:

[0041] (5)

[0042] In equation (5):

[0043] for The sensor node selected at any given time;

[0044] The operator represents the minimum value;

[0045] This indicates the point where the function value reaches its maximum value;

[0046] Available signals for the controller The One component;

[0047] For the first The adaptive weights of each component are updated according to the following rules: ,in: , They represent the first Upper and lower bounds of the adaptive weights of each component; Indicates the weighting factor;

[0048] S203: Based on the zero-order hold mechanism, set the update rules for the available signals of the controller:

[0049] (6)

[0050] when When the quantization result remains unchanged, no data transmission is required, thus effectively reducing redundant communication.

[0051] Furthermore, step S3 includes the following steps:

[0052] S301: Constructing a standard sliding surface ,in: Represents the sliding surface parameter matrix;

[0053] S302: If The first antecedent variable of the time system , The second antecedent variable of the time system ... The first time system one preceding variable Indicates the first A fuzzy rule, It is the first The first fuzzy rule Given a fuzzy set of variables, the sliding mode controller is:

[0054] (7)

[0055] In equation (7):

[0056] This represents the controller gain to be solved;

[0057] This represents the robustness gain of sliding mode control;

[0058] Based on the fuzzy inference mechanism, the defuzzified sliding mode controller is obtained as follows:

[0059] (8)

[0060] In equation (8):

[0061] It is the first The membership function of a fuzzy rule, and ;

[0062] To reconstruct the sliding surface;

[0063] S303: Obtain the closed-loop system based on the defuzzified system and the defuzzified sliding mode controller:

[0064] (9)

[0065] In equation (9):

[0066] It is the identity matrix;

[0067] According to Selected sensor node at any time The generated diagonal matrix, It is the Kronecker function;

[0068] This is an equivalent representation of external disturbances;

[0069] This is for quantization error;

[0070] S304: Establish the membership function proportional relationship between the system and the controller's corresponding rules:

[0071] (10)

[0072] In formula (10):

[0073] for Time of the first The ratio of the membership functions of the controller and the system under fuzzy rules. and These are the upper and lower bounds of the membership function ratio;

[0074] S305: Define globally unified upper and lower bounds and Then the constraints between the proportionality coefficients can be obtained:

[0075] (11)

[0076] In equation (11):

[0077] This represents the upper and lower bounds of the range of values ​​for the proportionality coefficient.

[0078] Furthermore, the matrix form of the discrimination condition described in S4 is as follows:

[0079] (12)

[0080] In equation (12):

[0081] Represents the corresponding symmetric matrix block;

[0082] It is the first negative definite matrix; where:

[0083] It is a negative definite matrix of order 1. The first row and first column of the block matrix, where: ;

[0084] It is a negative definite matrix of order 1. The block matrix in the first row and second column;

[0085] It is a negative definite matrix of order 1. The block matrix in the 2nd row and 2nd column; where: , For given parameters;

[0086] It is the second negative definite matrix; where:

[0087] It is the second negative definite matrix The first row and first column of the block matrix, where: ;

[0088] It is the second negative definite matrix The block matrix in the first row and second column;

[0089] It is the second negative definite matrix The block matrix in the second row and second column;

[0090] It is the third negative definite matrix;

[0091] It is the third negative definite matrix The block matrix in the first row and first column;

[0092] It is the third negative definite matrix The block matrix in the first row and second column;

[0093] It is the third negative definite matrix The block matrix in the 1st row and 3rd column;

[0094] It is the third negative definite matrix The block matrix in the 3rd row and 3rd column;

[0095] It is the fourth negative definite matrix;

[0096] It is the fourth negative definite matrix. The block matrix in the first row and first column;

[0097] It is the fourth negative definite matrix. The block matrix in the first row and second column;

[0098] It is the fourth negative definite matrix. The block matrix in the 1st row and 3rd column;

[0099] It is the fourth negative definite matrix. The block matrix in the 3rd row and 3rd column;

[0100] This is a preset convergence index used to characterize the speed of algorithm convergence;

[0101] , , , , as well as All are coefficients to be solved;

[0102] , , , , as well as All are matrices to be solved, satisfying , and They are inverse matrices;

[0103] This is a diagonal matrix related to the upper bound of the adaptive parameters of the transmission protocol;

[0104] This is a diagonal matrix related to the lower bound of the adaptive parameters of the transmission protocol;

[0105] In order to be with the first The diagonal matrix related to the various transmission scenarios;

[0106] For the first Gain coefficients related to this situation.

