Risk-aware event-triggered saturated t-s fuzzy system reliable h∞ control method

Abstract

The application discloses a risk-aware event-triggered saturation T-S fuzzy system reliable H∞ control method, which comprises the following steps: constructing a global networked T-S fuzzy system coupled with actuator efficiency attenuation failure and input saturation constraint to construct a comprehensive operation risk index; constructing a drift and saturation-aware dynamic memory event trigger mechanism according to the comprehensive operation risk index; constructing a matching type saturation sector constraint model; constructing a non-PDC fuzzy fault-tolerant H∞ controller according to the global networked T-S fuzzy system combined with the drift and saturation-aware dynamic memory event trigger mechanism; and realizing risk-aware event-triggered saturation T-S fuzzy system reliable H∞ control. The application solves the technical problems of the prior art, such as insufficient flexibility of the event trigger mechanism, low precision of the regional performance configuration, strong saturation processing conservativeness, and difficulty in balancing communication efficiency and control performance.

Description

Technical Field

[0001] This invention relates to the fields of networked control systems, TS fuzzy systems, event-triggered control, reliable control, and input saturation control, and particularly to a reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system. Background Technology

[0002] Networked control systems achieve information exchange between sensors, controllers, and actuators through a shared communication network. Compared to traditional point-to-point control systems, they offer significant advantages such as lower wiring costs, stronger system scalability, easier maintenance, and resource sharing, and have been widely applied in complex engineering scenarios such as industrial automation, ship motion control, and smart grid dispatching. However, communication network bandwidth is limited. If a traditional time-triggered mechanism is used to continuously transmit system status, it will generate a large number of redundant data packets, causing network congestion, increased latency, and other problems, severely affecting system control performance. Therefore, non-periodic event-triggered transmission mechanisms have become the mainstream design direction. Current methods have the following drawbacks: (1) Existing event triggering schemes mostly adopt fixed threshold or monotonic dynamic threshold mechanisms, which only consider the magnitude of the state sampling error and do not adaptively adjust the trigger threshold in combination with the multi-dimensional characteristics such as the real-time operation risk of the system, the degree of working condition transition, and the depth of input saturation. This has obvious defects: under transient high-risk working conditions, an excessively large threshold will lead to untimely state updates and delayed control response; under steady-state low-risk working conditions, an excessively small threshold will generate a large amount of invalid transmission, wasting bandwidth resources and failing to achieve coordinated optimization of control performance and communication efficiency.

[0003] (2) The Takagi-Sugeno (TS) fuzzy model approximates the dynamics of a nonlinear system through a convex combination of local linear subsystems, providing a standardized solution framework for linear matrix inequalities (LMI) for the analysis and synthesis of nonlinear systems. Existing membership function dependency (MFD) fuzzy control methods mostly use membership information only to reduce the conservatism of stability analysis, without associating the system's regional operating characteristics with online communication scheduling. This makes it impossible to achieve differentiated performance configuration for the normal operating region of the system during long-term operation, resulting in insufficient control accuracy in the dominant region and performance redundancy in the non-dominant region.

[0004] (3) In practical engineering, actuators generally exhibit two types of non-ideal characteristics: efficiency decay faults and input saturation. Existing saturated fuzzy control methods mostly adopt generalized sector nonlinear models, which often require the additional introduction of sector effective ellipsoid constraints. This not only increases the design conservatism but also makes it easy to mismatch with the structure of the fuzzy controller actually deployed, causing the theoretical stability certificate to fail in engineering. It is difficult to simultaneously meet the comprehensive requirements of fault tolerance, saturation suppression, and communication optimization.

[0005] In summary, existing technologies suffer from problems such as insufficient flexibility in event triggering mechanisms, low accuracy in regional performance configuration, strong conservatism in saturation processing, and difficulty in balancing communication efficiency and control performance. There is an urgent need for a reliable H∞ control method for networked TS fuzzy systems that can solve the above defects in an integrated manner. Summary of the Invention

[0006] This invention provides a reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system to overcome the above-mentioned technical problems.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system specifically includes the following steps: S1: Construct a global networked TS fuzzy system corresponding to the coupled actuator efficiency decay fault and input saturation constraint; S2: Based on the global networked TS fuzzy system, construct a comprehensive operational risk index that includes state drift risk index, performance fluctuation risk index, dominant region deviation risk index, and input saturation risk index. S3: Construct a dynamic memory event triggering mechanism for drift and saturation perception based on comprehensive operational risk indicators; S4: Construct a matched saturated sector constraint model; based on the global networked TS fuzzy system combined with the drift and saturation-aware dynamic memory event triggering mechanism, construct a non-PDC fuzzy fault-tolerant H∞ controller; based on the matched saturated sector constraint model and the non-PDC fuzzy fault-tolerant H∞ controller, realize reliable H∞ control of the risk-aware event-triggered saturated TS fuzzy system.

[0008] Furthermore, the construction formula for the globally networked TS fuzzy system in S1 is as follows:

[0009]

[0010]

[0011] In the formula: The first derivative of the system state vector; express A 3D system state vector; Indicates the first The corresponding fuzzy rules 3D local state matrix; Indicates the first The corresponding fuzzy rules 3D local input matrix; express The actual output control quantity of the actuator; Indicates the first The corresponding fuzzy rules 3D local perturbation matrix; express An externally bounded perturbation vector; express The controlled output vector of the dimensional system; Indicates the first The corresponding fuzzy rules 3D local output matrix; Indicates the first The corresponding fuzzy rules 3D local feedforward matrix; The set of indices representing all fuzzy rules; Indicates the first The normalized membership degree corresponding to the fuzzy rule, and ; This represents the theoretical control command vector output by the controller. Represents the component-based standard saturation function; Represents a known saturation limit value and ; The theoretical control vector output by the controller is represented by the first... One component; This represents the actuator efficiency degradation fault matrix, and ; Indicates the first A matrix of fault vertices; Indicates the total number of faulty vertices; This indicates a non-negative coefficient.

[0012] Furthermore, the method for constructing the comprehensive operational risk indicators in S2 specifically includes the following steps: S21: Based on the aforementioned global networked TS fuzzy system, the region membership function dependency H∞ performance index is constructed as follows:

[0013] In the formula: The time-varying H∞ decay coefficient represents the dynamic change over time. This represents the global benchmark performance index H∞, which is a known positive constant. Indicates the first The decay weight coefficient of the dominant fuzzy rule and ; Indicates the dominant fuzzy rule set; This represents a non-dominant fuzzy rule set; The constant term in the performance inequality; express Transpose of; express Transpose of; S22: Based on the system state vector, the system nominal state vector and the trigger state error vector are defined as follows:

[0014] In the formula: Represents the nominal state vector of the system; Represents the fuzzy premise variable vector of the system; This represents the trigger state error vector; Indicates the time of the most recent event trigger. The original state vector of the system obtained by sampling; Represents the fuzzy weighted positive definite transformation matrix; S23: Based on the system's nominal state vector and the region membership function dependency H∞ performance index, construct state drift risk index and performance fluctuation risk index: The state drift risk indicator is:

[0015] In the formula: Indicators representing state drift risk; Indicates in The system nominal state vector at time 1; Indicates the length of the time window for risk assessment; The performance fluctuation risk indicator is:

[0016] In the formula: Indicators representing performance volatility risk; Indicates in The time-varying H∞ decay coefficient at time t; According to the The normalized membership degrees corresponding to the fuzzy rules are used to construct the dominant region deviation risk indicator as follows:

[0017] In the formula: This indicates that the dominant region deviates from the risk indicator; This indicates a deviation from the baseline threshold; Based on the theoretical control command vector output by the controller With component-based standard saturation function The input saturation risk index is constructed as follows:

[0018] In the formula: This indicates an input saturation risk indicator; S24: The comprehensive operational risk indicators obtained based on S23 are as follows:

[0019] In the formula: Indicates comprehensive operational risk indicators; The weighting coefficients represent the four types of risks and .