[0107] Furthermore, step S5 includes the following steps:

[0108] S501: Reconstructing Equality Constraints Using Cone Complementary Linearization Method The minimization objective is: , For the trace of the matrix, impose constraints: ;

[0109] S502: Combining the inequalities in S4, the above constraint problem is solved using the linear matrix toolbox in MATLAB;

[0110] If the minimization problem has a feasible solution and the optimal value is... Approximately equal to the system state dimension Then, the matrix to be designed that allows the closed-loop system to satisfy exponential boundedness and reachability of the sliding surface can be determined. ;

[0111] If the solution to the minimization problem cannot approach the This indicates that the system lacks controllability;

[0112] S503: The matrix to be designed Substituting the known parameter matrix back into the matrix inequality in S4, we obtain the linear matrix inequality constraints that ensure the desired control performance.

[0113] Furthermore, step S6 includes the following steps:

[0114] S601: Define decision variables Introduce inequality constraints: Combined with the linear matrix inequalities obtained from S503, these together form the constraints for solving the linear matrix inequalities.

[0115] S602: Define the objective function:

[0116] (13)

[0117] In equation (13):

[0118] and Given weight parameters, satisfying , and ;

[0119] This is the final upper bound of the closed-loop system state;

[0120] This is the upper bound of the sliding surface reaching the neighborhood;

[0121] This is the upper bound of the quantization error in the system;

[0122] and They represent finding the matrix respectively. The minimum and maximum eigenvalues;

[0123] S603: Set upper and lower limits for each parameter of the decision variable. and Satisfying constraints Randomly generated within this range 100 particles as the initial population;

[0124] S604: For each particle, use the MATLAB linear matrix inequality solver based on its current parameter values ​​to verify the feasibility of the constraints.

[0125] If the linear matrix inequality has a feasible solution, then calculate the corresponding fitness function value. ;

[0126] If the linear matrix inequality is not satisfied, then a penalty value is assigned to the particle's fitness. To guide them away from infeasible areas;

[0127] S605: Update the particle velocity and position based on the individual optimal solution and the swarm optimal solution to achieve dynamic optimization of the parameter space; if the update result does not meet the constraints, perform feasibility correction, return to S604 to calculate the objective function based on the updated particle swarm, until the number of iterations reaches the preset upper limit;

[0128] S606: When the iteration ends, take the parameter vector corresponding to the globally optimal particle. As the optimal solution, the optimal control gain matrix is ​​obtained. .

[0129] Compared with the prior art, the beneficial effects of the present invention are:

[0130] This invention employs an adaptive weight update mechanism that integrates instantaneous error and historical frequency as dual indicators to dynamically optimize node transmission priority. This improves system response speed and anti-disturbance performance while ensuring closed-loop stability and boundedness. A TS fuzzy system model containing time-varying delays and quantization errors is constructed. Combining mode-dependent sliding mode controllers and Lyapunov stability theory, LMI constraints are used to uniformly characterize exponential boundedness and sliding surface reachability, solving the control performance degradation problem of traditional methods in scenarios with both delays and quantization errors. Furthermore, by combining conical complementary linearization and a hierarchical optimization strategy using particle swarm optimization, this invention overcomes the limitation of traditional LMI toolchains that only determine feasibility, achieving the minimization of the final upper bound of the closed-loop state and the upper bound of the sliding surface's reachability in the neighborhood. This ensures a synergistic improvement in control performance and communication efficiency, providing a verifiable and easily implemented unified analysis and design framework for bandwidth-constrained networked nonlinear systems. Attached Figure Description

[0131] Figure 1 This is a flowchart of the present invention;

[0132] Figure 2 It is a graph showing the change of the objective function value obtained by solving the minimization problem using the particle swarm optimization algorithm;

[0133] Figure 3 This is a schematic diagram of the state trajectory of an open-loop system;

[0134] Figure 4 This is a schematic diagram of the state trajectory of a closed-loop system under the adaptive WTOD protocol with integrated uniform quantization mechanism;

[0135] Figure 5 This is a schematic diagram illustrating the selection of sensor nodes in the adaptive WTOD protocol with an integrated uniform quantization mechanism.

[0136] Figure 6 This is a schematic diagram of the trajectory of the control input of the closed-loop system under the adaptive WTOD protocol with integrated uniform quantization mechanism;

[0137] Figure 7 This is a schematic diagram of the trajectory of the sliding variable in a closed-loop system under an adaptive WTOD protocol with an integrated uniform quantization mechanism.

[0138] Figure 8 This is a schematic diagram of the state trajectory of a closed-loop system under the adaptive WTOD protocol;

[0139] Figure 9 This is a schematic diagram illustrating the selection of sensor nodes in the adaptive WTOD protocol. Detailed Implementation

[0140] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0141] A fuzzy sliding mode control method for bandwidth-constrained systems (TS) based on the adaptive WTOD protocol, the method comprising the following steps:

[0142] S1: Establish a fuzzy networked system model of TS with time-varying time delay;

[0143] S2: Design an adaptive WTOD transmission protocol with integrated uniform quantization mechanism;

[0144] S3: Construct a fuzzy sliding mode controller based on available system state information;

[0145] S4: The criteria for ensuring that the exponent of the TS fuzzy network system is bounded and the sliding surface is reachable are given in the form of a system of inequalities.

[0146] To achieve stability and sliding surface reachability in the TS fuzzy network system, a sufficiency criterion is derived through a combination of Lyapunov stability theory and sliding mode control theory, ensuring that both properties hold simultaneously.

[0147] S5: Conical complementary linearization is used to transform the discrimination conditions of the system of inequalities with linear coupling into a minimization problem;

[0148] S6: Optimize the final upper bound of the closed-loop system state and the upper bound of the sliding mode surface reaching the neighborhood based on the particle swarm optimization algorithm.

[0149] Furthermore, step S1 includes the following steps:

[0150] S101: If The first antecedent variable of the time system , The second antecedent variable of the time system ... The first time system one preceding variable , Indicates the first A fuzzy rule, It is a fuzzy rule number. It is the first The first fuzzy rule A fuzzy set of variables, where the time-varying, time-delay (TS) fuzzy network system satisfies:

[0151] (1)

[0152] In formula (1):

[0153] express The system state at any given moment; For system state dimensions;

[0154] express The system state at any given moment;

[0155] Represents the time delay term, representing The historical state of a moment It is time-varying and time-delayed, satisfying , and These are the upper and lower bounds of the time delay, respectively;

[0156] express Time-based control input, The dimension of the controller;

[0157] express The external disturbances experienced by the time system satisfy the following conditions: , These are known constants;

[0158] It is the first The known system state transition matrix corresponding to the fuzzy rules;

[0159] It is the first The known time-delay state matrix corresponding to the fuzzy rule;

[0160] It is the first The known input matrix corresponding to the fuzzy rules;

[0161] It is the first The parameters related to the fuzzy rule are uncertain, among which: and The system parameter matrix is ​​known. It is an unknown, uncertain matrix that satisfies , for transpose, It is the identity matrix;

[0162] At the same time, the initial state of the system ;

[0163] S102: Definition of the first Membership function of a fuzzy rule It meets the following two conditions:

[0164] Condition 1: Activation level is bounded:

[0165] (2)

[0166] In formula (2):

[0167] express The first time system one preceding variable In the The first fuzzy rule Fuzzy set of variables Membership degree in;

[0168] Condition 2: Global Normalization:

[0169] (3)

[0170] S103: The system model for defuzzification of the time-varying time-delay (TS) fuzzy network system, obtained based on fuzzy inference, is as follows:

[0171] (4)

[0172] The system state remains initially unchanged. .

[0173] Furthermore, step S2 includes the following steps:

[0174] S201: Set the uniform quantizer independently for each sensor node;

[0175] Given the first The step size of each node is Adjust the real number line according to the step size Divided into countless intervals ( ), The set is an integer set; when the system state is... Each component At that time, the quantized output is defined as From the above construction, the quantization error can be obtained by satisfying the following conditions: ;

[0176] S202: Introduction of Adaptive WTOD Transmission Protocol:

[0177] (5)

[0178] In equation (5):

[0179] for The sensor node selected at any given time;

[0180] The operator represents the minimum value;

[0181] This indicates the point where the function value reaches its maximum value;

[0182] Available signals for the controller The One component;

[0183] For the first The adaptive weights of each component are updated according to the following rules: ,in: , They represent the first Upper and lower bounds of the adaptive weights of each component; Indicates the weighting factor;

[0184] S203: Based on the zero-order hold mechanism, set the update rules for the available signals of the controller:

[0185] (6)

[0186] when When the quantization result remains unchanged, no data transmission is required, thus effectively reducing redundant communication.