[0020] Furthermore, step S3 specifically includes the following steps: S31: A first-order low-pass filter is introduced to smooth the comprehensive operational risk index. Its expression is:

[0021] In the formula: express The first derivative; This represents the overall operational risk index after filtering. Indicates the filter attenuation coefficient; Indicates the filter gain coefficient; S32: Construct the desired triggering coefficient based on step S31 for:

[0022] In the formula: These represent the lower and upper bounds of the trigger coefficient, respectively; This represents the risk adjustment sensitivity parameter; S33: Introducing a first-order dynamic tracking equation for the desired trigger coefficient After filtering, the actual trigger coefficients are obtained as follows:

[0023] In the formula: Represents the tracking rate coefficient; Indicates the actual trigger coefficient; express The first derivative; S34: Based on the actual triggering coefficient and the triggering state error vector, a dynamic memory variable with both exponential decay and delayed feedback characteristics is constructed as follows:

[0024] In the formula: express The first derivative; Represents a dynamic memory variable; Indicates the decay coefficient of the memory variable; Indicates a positive definite triggering weight matrix and ; Indicates the time-varying delay gain; Indicates the delay feedback coefficient; Indicates the time delay constant; express Transpose of; express Transpose of; S35: The event triggering determination function is constructed based on the aforementioned dynamic memory variable as follows:

[0025] In the formula: Indicates the event trigger determination function and ; S36: Constructing a drift and saturation-aware dynamic memory event triggering mechanism based on an event-triggered decision function:

[0026] In the formula: Indicates the maximum trigger interval and ; Indicates the time when the most recent event was triggered; Indicates the next trigger time.

[0027] Furthermore, the matched saturated sector constraint model constructed in S4 is as follows:

[0028]

[0029] In the formula: Represent the scalar form of the saturation dead zone deviation function; Represents the diagonal sector multiplier matrix; express The transpose of .

[0030] Furthermore, the non-PDC fuzzy fault-tolerant H∞ controller constructed in S4 is as follows:

[0031]

[0032] In the formula: Represents the gain matrix of the fuzzy weighted controller; Indicates the first Normalized membership degree of a fuzzy rule; Indicates the first The local controller gain matrix corresponding to the fuzzy rule; Indicates the first The local positive definite transformation matrix corresponding to the fuzzy rule.

[0033] This invention provides a reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system, with the following beneficial effects: (1) Higher communication efficiency and significant bandwidth saving: The drift and saturation sensing dynamic memory event triggering mechanism constructed in this invention can adaptively adjust the triggering threshold according to the real-time operation risk of the system, and can effectively alleviate network congestion problem without reducing control performance.

[0034] (2) More precise performance configuration and excellent regional control effect: By introducing the regional membership function-dependent H∞ performance index, this invention applies more stringent disturbance attenuation constraints to the dominant working region of the system at high frequency operation, realizing differentiated regulation of "high precision in normal region and stability in transient region", avoiding performance redundancy and deficiencies caused by the global unified index.

[0035] (3) Lower conservative saturation handling and strong fault tolerance: By constructing a matched saturated sector constraint model and a non-PDC fuzzy fault-tolerant H∞ controller, this invention does not require the introduction of additional sector effective ellipsoid constraints, which effectively reduces the conservatism of input saturation and actuator fault handling; under deep saturation conditions where the control command exceeds the saturation limit and fault conditions where the actuator efficiency decays, the system can still operate stably, and its robustness is significantly better than that of traditional solutions. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0037] Figure 1 This is a flowchart of the reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system according to the present invention; Figure 2 This is the overall control architecture diagram in this embodiment; Figure 3 This is a piecewise linear membership function graph of the roll angle in this embodiment; Figure 4 This is the piecewise linear membership function of the roll angular velocity in this embodiment; Figure 5 This is a graph showing the variation of the regional MFD attenuation rate with the membership degree of the dominant rule in this embodiment. Figure 6 This is a state-dependent decay ratio thermodynamic distribution diagram in this embodiment; Figure 7 This is a comparison chart of the roll angle response in this embodiment; Figure 8This is a comparison chart of the roll angular velocity response in this embodiment; Figure 9 This is a regional Lyapunov ratio curve in this embodiment; Figure 10 This is a plot of the Lyapunov energy function curve for the region in this embodiment; Figure 11 This is a graph showing the MFD decay rate of the Lyapunov function in the region in this embodiment; Figure 12 This is a performance comparison chart of triggering times in this embodiment; Figure 13 This is a performance comparison chart of the number of triggers in this embodiment; Figure 14 This is a comparison chart of trigger interval performance in this embodiment; Figure 15 This is a graph showing the communication savings rate in this embodiment; Figure 16 This is a response curve diagram of the dynamic triggering coefficients within the event triggering mechanism in this embodiment; Figure 17 This is a response curve diagram of the dynamic memory variable inside the event triggering mechanism in this embodiment; Figure 18 This is a response curve of the internal filtered drift signal of the event triggering mechanism in this embodiment; Figure 19 This is the activation curve of the dominant rule in this embodiment; Figure 20 This is a comparison chart of the actual attenuation rates under the operating conditions in this embodiment; Figure 21 This is a comparison chart of the cumulative disturbance output ratio in this embodiment; Figure 22 This is a graph showing the relationship between the average regional MFD attenuation rate and the attenuation weighting coefficient in this embodiment; Figure 23 This is a graph showing the relationship between the cumulative perturbation output ratio and the attenuation weighting coefficient in this embodiment; Figure 24 This is a graph showing the relationship between the number of triggers and the attenuation weight coefficient in this embodiment; Figure 25 This is a graph showing the relationship between control commands and saturation input in this embodiment; Figure 26 This is a graph showing the saturation level index results in this embodiment; Figure 27 This is a function graph of the matched saturated sector constraint model in this embodiment. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] This embodiment provides a reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system, such as... Figure 1 As shown, the specific steps include: S1: Construct a global networked TS fuzzy system corresponding to the coupled actuator efficiency decay fault and input saturation constraint; Specifically, traditional nonlinear control schemes often employ a globally unified modeling approach, neglecting the fact that over 90% of the system's operating time is concentrated in a few high-frequency steady-state conditions. This globally unified design cannot differentiate control requirements for different operating conditions, resulting in either insufficient normal-state accuracy or redundant transient performance. Therefore, this embodiment first completes the accurate modeling of the controlled object, and then divides the dominant and non-dominant operating regions based on long-term operational statistical characteristics, providing a foundation for subsequent differentiated design. This embodiment uses IF-THEN form TS fuzzy rules to locally linearize the nonlinear controlled object. Each fuzzy rule corresponds to a linear subsystem at an operating point. The form of a fuzzy rule is: set up For fuzzy premise variable vectors, Indicates the first The first premise variable corresponds to the first... A fuzzy set Indicates the total number of prerequisite variables; rules :like belong , ..., belong ,but:

[0040] In this embodiment, for the first... The fuzzy premise variable vector, corresponding to the th fuzzy premise variable vector. The original membership degree of a fuzzy set is denoted as . To satisfy the mathematical properties of convex combinations, for the th The membership degrees of the premise variables are normalized:

[0041] In the formula: Indicates the first Under the premise variable, the first The normalized membership degrees corresponding to each fuzzy set; where Indicates the first The total number of fuzzy sets of the given variables; Multiplying the normalized membership degrees of all premise variables, we obtain the normalized membership function of the entire fuzzy rule as follows:

[0042] In the formula: and The meanings are the same; both refer to the membership degree after normalization. Let the set of indices for all fuzzy rules be denoted as . The total number of rules is , Let the set of indices representing the overall fuzzy rules, i.e., the set of all fuzzy rule numbers, be given by: And for any satisfy This normalization process ensures that the sum of the membership degrees of all rules is always 1, satisfying the convex combination constraint and providing a rigorous mathematical foundation for subsequent global modeling and analysis. In this embodiment, the linear subsystems corresponding to each rule are weighted and summed according to their membership degrees to obtain the state equation and output equation of the global networked TS fuzzy system as follows:

[0043]

[0044]

[0045] In the formula: The first derivative of the system state vector; express A 3D system state vector; Indicates the first The corresponding fuzzy rules 3D local state matrix; Indicates the first The corresponding fuzzy rules 3D local input matrix; express The actual output control quantity of the actuator; Indicates the first The corresponding fuzzy rules 3D local perturbation matrix; express An externally bounded perturbation vector; express The controlled output vector of the dimensional system; Indicates the first The corresponding fuzzy rules 3D local output matrix; Indicates the first The corresponding fuzzy rules 3D local feedforward matrix; The set of indices representing all fuzzy rules; Indicates the first The normalized membership degree corresponding to the fuzzy rule, and ; This represents the theoretical control command vector output by the controller. Represents the component-based standard saturation function; Represents a known saturation limit value and ; The theoretical control vector output by the controller is represented by the first... One component; This represents the actuator efficiency degradation fault matrix, and ; Indicates the first A matrix of fault vertices; Indicates the total number of faulty vertices; This represents a non-negative coefficient. In this embodiment, the global model is used to accurately approximate the nonlinear system using multiple linear subsystems through a convex combination method, providing a standardized LMI solution framework for subsequent stability analysis and controller design. In this embodiment, the actuator side simultaneously considers the dual non-ideal characteristics of efficiency decay faults and input saturation; the actual actuator output is the fault matrix multiplied by the saturated control command. The actuator fault matrix... The matrix is ​​a diagonal matrix with bounded values ​​for each element. All fault conditions can be represented as a convex combination of a finite number of fault vertices: The controller design only needs to utilize the upper and lower bounds or vertex information of the fault, without requiring online measurement of real-time fault values, thus ensuring the engineering practicality of the solution. In this embodiment, after completing the modeling, the dominant working region is divided based on the probability distribution of the prerequisite variables for long-term system operation: Let the first... The high-frequency working fuzzy set of the premise variables is ,in Indicates the first The complete fuzzy set of all premise variables is the dominant fuzzy rule set. Defined as:

[0046] In the formula: Indicates the first Fuzzy set numbering on the dimension of each premise variable; Indicates the first The fuzzy set numbering of each prerequisite variable dimension; the dominant fuzzy rule set. The rules correspond to the dominant working region of the system's high-frequency steady-state operation, while the remaining rules correspond to the non-dominant working region of low-frequency transient operation. This region division is the basis for all subsequent differentiated designs, fundamentally solving the contradiction of "insufficient normal accuracy and redundant transient performance" brought about by traditional global unified indicators.

[0047] In this embodiment, the design of the region membership function-dependent H∞ performance index and risk perception event triggering mechanism is as follows: Traditional H∞ control uses a globally uniform attenuation coefficient, which cannot adapt to the differentiated needs of different regions: setting a strict attenuation coefficient globally will lead to excessive controller gain, control saturation, and a surge in communication; setting a lenient attenuation coefficient globally will lead to insufficient control accuracy in the dominant region. Therefore, based on the aforementioned region division results, this invention starts from the standard H∞ energy definition, introduces a region weight coefficient, and derives a time-varying H∞ attenuation coefficient dependent on the region membership function, achieving differentiated control of "high precision in normal regions and stability in transient regions". The specific steps are as follows: S2: Based on the aforementioned global networked TS fuzzy system, construct a comprehensive operational risk index that includes state drift risk indicators, performance fluctuation risk indicators, dominant region deviation risk indicators, and input saturation risk indicators. This specifically includes the following steps: S21: In this embodiment, the defined region MFD H∞ performance is strongly bound to the region's positive invariance, and this is only applied during augmentation. This holds true within the level set. First, define the initial conditions for permission and the set of perturbation energies: for a given performance level... Permission to initially satisfy historical memory For all Established, in this embodiment, the permitted perturbation set Defined as:

[0048] In the formula: This represents a positive relaxation constant; Indicates the design parameters for the delay term; This represents the bounded external energy disturbance input to the system; This indicates the H∞ disturbance attenuation level, which is the system's performance index in suppressing external disturbances; This represents a dynamic memory function, i.e., a function within the memory window. Historical trigger state-related memory variables at any given moment; express The upper bound of the level set is used to constrain the magnitude of the initial memory history; This represents the memory lag offset variable, which represents a historical time point within the memory window; This represents the maximum memory window length, which is the upper bound of the maximum time delay for triggering dynamic memory events, corresponding to the duration of historical memory. The initial value representing the performance level; In the above set of permitted disturbances Within this framework, the performance index of the region membership function dependency H∞ constructed based on the global networked TS fuzzy system is defined as follows: (1) Under undisturbed operating conditions, the closed-loop system asymptotically stabilizes and increases. level set It is a positive invariant set; (2) Under zero initial conditions, for any permitted disturbance, the system trajectory always remains at Within the level set, and for any satisfy:

[0049] Where: constant term , Denotes arbitrarily small relaxation amount and ; The squared term of the time-varying H∞ decay coefficient is obtained by weighted summation of the dominant and non-dominant rules respectively:

[0050] In the formula: The time-varying H∞ decay coefficient represents the dynamic change over time. This represents the global benchmark performance index H∞, which is a known positive constant. Indicates the dominant fuzzy rule set; This represents a non-dominant fuzzy rule set; The constant term in the performance inequality; express Transpose of; express Transpose of; This represents the initial value of the dynamic memory function; Indicates the first The decay weight coefficient of the dominant fuzzy rule and The smaller the value, the stronger the anti-disturbance capability in the corresponding region. This performance index achieves a smooth transition through the membership function. The attenuation is most severe when the system is completely in the dominant region, and it gradually recovers to the global benchmark level when it deviates from the dominant region, thus balancing normal accuracy and global stability. To achieve coordinated optimization of communication resources and control performance, this embodiment designs a drift and saturation sensing dynamic memory event triggering mechanism (DSA-DMETM) and constructs a risk assessment system from four core dimensions. Based on the real-time operational risk of the system, the triggering threshold is adaptively adjusted to achieve intelligent scheduling of "high-risk, high-volume transmission; low-risk, low-volume transmission." Specifically, this includes: S22: In this embodiment, to maintain consistency with the analysis framework for non-PDC controllers, the system nominal state vector and trigger state error vector are defined based on the system state vector as follows:

[0051] In the formula: Represents the nominal state vector of the system; Represents the fuzzy premise variable vector of the system; This represents the trigger state error vector; Indicates the time of the most recent event trigger. The original state vector of the system obtained by sampling; Represents the fuzzy weighted positive definite transformation matrix; Indicates the interval between adjacent trigger times; S23: Based on the system's nominal state vector and the region membership function dependency H∞ performance index, construct state drift risk index and performance fluctuation risk index: The state drift risk indicator is:

[0052] In the formula: Indicators representing state drift risk; Indicates in The system nominal state vector at time 1; This indicates the length of the time window for risk assessment; in this embodiment, the state drift risk indicator quantifies the magnitude of changes in the system state within the time window, reflecting the dynamic activity level of the system. The performance fluctuation risk indicator is:

[0053] In the formula: Indicators representing performance volatility risk; Indicates in The time-varying H∞ decay coefficient at time t; The 2-norm of a vector is used to represent the performance fluctuation risk index in this embodiment: the dynamic fluctuation of the time-varying decay coefficient is quantified to reflect the changing trend of system performance. According to the The normalized membership degrees corresponding to the fuzzy rules are used to construct the dominant region deviation risk indicator as follows:

[0054] In the formula: This indicates that the dominant region deviates from the risk indicator; This indicates a deviation from the baseline threshold, used to avoid misjudgments caused by minor fluctuations; in this embodiment, the dominant region deviation risk index quantifies the degree to which the system deviates from the dominant working region, reflecting the degree of abnormality in the working condition; Based on the theoretical control command vector output by the controller With component-based standard saturation function The input saturation risk index is constructed as follows:

[0055] In the formula: This represents the input saturation risk index; in this embodiment, the input saturation risk index quantifies the severity of actuator saturation, reflecting the risk of limited control. This embodiment constructs a normalized unidimensional risk index from four dimensions, with all indicators mapped to... The interval facilitates weighted fusion; S24: The comprehensive operational risk indicators obtained based on S23 are as follows:

[0056] In the formula: Indicates comprehensive operational risk indicators; The weighting coefficients representing the four types of risks can be flexibly adjusted according to project requirements. .