[0187] Furthermore, step S3 includes the following steps:

[0188] S301: Constructing a standard sliding surface ,in: Represents the sliding surface parameter matrix;

[0189] S302: If The first antecedent variable of the time system , The second antecedent variable of the time system ... The first time system one preceding variable Indicates the first A fuzzy rule, It is the first The first fuzzy rule Given a fuzzy set of variables, the sliding mode controller is:

[0190] (7)

[0191] In equation (7):

[0192] This represents the controller gain to be solved;

[0193] This represents the robustness gain of sliding mode control;

[0194] Based on the fuzzy inference mechanism, the defuzzified sliding mode controller is obtained as follows:

[0195] (8)

[0196] In equation (8):

[0197] It is the first The membership function of a fuzzy rule, and ;

[0198] To reconstruct the sliding surface;

[0199] S303: Obtain the closed-loop system based on the defuzzified system and the defuzzified sliding mode controller:

[0200] (9)

[0201] In equation (9):

[0202] It is the identity matrix;

[0203] According to Selected sensor node at any time The generated diagonal matrix, It is the Kronecker function;

[0204] This is an equivalent representation of external disturbances;

[0205] This is for quantization error;

[0206] S304: Establish the membership function proportional relationship between the system and the controller's corresponding rules:

[0207] (10)

[0208] In formula (10):

[0209] for Time of the first The ratio of the membership functions of the controller and the system under fuzzy rules. and The upper and lower bounds of the membership function ratio are constants that can be estimated in advance and are considered known based on the characteristics of the membership function.

[0210] S305: Define globally unified upper and lower bounds and Then the constraints between the proportionality coefficients can be obtained:

[0211] (11)

[0212] In equation (11):

[0213] This represents the upper and lower bounds of the range of values ​​for the proportionality coefficient.

[0214] Furthermore, the matrix form of the discrimination condition described in S4 is as follows:

[0215] (12)

[0216] In equation (12):

[0217] Represents the corresponding symmetric matrix block;

[0218] It is the first negative definite matrix; where:

[0219] It is a negative definite matrix of order 1. The first row and first column of the block matrix, where: ;

[0220] It is a negative definite matrix of order 1. The block matrix in the first row and second column;

[0221] It is a negative definite matrix of order 1. The block matrix in the 2nd row and 2nd column; where: , For given parameters;

[0222] It is the second negative definite matrix; where:

[0223] It is the second negative definite matrix The first row and first column of the block matrix, where: ;

[0224] It is the second negative definite matrix The block matrix in the first row and second column;

[0225] It is the second negative definite matrix The block matrix in the second row and second column;

[0226] It is the third negative definite matrix;

[0227] It is the third negative definite matrix The block matrix in the first row and first column;

[0228] It is the third negative definite matrix The block matrix in the first row and second column;

[0229] It is the third negative definite matrix The block matrix in the 1st row and 3rd column;

[0230] It is the third negative definite matrix The block matrix in the 3rd row and 3rd column;

[0231] It is the fourth negative definite matrix;

[0232] It is the fourth negative definite matrix. The block matrix in the first row and first column;

[0233] It is the fourth negative definite matrix. The block matrix in the first row and second column;

[0234] It is the fourth negative definite matrix. The block matrix in the 1st row and 3rd column;

[0235] It is the fourth negative definite matrix. The block matrix in the 3rd row and 3rd column;

[0236] This is a preset convergence index used to characterize the speed of algorithm convergence;

[0237] , , , , as well as All are coefficients to be solved;

[0238] , , , , as well as All are matrices to be solved, satisfying , and They are inverse matrices;

[0239] This is a diagonal matrix related to the upper bound of the adaptive parameters of the transmission protocol;

[0240] This is a diagonal matrix related to the lower bound of the adaptive parameters of the transmission protocol;

[0241] In order to be with the first The diagonal matrix related to the various transmission scenarios;

[0242] For the first Gain coefficients related to this situation.