[0057] S3: Construct a dynamic memory event triggering mechanism for drift and saturation perception based on comprehensive operational risk indicators; specifically including the following steps: S31: To avoid frequent jumps in the risk signal due to measurement noise and instantaneous disturbances, a first-order low-pass filter is introduced to smooth the comprehensive operational risk index. Its expression is:

[0058] In the formula: express The first derivative; This represents the overall operational risk index after filtering. Indicates the filter attenuation coefficient; This represents the filter gain coefficient; the input terms are in saturated normalized form to ensure that the filter output is always bounded. S32: Construct the desired triggering coefficient based on step S31 for:

[0059] In the formula: These represent the lower and upper bounds of the trigger coefficient, respectively; This represents the risk adjustment sensitivity parameter. In this embodiment, based on the filtered risk index, the expected trigger coefficient is obtained using an inverse fractional mapping: the higher the risk, the smaller the expected trigger coefficient, and the stricter the trigger threshold; the lower the risk, the larger the expected trigger coefficient, and the more lenient the trigger threshold. S33: To avoid the impact of trigger coefficient jumps on system stability, a first-order dynamic tracking equation is introduced for the desired trigger coefficient. After filtering, the actual trigger coefficients are obtained as follows:

[0060] In the formula: This represents the tracking rate coefficient, used to control the speed at which the actual triggering coefficient converges to the desired value; Indicates the actual trigger coefficient; express The first derivative; S34: Based on the actual triggering coefficient and the triggering state error vector, a dynamic memory variable with both exponential decay and delay feedback characteristics is constructed. This embodiment represents the aperiodic transmission characteristics of a coupled networked system. Simultaneously, to theoretically avoid Zeno triggering, a dynamic memory variable with both exponential decay and delay feedback characteristics is designed, incorporating communication scheduling behavior into the stability analysis framework. Its differential equation is:

[0061] In the formula: express The first derivative; Represents a dynamic memory variable; Indicates the decay coefficient of the memory variable; Indicates a positive definite triggering weight matrix and ; Indicates the time-varying delay gain; Indicates the delay feedback coefficient; Indicates the time delay constant; express Transpose of; express The transpose of the variable; in this embodiment, the dynamic memory variable can weaken the influence of instantaneous disturbances on the trigger determination, and at the same time, it is theoretically proven that all trigger intervals have a strict positive lower bound, thus completely avoiding the Zeno triggering problem; S35: The event triggering determination function is constructed based on the aforementioned dynamic memory variable as follows:

[0062] In the formula: Indicates the event trigger determination function and ; S36: Constructing a drift and saturation-aware dynamic memory event triggering mechanism based on an event-triggered decision function:

[0063] In the formula: Indicates the maximum trigger interval and This serves as a fallback constraint to ensure, from an engineering perspective, that there will not be an extreme situation where updates are not performed for an extended period of time. Indicates the time when the most recent event was triggered; This indicates the next trigger time; in this embodiment, the next status data packet transmission is triggered when the next time determination function is greater than or equal to 0, or when the interval reaches the maximum trigger interval. Traditional input saturation handling methods employ generalized sector nonlinear models, often requiring the introduction of additional sector effective ellipsoidal constraints. This not only increases design conservatism but also easily leads to mismatches with the actual deployed controller structure, causing theoretical stability certificates to fail in engineering applications. Therefore, this embodiment selects a sector mapping that is completely consistent with the gain of the non-PDC controller to construct a globally effective saturated sector inequality constraint, i.e., a matched saturated sector constraint model. This eliminates the need for any additional constraints, fundamentally reducing the conservatism of saturation handling.

[0064] S4: Construct the matched saturated sector constraint model as follows:

[0065] In the formula: The scalar form of the saturation dead zone deviation function represents the difference between the theoretical control quantity and the actual control quantity after saturation. Represents the diagonal sector multiplier matrix; express The transpose of has component form as follows: , ; The theoretical control vector representing the controller output. The One component; The selected sector mapping is completely consistent with the controller gain, i.e. Then for any diagonal multiplier matrix The saturation dead zone deviation satisfies the global sector inequality as follows:

[0066] in, express A set of positive definite diagonal matrices; Represents the sector mapping matrix; This represents the gain matrix of the fuzzy weighted controller. This inequality holds for any control input and does not require additional sector effective ellipsoid constraints, which is the core advantage of this embodiment compared to the traditional generalized sector method. Based on the global networked TS fuzzy system and the aforementioned drift and saturation sensing dynamic memory event triggering mechanism, a non-PDC fuzzy fault-tolerant H∞ controller is constructed. Specifically, the non-PDC fuzzy fault-tolerant H∞ controller constructed in this embodiment is:

[0067]

[0068] In the formula: Represents the gain matrix of the fuzzy weighted controller; Indicates the first Normalized membership degree of a fuzzy rule; Indicates the first The local controller gain matrix corresponding to the fuzzy rule; Indicates the first The local positive definite transformation matrix corresponds to each fuzzy rule. In this embodiment, a non-parallel distributed compensation (non-PDC) strategy is used to design the fuzzy controller. The controller gain and the transformation matrix are weighted and summed according to membership degrees and decoupled from each other, resulting in a design freedom far exceeding that of traditional PDC controllers. The controller only uses the latest state transmitted at the trigger moment to calculate the control command, which conforms to the actual scenario of networked non-periodic updates.

[0069] Based on the matched saturated sector constraint model and the non-PDC fuzzy fault-tolerant H∞ controller, reliable H∞ control of the risk-aware event-triggered saturated TS fuzzy system is achieved. This embodiment substitutes the non-PDC fuzzy fault-tolerant H∞ controller into the original system state equations, and combines the saturation dead zone deviation function and fault convex hull characteristics to derive the... The state equations and output equations of the closed-loop system under each fault vertex are as follows:

[0070] Among them, each closed-loop coefficient matrix , They are defined as follows:

[0071]

[0072]

[0073] In the formula: , , , The weighted system matrix of the globally networked TS fuzzy system is obtained by weighted convex combination of the local matrices of each fuzzy rule through membership degree, and describes the dynamic characteristics of the global nonlinear system: where Represents the global state matrix, describing the dynamic state of the system; This represents the global control input matrix, describing the effect of the control input on the state. This represents the global output matrix, which describes the mapping from the state to the controlled output. This represents the global feedthrough matrix, describing the direct effect of the control input on the controlled output; where... ; Indicates the first The state matrix of the local linear subsystem corresponding to the fuzzy rule, and the state matrix of the remaining global weighted matrix are similar; for any fault condition The corresponding closed-loop matrices can all be represented as convex combinations of vertex closed-loop matrices.

[0074] The stability analysis in this embodiment uses augmented fuzzy logic. The functional integrates system state energy and communication scheduling memory terms into an energy metric framework:

[0075] In the formula: Indicates augmented fuzziness The dynamic memory term in the functional; the core idea of ​​the stability derivation in this embodiment is: for Differentiating the functional along the closed-loop system, substituting it into the closed-loop state equations, and introducing the matched sector inequality to scale the saturation term, while handling the sampling error term in conjunction with event triggering conditions, are then applied. The supplementary lemma transforms the nonlinear matrix inequality into a linear matrix inequality, ultimately yielding sufficient conditions that can be solved offline. During the derivation, the convex hull property of the fault is utilized, meaning that verifying only the fault vertices guarantees stability under all fault conditions. Furthermore, the polytopic property of the derivatives of membership functions is utilized, meaning that verifying only the derivative vertices guarantees feasibility under all membership rates of change. The final sufficient conditions for LMI have the following block structure: for each fault vertex… There exists a positive definite matrix. diagonal matrix and scalar This makes the following equation true:

[0076] In the formula: Indicates the first The (1,1) block term of the LMI matrix under each fault vertex corresponds to the augmented fuzzy matrix. The state quadratic terms of the functional derivative are divided into blocks, consisting of the closed-loop system state matrix, controller gain, Composed of matrices, these are the core components of the closed-loop stability condition; The denoting identity matrix is ​​a standard notation in linear algebra and control theory, namely a square matrix whose diagonal elements are all 1s and the rest are all 0s; The elements of the LMI matrix are represented by the LMI matrix, where each block element is composed of a combination of closed-loop coefficient matrix, triggering parameters and performance parameters. By solving this set of inequalities offline using MATLAB's LMI convex optimization tool, all control and triggering parameters can be obtained. The solution can simultaneously guarantee the four core performance characteristics of the closed-loop system: regional positive invariance, disturbance-free asymptotic stability, regional MFD H∞ performance, and Zeno-free transfer characteristics.

[0077] Compared with the prior art, the beneficial effects of the method described in this embodiment are as follows: (1) Higher communication efficiency and significant bandwidth saving: The constructed drift and saturation sensing dynamic memory event triggering mechanism can adaptively adjust the trigger threshold according to the real-time operation risk of the system. Under the premise of ensuring that the control performance does not decline, the amount of state data packet transmission can be reduced by 51.85%, the average trigger interval is increased from 0.0743s to 0.1548s, and the bandwidth utilization rate is more than doubled, which can effectively alleviate the network congestion problem.

[0078] (2) More precise performance configuration and excellent regional control effect: By introducing the regional membership function dependent H∞ performance index, more stringent disturbance attenuation constraints are applied to the dominant working area of ​​the system at high frequency, realizing differentiated regulation of "high precision in normal area and stability in transient area". The cumulative disturbance output energy of the dominant area is reduced by 12.18%, the anti-disturbance performance is significantly improved, and the performance redundancy and insufficiency brought about by the global unified index are avoided.

[0079] (3) Lower conservative saturation handling and strong fault tolerance: By constructing a matched saturated sector constraint model and a non-PDC fuzzy fault-tolerant H∞ controller, there is no need to introduce an additional sector effective ellipsoid constraint, which effectively reduces the conservatism of input saturation and actuator fault handling; the system can still operate stably under deep saturation conditions where the control command exceeds the saturation limit and fault conditions where the actuator efficiency decays to 78%, and its robustness is significantly better than that of traditional schemes.

[0080] (4) Strong engineering applicability and convenient deployment: All control and triggering parameters of the method described in this embodiment can be solved offline by linear matrix inequalities. Online operation only requires calculating the normalized membership degree, updating the first-order scalar filter, and determining the scalar triggering function. The amount of calculation is small and no high-speed computing hardware is required. It is easy to deploy and implement in engineering platforms such as embedded control equipment and industrial PLC.

[0081] This embodiment uses a networked control system for a ship's roll damping fin with nine fuzzy rules as the simulation object to specifically illustrate and verify the reliable H∞ control method for a saturated networked TS fuzzy system based on risk-aware event triggering proposed in this embodiment. This embodiment describes the nonlinear dynamic characteristics of ship roll using a TS fuzzy model, divides the operating regions into dominant and non-dominant areas to achieve differentiated performance configurations, employs a drift and saturation-aware dynamic memory event triggering mechanism to save network communication bandwidth, combines matched saturated sector certificates and a non-PDC fuzzy controller to handle the dual non-ideal characteristics of actuator efficiency decay and input saturation, and finally solves all parameters offline using linear matrix inequalities. This significantly reduces communication overhead while ensuring control performance, improving the system's robustness and engineering practicality.

[0082] The control objectives of the method described in this embodiment include the following four aspects: (1) Under the combined effect of actuator efficiency decay fault and input saturation constraint, ensure the region positive invariance and disturbance-free asymptotic stability of the closed-loop system; (2) For the small and medium angles that dominate the high-frequency operation of the ship's roll system, achieve disturbance suppression performance superior to the global standard and improve the roll reduction control accuracy under normal operating conditions; (3) Reduce the number of state data packet transmissions from sensors to controllers without sacrificing control performance, thereby saving network communication bandwidth resources; (4) Ensure that there is no Zeno phenomenon in the event triggering process, and that all triggering intervals have a strict positive lower bound, so as to meet the actual feasibility requirements of the project.

[0083] To achieve the above control objectives, this embodiment provides the following basic system settings and mathematical lemmas as the theoretical basis for subsequent controller design and stability analysis.

[0084] Setting 1: The membership function is continuously differentiable along the system's trajectory, and its derivative vector belongs to a known compact multiple cell. for: in, It is a column vector of all 1s. For the first The time derivative of the membership function is defined by the rule, and this polytopic constraint covers all possible rate of change ranges for the piecewise linear membership function in this embodiment.

[0085] Setting 2: All operating conditions of actuator efficiency failure can be represented as a convex combination of three failure vertices: That is, the actuator efficiency coefficient at any time can be expressed as the non-negative weighted sum of the three vertices mentioned above, and the sum of the weight coefficients is 1.

[0086] Lemma 1 (Matching Sector Inequality Lemma): For any diagonal matrix , arbitrary vector The following equation holds true:

[0087] in This is the saturation dead zone deviation function. This lemma is the core mathematical tool for handling input saturation nonlinearity in this embodiment.

[0088] Lemma 2 (Matrix Inequality Lemma): For any matrix of the same dimension... and any positive number The following equation holds true: This lemma is used for cross-term scaling in the stability derivation process, transforming nonlinear matrix inequalities into solvable linear matrix inequalities.

[0089] Step 1: Establish a networked TS fuzzy system model containing non-ideal characteristics of actuators and divide the working region; In a specific embodiment, based on the aforementioned networked TS fuzzy modeling method, the roll system of a stabilized fin ship is taken as the controlled object, and concrete modeling and working region division are completed. This embodiment selects the absolute value of the roll angle. With the absolute value of the roll angular velocity As fuzzy premise variables, each premise variable is divided into three fuzzy sets: "small," "medium," and "large." These sets are combined in pairs to form a total of nine fuzzy rules, which constitute the total number of rules. The original membership degree of each fuzzy set is calculated using a piecewise linear membership function. Taking the roll angle as an example, the membership degree of the first fuzzy set (small) is calculated as follows:

[0090] The membership degree calculation formula for the second fuzzy set (in the middle) is:

[0091] The membership degree calculation formula for the third fuzzy set (large) is:

[0092] Similarly, the membership function of the roll angular velocity has the breakpoint as follows: .

[0093] Multiply the membership degrees of the two premise variables, then normalize the result to obtain the first... Normalized membership functions of the rules:

[0094] in , These are the fuzzy set indices corresponding to the roll angle and roll angular velocity, respectively, and satisfy the following conditions: In this embodiment, the system state vector is defined as follows: ,in The roll angle, For roll angular velocity, state dimension Control input dimensions Perturbation dimension Controlled output dimension .