[0243] Furthermore, step S5 includes the following steps:

[0244] S501: Reconstructing Equality Constraints Using Cone Complementary Linearization Method The minimization objective is: , For the trace of the matrix, impose constraints: ;

[0245] S502: Combining the inequalities in S4, the above constraint problem is solved using the linear matrix toolbox in MATLAB;

[0246] If the minimization problem has a feasible solution and the optimal value is... Approximately equal to the system state dimension This indicates that the designed control algorithm can stabilize the system. Based on this optimal solution, the matrix to be designed that allows the closed-loop system to satisfy exponential boundedness and reachability of the sliding surface can be determined. ;

[0247] If the solution to the minimization problem cannot approach the This indicates that the system lacks controllability under the designed control algorithm.

[0248] S503: The matrix to be designed Substituting the known parameter matrix back into the matrix inequality in S4, we obtain the linear matrix inequality constraints that ensure the desired control performance.

[0249] Furthermore, step S6 includes the following steps:

[0250] S601: Define decision variables Let be the set of parameters to be optimized, and introduce inequality constraints: Combined with the linear matrix inequalities obtained from S503, these together form the constraints for solving the linear matrix inequalities.

[0251] S602: Define the objective function:

[0252] (13)

[0253] In equation (13):

[0254] and Given weight parameters, satisfying , and ;

[0255] This is the final upper bound of the closed-loop system state;

[0256] This is the upper bound of the sliding surface reaching the neighborhood;

[0257] This is the upper bound of the quantization error in the system;

[0258] and They represent finding the matrix respectively. The minimum and maximum eigenvalues;

[0259] S603: Set upper and lower limits for each parameter of the decision variable. and Satisfying constraints Randomly generated within this range The initial group consists of 10 particles, each particle's position vector corresponds to a set of parameter values, and its velocity vector is randomly distributed within a given velocity range.

[0260] S604: For each particle, use the MATLAB linear matrix inequality solver based on its current parameter values ​​to verify the feasibility of the constraints.

[0261] If the linear matrix inequality has a feasible solution, then calculate the corresponding fitness function value. ;

[0262] If the linear matrix inequality is not satisfied, then a sufficiently large penalty value is assigned to the particle's fitness. To guide them away from infeasible areas;

[0263] S605: Update the particle velocity and position based on the individual optimal solution and the swarm optimal solution to achieve dynamic optimization of the parameter space; if the update result does not meet the constraints, perform feasibility correction, return to S604 to calculate the objective function based on the updated particle swarm, until the number of iterations reaches the preset upper limit;

[0264] S606: When the iteration ends, take the parameter vector corresponding to the globally optimal particle. As the optimal solution, the optimal control gain matrix is ​​obtained. .

[0265] Example 1:

[0266] This embodiment uses a DC motor model with time delay as an example, and performs the following simulation using the present invention:

[0267] The dynamic equation of a DC motor is:

[0268] (14)

[0269] In equation (14):

[0270] Indicates time;

[0271] Represents system state variables. This indicates the deviation between the actual value and the reference value of the angular velocity. This indicates the deviation between the actual value and the reference value of the current;

[0272] Indicates the coefficient of viscous friction;

[0273] Represents the moment of inertia;

[0274] Represents the back electromotive force constant;

[0275] Indicates the inductance of the coil winding;

[0276] Indicates armature inductance;

[0277] Indicates resistance;

[0278] This indicates the deviation between the actual voltage value and the reference value;

[0279] Define a non-singular similarity transformation matrix to transform the system state, that is, let .

[0280] During the sampling period The transformed system is then discretized, and the effect of system time delay is introduced; thus, the state-space model of the discrete-time TS fuzzy system is obtained:

[0281] (15)

[0282] In equation (15):

[0283] This is the transformed state vector of the discrete system;

[0284] To indicate The discrete system state vector at time t;

[0285] The parameters of this discretized TS fuzzy model are as follows:

[0286] , ,

[0287] , , , ,

[0288] , , , , , ,

[0289] The membership function expression is:

[0290] (16)

[0291] Parameter selection in adaptive WTOD is , The quantization parameter is set to... The sliding surface parameter matrix is ​​given as follows: The ratio constraint between the proportionality coefficients can be obtained through estimation, and the specific estimation result is as follows: , In linear matrix inequalities, other parameters are chosen as follows: , , By solving the minimization problem using S501, the Lyapunov matrix to be designed is obtained as follows: In the particle swarm optimization algorithm, the upper and lower bound parameters for constraints are selected as follows: and The number of particles is set to The number of iterations is set to By using the particle swarm optimization algorithm to solve the minimization problem, the controller gain matrix and event triggering weight matrix can be obtained as follows:

[0292] ,

[0293] ,

[0294] The initial conditions for the system state are chosen as follows: , , as well as Set the total runtime .