[0095] By summing the local linear subsystems of the nine fuzzy rules according to their membership degrees, we obtain the component-form state equation of the global system:

[0096] in Local state matrix The Line 1 For column elements, the same applies to other symbols; Represents the local input matrix Elements in; Represents the local perturbation matrix Elements in; No. Rule ( The specific values ​​of the local system matrix corresponding to the fuzzy set indices of roll rate and roll angle are as follows:

[0097]

[0098] Among them, the restoring torque coefficient Damping coefficient The actuator-side coupling efficiency degradation fault and input saturation are both non-ideal characteristics. The actual output satisfies:

[0099] In this embodiment, the saturation limiting reference value is taken as... The saturation depth verification condition was lowered to The piecewise form of the saturation function is:

[0100] The actuator efficiency coefficient changes over time in three stages to simulate the wear and degradation process of the anti-roll fin actuator:

[0101] The fault profile falls entirely within the fault convex hull range described in setting 2, satisfying the design prerequisites for fault-tolerant control. External wave disturbances are simulated using multi-frequency superimposed signals to mimic the wave disturbance torque under sea state 4.

[0102] Based on the statistical characteristics of actual ship navigation, four fuzzy rules corresponding to small and medium roll angles and roll angular velocities are selected to form the dominant rule set: This set corresponds to the normal operating region where the system operates for more than 90% of its runtime, while the remaining rules correspond to the transient, non-dominant operating region with large-angle roll.

[0103] The overall control architecture of this embodiment is as follows: Figure 2 As shown, the system consists of a state acquisition module, a risk-aware dynamic triggering module (DSA-DMETM), a non-PDC fuzzy fault-tolerant H∞ controller, actuators, and a networked TS fuzzy controlled object forming a closed loop. The controller integrates three functional modules: state feedback, actuator fault compensation, and matched saturated sector constraint processing, achieving an integrated design of communication scheduling, fault-tolerant control, and saturation suppression.

[0104] Step 2: Constructing a framework for analyzing regionally differentiated H∞ performance indicators and augmented stability. In a specific embodiment, based on the aforementioned regional MFD H∞ performance design method, the regional division results and performance parameters of this embodiment are substituted to construct a concrete performance index and stability analysis framework.

[0105] This embodiment sets a global reference attenuation coefficient. Unified attenuation weight in the dominant region Substituting the formula for calculating the time-varying attenuation coefficient, we can obtain the specific expression for this embodiment:

[0106] After sorting, it can be written as:

[0107] When the system is completely in the dominant region, that is At this time, the effective attenuation coefficient reaches its minimum value: The attenuation coefficient is reduced by approximately 27.2% compared to the global baseline, resulting in a significant improvement in the anti-interference performance of the dominant region. When the system deviates from the dominant region, the attenuation coefficient smoothly recovers to the global baseline value of 1.90, ensuring global stability.

[0108] like Figures 3 to 6 The diagram illustrates the membership function distribution and regional MFD decay characteristics of this embodiment. Figures 3 to 4The piecewise linear membership functions for roll angle and roll angular velocity respectively visually represent the coverage range of the three fuzzy sets; Figure 5 The decay rate of regional MFD varies with the membership degree of the dominant rule. The variation curve of the attenuation coefficient verifies the characteristic of smooth transition with operating conditions. Figure 6 The diagram shows the state-dependent decay ratio thermal distribution. The dashed boxes mark the working areas corresponding to the dominant rules, reflecting the spatially differentiated distribution characteristics of performance indicators.

[0109] Stability analysis uses common The matrix reduces the solution complexity, meaning all rules correspond to the same positive definite transformation matrix. to expand The functional is composed of a state energy term and a dynamic memory term, and is used to uniformly measure the combined energy of system state and communication scheduling.

[0110] Step 3: Design a dynamic memory event triggering mechanism for drift and saturation perception In a specific embodiment, based on the aforementioned four-dimensional risk assessment and adaptive triggering method, all triggering parameters of this embodiment are configured to form an event triggering scheduling rule that can be directly deployed.

[0111] This embodiment uses the state variables after coordinate transformation for risk assessment and trigger determination. The transformed state and the transformed error are as follows:

[0112] in , These are the transformed state components corresponding to the roll angle and roll angular velocity, respectively. Based on the above components, the normalized risk indicators for the four dimensions are calculated as follows: State drift risk indicators: ; Risk assessment time window in this embodiment .

[0113] Performance fluctuation risk indicators: ; Main region deviation risk indicator: ; Input saturation risk indicators: ; The four types of single-dimensional indicators are weighted and integrated according to preset weights to obtain a comprehensive operational risk indicator:

[0114] To avoid frequent fluctuations in the risk signal due to measurement noise and instantaneous disturbances, a first-order low-pass filter is introduced to smooth the overall risk. In the engineering implementation, Euler discretization is used for updating, with a sampling period of [value missing]. Then the first The filter update formula for the step is:

[0115] In this embodiment, the filter attenuation coefficient Filter gain coefficient The input terms are saturated and normalized to ensure that the filter output is always bounded.

[0116] Based on the filtered risk index, the expected triggering coefficient is obtained using inverse fractional mapping:

[0117] Summarized as follows:

[0118] To avoid trigger coefficient jumps impacting system stability, a first-order dynamic tracking equation is used to generate the actual trigger coefficients, with the discrete update form as follows:

[0119] Tracking rate coefficient in this embodiment This controls the speed at which the actual trigger coefficients converge to the expected value. The dynamic memory variable also uses Euler discrete updates, its first... The recurrence relation for the step is:

[0120] in To determine the delay steps, the dynamic memory-related parameters in this embodiment are set as follows: attenuation coefficient. initial gain decay rate Delay feedback coefficient Delay time constant This dynamic memory variable can mitigate the impact of instantaneous disturbances on trigger determination, while theoretically ensuring that all trigger intervals have a strict positive lower bound. Combining the transformed state error, adaptive trigger coefficient, and dynamic memory variable, an event trigger determination function is constructed:

[0121] When the next time step determination function is greater than or equal to 0, or the interval reaches the maximum trigger interval, the next status data packet transmission is triggered, that is, the next trigger time satisfies:

[0122] Maximum trigger interval in this embodiment This serves as a safety net, ensuring from an engineering perspective that there won't be an extreme situation where updates are not performed for an extended period.

[0123] Step 4: Design Matched Saturated Sector Certificates and Non-PDC Fuzzy Controller In a specific embodiment, the controller parameter tuning of this embodiment is completed based on the aforementioned matched saturated sector constraint and non-PDC controller design method.

[0124] First, define the scalar form of the saturation dead zone deviation function:

[0125] Its physical meaning is the difference between the theoretical output of the controller and the actual output after saturation, reflecting the degree of limitation of the actuator, and its value is always equal to... Same number.

[0126] If the sector mapping is perfectly matched to the controller gain, that is, the sector multiplier matrix is ​​consistent with the controller gain structure, then for any diagonal multiplier... The saturation dead zone deviation satisfies the global sector inequality:

[0127] This inequality holds for any control input, eliminating the need for additional sector effective ellipsoid constraints and effectively reducing the conservatism of saturation processing. In this embodiment, the sector multiplier is preset to... This value is determined through offline one-dimensional grid search, achieving an optimal balance between the conservatism of saturation treatment and control performance.

[0128] A fuzzy controller is designed using a non-parallel distributed compensation (non-PDC) strategy. The controller calculates control commands only using the latest state transmitted at the trigger moment.

[0129] in For the first The row vector of the local controller gain corresponding to each rule, and the common positive definite transformation matrix Together, they serve as the decision variables to be solved. This non-PDC structure and... The transformation terms in the function are one-to-one, ensuring consistency between the analysis framework and the engineering implementation.

[0130] Substituting the controller into the original system state equations, and combining the saturation dead zone deviation function and the fault convex hull characteristics, the first... Component form of the closed-loop system under each fault vertex:

[0131] in These are the elements of the transformed state matrix. The first of the controller gain vectors One element, For the first The efficiency coefficient of each fault vertex for any fault condition The corresponding closed-loop dynamics can all be represented as a convex combination of vertex closed loops.

[0132] Step 5: Derive the sufficient conditions for LMI and solve the control parameters offline. In a specific embodiment, all the aforementioned constraints are transformed into sufficient conditions in the form of linear matrix inequalities, and all control and triggering parameters are solved offline using MATLAB's LMI toolbox.

[0133] The core idea of ​​the stability derivation is: for augmentation Differentiating the functional along the closed-loop system, substituting it into the closed-loop state equations, and introducing the matched sector inequality to scale the saturation term, while handling the sampling error term in conjunction with event triggering conditions, are then applied. The supplementary lemma transforms nonlinear matrix inequalities into linear matrix inequalities, ultimately yielding sufficient conditions that can be solved offline.

[0134] The final sufficient conditions for LMI have the following block structure: for each fault vertex There exists a positive definite matrix. diagonal matrix and scalar This makes the following equation true:

[0135] Each block element is composed of a closed-loop coefficient matrix, triggering parameters, and performance parameters. The derivation utilizes the fault convex hull property and the multi-cell property of the membership function derivative; verifying only the fault vertex and derivative vertex ensures feasibility across all operating conditions. This embodiment uses MATLAB's LMI toolbox to solve the above linear matrix inequalities offline, obtaining all control gain matrices, transformation matrices, triggering weight matrices, and performance parameters. The solution simultaneously guarantees four core performance characteristics of the closed-loop system: regional positive invariance, perturbation-free asymptotic stability, regional MFD H∞ performance, and Zeno-free transfer characteristics. Online execution only requires calculating membership degrees, updating the first-order scalar filter, and determining the scalar triggering function, resulting in minimal computation and easy embedded deployment.

[0136] This embodiment also includes simulation results and verification analysis: To demonstrate the superiority of the method described in this embodiment, a traditional fixed-coefficient dynamic event-triggered control scheme is set as a comparison benchmark. The two schemes use the same controller, controlled object, fault profile and disturbance signal, with only the event triggering mechanism being different to ensure the fairness of the comparison. The simulation time is 20 seconds, covering the complete fault switching and disturbance process.

[0137] A: Regional stability verification and communication efficiency analysis Figures 7 to 8 The system state response comparison between the DSA-DMETM mechanism proposed in this embodiment and the traditional fixed-coefficient DETM mechanism is shown, including two time-domain curves for roll angle and roll angular velocity.

[0138] Define the steady-state error of the roll angle as the root mean square value during the steady-state phase:

[0139] Among them, take , The steady-state region is defined in the figure. As can be seen from the figure, the convergence curves of the two schemes almost completely overlap, both entering the steady-state region in approximately 8 seconds. The steady-state error of the roll angle remains within 0.5°, and there is no significant difference in overshoot and settling time. These results demonstrate that the risk-aware event triggering mechanism of this invention significantly reduces communication frequency without sacrificing the dynamic response quality and steady-state control accuracy of the closed-loop system, verifying the technical effect of synergistic optimization of communication efficiency and control performance.

[0140] Figures 9 to 11 The region of the closed-loop system is shown. Energy function variation curve. The normalized energy ratio is defined as:

[0141] in This represents the upper bound of the permissible energy. As can be seen from the figure, throughout the entire simulation process... The cumulative controlled output energy remains consistently less than 1, always within the upper bound of the regional certification. This result rigorously verifies the regional positive invariance of the closed-loop system; the system trajectory remains within the preset permissible operating region, consistent with the theoretical analysis conclusions.

[0142] Figures 12 to 15 The comparison of communication performance between the two event triggering schemes is shown, including the distribution of trigger times, the cumulative number of triggers, the statistics of trigger intervals, and the communication savings rate.

[0143] Define the communication traffic saving rate as:

[0144] in This represents the total number of triggers for the fixed-coefficient scheme. This represents the total number of triggers in this embodiment. The quantitative calculation results are as follows: Total number of triggers for the fixed coefficient scheme. Total number of triggers in this embodiment Substituting, we get: The average trigger interval is defined as:

[0145] in Let be the total simulation duration. The average trigger intervals for the two schemes were calculated as follows: and The improvement reached 108%; the minimum trigger intervals were 0.026s and 0.027s, respectively, which are basically equivalent.

[0146] The results fully demonstrate the effectiveness of the risk perception triggering mechanism: it automatically relaxes the triggering threshold during the steady-state low-risk phase of the system to reduce redundant transmission; and automatically tightens the threshold during the transient high-risk phase to ensure control response speed, thereby realizing intelligent optimization of communication resources.

[0147] Figures 16 to 18 The internal variable response curves of the event triggering mechanism described in this embodiment are shown, including the time-domain changes of the filtered comprehensive risk index, adaptive triggering coefficient, and dynamic memory variable. As can be seen from the figure, in the initial stage of the simulation, the system state drift is large and the operational risk is high, with the comprehensive risk index at a high level. The triggering coefficient is automatically adjusted down to near its lower bound to ensure timely state updates. As the system gradually converges, the risk index continues to decrease, and the triggering coefficient automatically rises back to near its upper bound, expanding the trigger interval to save bandwidth. The entire adjustment process is smooth and continuous, without any abrupt changes or shocks, and the dynamic memory variable remains non-negative throughout, verifying the effectiveness and stability of the bidirectional adaptive adjustment mechanism.

[0148] B: Regional MFD H∞ Performance Verification and Parameter Sensitivity Analysis Figures 19 to 21 The diagram shows a comparison curve of the dominant rule activation, actual decay rate, and cumulative perturbation output ratio. The cumulative perturbation output ratio is defined as:

[0149] The smaller the ratio, the smaller the controlled output energy under the same disturbance input, and the stronger the disturbance rejection performance.

[0150] The activation curve of the dominant rule shows that the simulation conditions in this embodiment remain within the dominant working region throughout the entire process, with the activation level consistently above 0.9. The actual decay rate curve shows that the effective decay ratio of the MFD scheme in this embodiment remains stable at approximately 0.728, significantly lower than the 1.0 of the traditional global scheme. The cumulative perturbation output ratio curve shows that, over time, the ratio of the scheme in this embodiment is significantly lower than that of the traditional global scheme. Quantization results show that the cumulative controlled output energy of the method described in this embodiment at the end of the simulation is... Traditional full-domain solutions are Therefore, the performance improvement in the dominant region is:

[0151] The number of data packet transmissions for the two schemes was roughly the same (361 and 364 times), indicating that the improvement in the anti-interference performance of the dominant area did not come at the cost of increased communication burden, and that performance and communication were optimized in a coordinated manner.

[0152] Figures 22 to 24 The results of sensitivity analysis are shown for different ρ values. The figure shows that as... As the weighting factor decreased from 0.65 to 0.45, the average effective attenuation ratio decreased from 0.806 to 0.671, and the final cumulative perturbation output ratio continued to decrease; the number of triggers remained around 360 with slight fluctuations. This result indicates that the weighting factor... It can be used as a flexible adjustment knob to balance control accuracy and solution feasibility according to engineering needs, providing a convenient basis for parameter tuning in practical engineering applications.

[0153] C: Robustness verification under input saturation conditions In this case, the normalized saturation limit of the anti-roll fin was lowered to 0.012, causing the control command to exceed the saturation limit in the initial transient phase, actively activating the input saturation nonlinearity, and verifying the effectiveness of the matched sector certificate.