[0295] Fuzzy sliding mode control effect:

[0296] Figure 2 The study demonstrates the trend of the optimal value during the particle swarm optimization process, showing that the objective function stabilizes after decreasing from 0.0108 to 0.0097.

[0297] Figure 3 The open-loop system trajectory without control input exhibits highly volatile and unstable characteristics. Under the fuzzy sliding mode control framework with an adaptive WTOD protocol integrating a uniform quantization mechanism proposed in this invention, Figure 4 The closed-loop system trajectory is shown, and the system state eventually converges to the neighborhood near the equilibrium point.

[0298] Figure 5 For sensor node selection and transmission results, the node selection distribution is relatively uniform, and there is no excessive reliance on a single node. Moreover, as the system tends to stabilize, the quantized measurement value remains constant, which significantly reduces the network transmission burden.

[0299] Figure 6 , Figure 7 The trajectories of the control input and the sliding variable are presented respectively. This invention can effectively ensure system stability, while realizing the rational allocation and scheduling of sensor measurement data and saving network resources; the designed particle swarm optimization algorithm further ensures the superior performance of the system.

[0300] Figure 8 , Figure 9 The system state trajectory and sensor node selection are shown separately for scenarios without a uniform quantizer. (Comparison) Figure 4 , Figure 5It can be observed that the system exhibits better stability in this scenario, but the amount of sensor information transmitted increases significantly. This comparative result fully demonstrates that the present invention, through the combination of a uniform quantizer and an adaptive WTOD protocol, effectively avoids redundant data transmission, and significantly reduces network resource consumption while ensuring that system performance meets requirements.

[0301] This invention, under a unified information importance metric, fully integrates two types of indicators: instantaneous state error and its rate of change, and historical selection frequency. It adopts an online iterative weight update mechanism to adaptively adjust node priorities. Furthermore, through differentiated access and preemptive scheduling, it prioritizes the transmission of critical data within limited bandwidth. Under the premise of ensuring closed-loop stability and boundedness, it achieves on-demand allocation and efficient utilization of communication resources, significantly improving system response speed, robustness, and anti-interference performance, while maintaining low implementation overhead and ease of engineering deployment and expansion.

[0302] This invention, based on adaptive WTOD dynamic scheduling, addresses the challenges of bandwidth-constrained TS fuzzy systems with both quantization errors and time delays by constructing a mode-dependent sliding mode controller. Utilizing Lyapunov stability theory, the requirements for exponential boundedness and sliding surface reachability are uniformly expressed as a set of matrix inequality constraints. Furthermore, the CCL algorithm is combined to handle equality coupling, constructing an iterative LMI solution process based on convex optimization, thus providing verifiable and sufficient criteria. Accordingly, the designed controller ensures exponential boundedness and sliding surface reachability in the TS fuzzy system under bandwidth-constrained conditions, achieving a synergistic improvement in closed-loop performance and communication efficiency.

[0303] This invention addresses the limitations of traditional LMI toolchains, which primarily focus on feasibility assessment and struggle to directly handle nonlinear objective function optimization problems. It proposes a hierarchical optimization method combining particle swarm optimization (PSO) and LMI criteria. By introducing multiple decision variables to impose range constraints such as amplitude and condition number on the parameters obtained from the LMI solution, and by introducing a scaling penalty term into the objective function, feasible but poorly performing solutions are avoided. Based on this, the PSO algorithm performs a global search within the feasible region to minimize the final upper bound of the closed-loop state and the radius of the sliding mode surface's reach neighborhood, achieving robust optimization of performance metrics and numerical realizability of design variables.

[0304] This invention solves the problem that existing communication scheduling schemes cannot simultaneously take into account the importance index of node information and the frequency of historical selection. At the same time, it overcomes the defect that the system performance is difficult to ensure when solving the controller based on linear matrix inequalities. It provides a reliable control solution for TS fuzzy systems with time-varying delays in bandwidth-constrained scenarios.

[0305] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0306] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol, characterized in that: The method includes the following steps: S1: Establish a fuzzy networked system model of TS with time-varying time delay; S2: Design an adaptive WTOD transmission protocol with integrated uniform quantization mechanism; S3: Construct a fuzzy sliding mode controller based on available system state information; S4: The criteria for ensuring the boundedness of the exponent and the reachability of the sliding surface of the TS fuzzy network system are given in the form of a system of inequalities. S5: Conical complementary linearization is used to transform the discrimination conditions of the system of inequalities with linear coupling into a minimization problem; S6: Optimize the final upper bound of the closed-loop system state and the upper bound of the sliding surface reaching the neighborhood based on the particle swarm optimization algorithm.

2. The fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol according to claim 1, characterized in that: S1 includes the following steps: S101: If The first antecedent variable of the time system , The second antecedent variable of the time system ... The first time system one preceding variable , Indicates the first A fuzzy rule, It is a fuzzy rule number. It is the first The first fuzzy rule A fuzzy set of variables, where the time-varying, time-delay (TS) fuzzy network system satisfies: (1) In formula (1): express The system state at any given moment. For system state dimensions; express The system state at any given moment; Represents the time delay term, representing The historical state of a moment It is time-varying and time-delayed, satisfying , and These are the upper and lower bounds of the time delay, respectively; express Time-based control input, The dimension of the controller; express The external disturbances experienced by the time system satisfy the following conditions: , These are known constants; It is the first The known system state transition matrix corresponding to the fuzzy rule; It is the first The known time-delay state matrix corresponding to the fuzzy rule; It is the first The known input matrix corresponding to the fuzzy rules; It is the first The parameters related to the fuzzy rule are uncertain, among which: and The system parameter matrix is ​​known. It is an unknown, uncertain matrix that satisfies , for transpose, It is the identity matrix; At the same time, the initial state of the system ; S102: Definition of the first Membership function of a fuzzy rule It meets the following two conditions: Condition 1: Activation level is bounded: (2) In formula (2): express The first time system one preceding variable In the The first fuzzy rule Fuzzy set of variables Membership degree in; Condition 2: Global Normalization: (3) S103: The system model for defuzzification of the time-varying time-delay (TS) fuzzy network system, obtained based on fuzzy inference, is as follows: (4) The system state remains initially unchanged. .

3. The fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol according to claim 2, characterized in that: S2 includes the following steps: S201: Set the uniform quantizer independently for each sensor node; Given the first The step size of each node is Adjust the real number line according to the step size Divided into countless intervals ( ), The set is an integer set; when the system state is... Each component At that time, the quantized output is defined as The quantization error can be obtained by satisfying the following conditions. ; S202: Introduction of Adaptive WTOD Transmission Protocol: (5) In equation (5): for The sensor node selected at any given time; The operator represents the minimum value; This indicates the point where the function value reaches its maximum value; Available signals for the controller The One component; For the first The adaptive weights of each component are updated according to the following rules: ,in: , They represent the first Upper and lower bounds of the adaptive weights of each component; Indicates the weighting factor; S203: Based on the zero-order hold mechanism, set the update rules for the available signals of the controller: (6) when When the quantization result remains unchanged, no data transmission is required, thus effectively reducing redundant communication.

4. The fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol according to claim 3, characterized in that: S3 includes the following steps: S301: Constructing a standard sliding surface ,in: Represents the sliding surface parameter matrix; S302: If The first antecedent variable of the time system , The second antecedent variable of the time system ... The first time system one preceding variable Indicates the first A fuzzy rule, It is the first The first fuzzy rule Given a fuzzy set of variables, the sliding mode controller is: (7) In equation (7): This represents the controller gain to be solved; This represents the robustness gain of sliding mode control; Based on the fuzzy inference mechanism, the defuzzified sliding mode controller is obtained as follows: (8) In equation (8): It is the first The membership function of a fuzzy rule, and ; To reconstruct the sliding surface; S303: Obtain the closed-loop system based on the defuzzified system and the defuzzified sliding mode controller: (9) In equation (9): It is the identity matrix; According to Selected sensor node at any time The generated diagonal matrix, It is the Kronecker function; This is an equivalent representation of external disturbances; This is for quantization error; S304: Establish the membership function proportional relationship between the system and the controller's corresponding rules: (10) In formula (10): for Time of the first The ratio of the membership function of the controller to the system under fuzzy rules. and These are the upper and lower bounds of the membership function ratio; S305: Define globally unified upper and lower bounds and Then the constraints between the proportionality coefficients can be obtained: (11) In equation (11): This represents the upper and lower bounds of the range of values ​​for the proportionality coefficient.