[0154] Define saturation depth as the percentage by which the theoretical output exceeds the limit:

[0155] Figures 25 to 27 The simulation results under saturation conditions are presented, including control commands and saturation inputs, saturation level indices, matched sector supply functions, and regional characteristics. Four sets of ratio curves. The graphs show that during the initial transient phase, the control command exceeded the saturation limit. Substituting this into the calculation, the maximum saturation depth reached 104.3%, and the saturation activation time accounted for 7.27%, indicating a deep saturation condition. The saturation degree index increased synchronously, accurately reflecting the actuator's constraint level. The matched sector supply function remained non-negative throughout, proving that the sector inequality constraint remained effective. The maximum ratio is only 0.509, which is far less than the boundary of the region with a ratio of 1.

[0156] The above results fully verify the low conservatism of the matched saturated sector certificate of the method described in this embodiment. Even under deep saturation conditions, it can still guarantee the validity of the theoretical certificate and the stability of the system without the need to introduce additional sector effective ellipsoid constraints. Furthermore, the trigger interval statistics show that all trigger intervals of the method described in this embodiment are greater than the positive lower bound of 0.027s, and there are no trigger intervals infinitely approaching 0, with no Zeno phenomenon occurring throughout. This ensures the engineering feasibility of the method described in this embodiment, preventing hardware overload problems caused by the infinitely increasing trigger frequency, and meeting the deployment requirements of practical networked control systems. In summary, the simulation results show that the reliable H∞ control method for saturated networked TS fuzzy systems based on risk-aware event triggering proposed in this embodiment can ensure stable system operation under harsh conditions of actuator efficiency decay and input saturation, while significantly saving communication bandwidth and significantly improving the disturbance suppression performance in the dominant working region, possessing both excellent control quality and engineering practical value.

[0157] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system, characterized in that, Specifically, the following steps are included: S1: Construct a global networked TS fuzzy system corresponding to the coupled actuator efficiency decay fault and input saturation constraint; S2: Based on the global networked TS fuzzy system, construct a comprehensive operational risk index that includes state drift risk index, performance fluctuation risk index, dominant region deviation risk index, and input saturation risk index. S3: Construct a dynamic memory event triggering mechanism for drift and saturation perception based on comprehensive operational risk indicators; S4: Construct a matched saturated sector constraint model; based on the global networked TS fuzzy system combined with the drift and saturation-aware dynamic memory event triggering mechanism, construct a non-PDC fuzzy fault-tolerant H∞ controller; based on the matched saturated sector constraint model and the non-PDC fuzzy fault-tolerant H∞ controller, realize reliable H∞ control of the risk-aware event-triggered saturated TS fuzzy system.

2. The reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system according to claim 1, characterized in that, The construction formula for the global networked TS fuzzy system in S1 is: In the formula: The first derivative of the system state vector; express A 3D system state vector; Indicates the first The corresponding fuzzy rules 3D local state matrix; Indicates the first The corresponding fuzzy rules 3D local input matrix; express The actual output control quantity of the actuator; Indicates the first The corresponding fuzzy rules 3D local perturbation matrix; express An externally bounded perturbation vector; express The controlled output vector of the dimensional system; Indicates the first The corresponding fuzzy rules 3D local output matrix; Indicates the first The corresponding fuzzy rules 3D local feedforward matrix; The set of indices representing all fuzzy rules; Indicates the first The normalized membership degree corresponding to the fuzzy rules, and ; This represents the theoretical control command vector output by the controller. Represents the component-based standard saturation function; Represents a known saturation limit value and ; The theoretical control vector output by the controller is represented by the first... One component; This represents the actuator efficiency degradation fault matrix, and ; Indicates the first A matrix of fault vertices; Indicates the total number of faulty vertices; This indicates a non-negative coefficient.

3. A reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system according to claim 2, characterized in that, The method for constructing comprehensive operational risk indicators in S2 includes the following steps: S21: Based on the aforementioned global networked TS fuzzy system, the region membership function dependency H∞ performance index is constructed as follows: In the formula: The time-varying H∞ decay coefficient represents the dynamic change over time. This represents the global benchmark performance index H∞, which is a known positive constant. Indicates the first The decay weight coefficient of the dominant fuzzy rule and ; Indicates the dominant fuzzy rule set; This represents a non-dominant fuzzy rule set; The constant term in the performance inequality; express transpose; express transpose; S22: Based on the system state vector, the system nominal state vector and the trigger state error vector are defined as follows: In the formula: Represents the nominal state vector of the system; Represents the fuzzy premise variable vector of the system; This represents the trigger state error vector; Indicates the time of the most recent event trigger. The original state vector of the system obtained by sampling; Represents the fuzzy weighted positive definite transformation matrix; S23: Based on the system's nominal state vector and the region membership function dependency H∞ performance index, construct state drift risk index and performance fluctuation risk index: The state drift risk indicator is: In the formula: Indicators representing state drift risk; Indicates in The nominal state vector of the system at time 1; Indicates the length of the time window for risk assessment; The performance fluctuation risk indicator is: In the formula: Indicators representing performance volatility risk; Indicates in The time-varying H∞ decay coefficient at time t; According to the The normalized membership degrees corresponding to the fuzzy rules are used to construct the dominant region deviation risk indicator as follows: In the formula: This indicates that the dominant region deviates from the risk indicator; This indicates a deviation from the baseline threshold; Based on the theoretical control command vector output by the controller With component-based standard saturation function The input saturation risk index is constructed as follows: In the formula: This indicates an input saturation risk indicator; S24: The comprehensive operational risk indicators obtained based on S23 are as follows: In the formula: Indicates comprehensive operational risk indicators; The weighting coefficients represent the four types of risks and .

4. A reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system according to claim 3, characterized in that, S3 specifically includes the following steps: S31: A first-order low-pass filter is introduced to smooth the comprehensive operational risk index. Its expression is: In the formula: express The first derivative; This represents the overall operational risk index after filtering. Indicates the filter attenuation coefficient; Indicates the filter gain coefficient; S32: Construct the desired triggering coefficient based on step S31 for: In the formula: These represent the lower and upper bounds of the trigger coefficient, respectively; This represents the risk adjustment sensitivity parameter; S33: Introducing a first-order dynamic tracking equation for the desired trigger coefficient After filtering, the actual trigger coefficients are obtained as follows: In the formula: Represents the tracking rate coefficient; Indicates the actual trigger coefficient; express The first derivative; S34: Based on the actual triggering coefficient and the triggering state error vector, a dynamic memory variable with both exponential decay and delayed feedback characteristics is constructed as follows: In the formula: express The first derivative; Represents a dynamic memory variable; Indicates the decay coefficient of the memory variable; Indicates a positive definite triggering weight matrix and ; Indicates the time-varying delay gain; Indicates the delay feedback coefficient; Indicates the time delay constant; express transpose; express transpose; S35: The event triggering determination function is constructed based on the aforementioned dynamic memory variable as follows: In the formula: Indicates the event triggering determination function and ; S36: Constructing a drift and saturation-aware dynamic memory event triggering mechanism based on an event-triggered decision function: In the formula: Indicates the maximum trigger interval and ; Indicates the time when the most recent event was triggered; Indicates the next trigger time.

5. A reliable H∞ control method for a risk-perceived event-triggered saturated TS fuzzy system according to claim 4, characterized in that, The matched saturated sector constraint model constructed in S4 is as follows: In the formula: Represent the scalar form of the saturation dead zone deviation function; Represents the diagonal sector multiplier matrix; express The transpose of .

6. A reliable H∞ control method for a risk-aware event-triggered saturated TS fuzzy system according to claim 5, characterized in that, The non-PDC fuzzy fault-tolerant H∞ controller constructed in S4 is: In the formula: Represents the gain matrix of the fuzzy weighted controller; Indicates the first Normalized membership degree of a fuzzy rule; Indicates the first The local controller gain matrix corresponding to the fuzzy rule; Indicates the first The local positive definite transformation matrix corresponding to the fuzzy rule.

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