5. The fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol according to claim 4, characterized in that: The matrix form of the discrimination condition described in S4 is as follows: (12) In equation (12): Represents the corresponding symmetric matrix block; It is the first negative definite matrix; where: It is a negative definite matrix of order 1. The first row and first column of the block matrix, where: ; It is a negative definite matrix of order 1. The block matrix in the first row and second column; It is a negative definite matrix of order 1. The block matrix in the 2nd row and 2nd column; where: , For given parameters; It is the second negative definite matrix; where: It is the second negative definite matrix The first row and first column of the block matrix, where: ; It is the second negative definite matrix The block matrix in the first row and second column; It is the second negative definite matrix The block matrix in the second row and second column; It is the third negative definite matrix; It is the third negative definite matrix The block matrix in the first row and first column; It is the third negative definite matrix The block matrix in the first row and second column; It is the third negative definite matrix The block matrix in the 1st row and 3rd column; It is the third negative definite matrix The block matrix in the 3rd row and 3rd column; It is the fourth negative definite matrix; It is the fourth negative definite matrix. The block matrix in the first row and first column; It is the fourth negative definite matrix. The block matrix in the first row and second column; It is the fourth negative definite matrix. The block matrix in the 1st row and 3rd column; It is the fourth negative definite matrix. The block matrix in the 3rd row and 3rd column; This is a preset convergence index used to characterize the speed of algorithm convergence; , , , , as well as All are coefficients to be solved; , , , , as well as All are matrices to be solved, satisfying , and They are inverse matrices; This is a diagonal matrix related to the upper bound of the adaptive parameters of the transmission protocol; This is a diagonal matrix related to the lower bound of the adaptive parameters of the transmission protocol; In order to be with the first The diagonal matrix related to the various transmission scenarios; For the first Gain coefficients related to this situation.

6. The fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol according to claim 5, characterized in that: S5 includes the following steps: S501: Reconstructing Equality Constraints Using Cone Complementary Linearization Method The minimization objective is: , For the trace of the matrix, impose constraints: ; S502: Combining the inequalities in S4, the above constraint problem is solved using the linear matrix toolbox in MATLAB; If the minimization problem has a feasible solution and the optimal value is... Approximately equal to the system state dimension Then, the matrix to be designed that allows the closed-loop system to satisfy exponential boundedness and reachability of the sliding surface can be determined. ; If the solution to the minimization problem cannot approach the This indicates that the system lacks controllability; S503: The matrix to be designed Substituting the known parameter matrix back into the matrix inequality in S4, we obtain the linear matrix inequality constraints that ensure the desired control performance.

7. The fuzzy sliding mode control method for bandwidth-constrained systems based on the adaptive WTOD protocol according to claim 6, characterized in that: S6 includes the following steps: S601: Define decision variables Introduce inequality constraints: Combined with the linear matrix inequalities obtained from S503, these together form the constraints for solving the linear matrix inequalities. S602: Define the objective function: (13) In equation (13): and Given weight parameters, satisfying , and ; This is the final upper bound of the closed-loop system state; This is the upper bound of the sliding surface reaching the neighborhood; This is the upper bound of the quantization error in the system; and They represent finding the matrix respectively. The minimum and maximum eigenvalues; S603: Set upper and lower limits for each parameter of the decision variable. and Satisfying constraints Randomly generated within this range 100 particles as the initial population; S604: For each particle, use the MATLAB linear matrix inequality solver based on its current parameter values ​​to verify the feasibility of the constraints. If the linear matrix inequality has a feasible solution, then calculate the corresponding fitness function value. ; If the linear matrix inequality is not satisfied, then a penalty value is assigned to the particle's fitness. To guide them away from inaccessible areas; S605: Based on the individual optimal solution and the group optimal solution, the particle velocity and position are updated to achieve dynamic optimization of the parameter space; If the update result does not meet the constraints, a feasibility correction is performed, and the objective function is calculated based on the updated particle swarm and returned to S604 until the number of iterations reaches the preset upper limit. S606: When the iteration ends, take the parameter vector corresponding to the globally optimal particle. As the optimal solution, the optimal control gain matrix is ​​obtained. .

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