Fuzzy H-infinity closed-loop control method for implanted wearable medical equipment

Abstract

Compared with the prior art, the fuzzy H-infinity closed-loop control method for the implantable wearable medical equipment, provided by the invention, has the advantages that multiple types of network induction phenomena are innovatively coupled, and the fuzzy H-infinity closed-loop control method for the implantable wearable medical equipment is realized in a T-S fuzzy system communication network with parameter uncertainty and disturbance noise for the first time; meanwhile, dynamic quantization and random communication protocol (SCP) scheduling are considered, the limitation that multiple network induction phenomena are independently or partially considered in existing research is broken through, the method is more suitable for the scene of multi-class interference coupling in an actual networked control system, and the application range of a T-S fuzzy system in a complex network environment is expanded.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to fuzzy H-type communication for implantable wearable medical devices. ∞ Closed-loop control method. Background Technology

[0002] With the rapid development of communication technology, networked control systems (NCSs) have attracted much attention in engineering applications due to their advantages such as low cost, easy installation, reduced hardwiring, and high reliability. A large number of papers on related control and filtering problems have also emerged. However, the limited communication bandwidth of NCSs has caused many network-induced phenomena, such as packet loss, communication delay, data collision, and signal quantization. These phenomena seriously affect system performance and bring challenges to control system design.

[0003] In traditional NCSs research, it is often assumed that all sensors can simultaneously access the communication network to transmit signals. However, due to limited bandwidth, simultaneous access by multiple sensors can easily lead to data conflicts, and this assumption does not hold true in real-world scenarios. To address this issue, introducing communication protocols to schedule the order in which sensors access the network has become an effective approach. Common protocols include Round-Robin, Try-Once-Discard, and Random Communication Protocol (SCP). While existing research explores the performance analysis and control integration of NCSs under protocol scheduling—for example, modeling the closed-loop system under SCP as a multivariable time-varying delayed stochastic system to study output feedback control, or using Markov processes to model SCP and obtaining sufficient conditions for system stability and performance through the Riccati differential difference equation (RDE) method—most of these studies do not fully consider the coupling effects of various network-induced phenomena and have limitations in control strategy design, such as using only static output feedback or observer-based output feedback control. Signals need to be quantized before transmission through communication networks, and the quantization effect inevitably impacts the performance of NCSs. Currently, mainstream quantization modeling methods are divided into static and dynamic quantization strategies. Dynamic quantization strategies, due to their memory function, can dynamically adjust the quantization level, expand the attraction domain, and reduce the steady-state limit cycle, making them more versatile than static quantization strategies. Meanwhile, fuzzy control is widely used in solving practical engineering problems. The Takagi-Sugeno (TS) fuzzy model, through local linearization, approximates a nonlinear system as a set of linear models and utilizes fuzzy membership functions to achieve smooth connections, becoming an important tool for studying nonlinear systems. In recent years… Research on the analysis and synthesis of quantized TS fuzzy systems has been conducted, such as studies on nonfragile filtering of switched TS fuzzy systems and feedback control of fuzzy Markov jump systems. However, most studies are based on state feedback, assuming that the system state can be directly used for controller design. In reality, the system state is often difficult to obtain directly, making output feedback control more practical. In addition, existing research rarely considers the combined impact of quantization and communication protocol-induced phenomena on TS fuzzy systems. Research on dynamic output feedback control in such coupled scenarios is still lacking. How to design a suitable controller and obtain sufficient conditions for system stability and performance has become a key problem that urgently needs to be solved. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies and provide fuzzy H for implantable wearable medical devices. ∞ Closed-loop control method; To achieve the above objectives, the technical solution of the present invention is implemented as follows: This invention provides fuzzy H for implantable wearable medical devices ∞ The closed-loop control method includes the following steps: A. Establishing a TS fuzzy model for nonlinear NCSs: For discrete-time nonlinear systems, TS fuzzy rules are used to describe the system dynamics; the TS fuzzy model's first... The rule is expressed as: if equal ,…,and equal The output equation is: (1); in, For discrete time, , For the number of fuzzy rules, Indicates the premise variable, Indicates inclusion fuzzy sets, For system status, For measurement output, To control the output, To control the input, As an external disturbance and belonging to ; , , , , , Given a constant matrix of appropriate dimension; , For norm-bounded parameter uncertainty, the following condition must be met: (2); in To meet The uncertainty matrix, , , Given a constant matrix; define the normalized membership function: (3); in ,and , Therefore, the TS fuzzy system is rewritten as follows: (4); in: And in subsequent derivations Abbreviated as ; B. Design of communication network mechanisms: Employ dynamic quantization strategies to measure output signals. Quantization, basic quantization function satisfy: (5); in 0 represents the quantization range. 0 represents the quantization error boundary; the dynamic quantizer output is: (6); in For dynamic quantization parameters, quantization error satisfy (when When ), and simultaneously using the Random Communication Protocol (SCP) for scheduling ( Transmission, SCP via Markov chains describe, Indicates time The transition probability of a sensor connected to the network is: (7); Post-scheduling quantization measurement output satisfy (8); Further rewritten as (9); in , The Kronecker delta function; C. Constructing the augmenting system: Defining augmenting states Combining equations (4), (6), and (9), the TS fuzzy system is reconstructed as follows: (10); in, , , , , , For the corresponding appropriate dimension matrix; D. Design of a dynamic output feedback controller: A mode-dependent and fuzzy-dependent dynamic output feedback controller is adopted, whose first... The rule is: If equal ,…,and equal The output equation is: (11); in The controller is in a certain state. , , , The controller gain matrix is ​​defined. Combining equations (10) and (11), we obtain the closed-loop system: (12); where , , , .

[0005] 1. Compared with the prior art, the present invention addresses the fuzzy H-axis of implantable wearable medical devices. ∞ The closed-loop control method innovatively couples multiple network-induced phenomena. For the first time, it considers dynamic quantization and random communication protocol (SCP) scheduling simultaneously in the communication network of a TS fuzzy system with parameter uncertainty and disturbance noise. This breaks through the limitation of existing studies that mostly consider network-induced phenomena individually or partially. It is more in line with the scenario of multiple disturbance coupling in actual networked control systems and expands the application scope of TS fuzzy systems in complex network environments. 2. The designed dynamic output feedback controller relies on both Markov mode and fuzzy rules, which can fully adapt to the system mode switching characteristics caused by SCP scheduling and the nonlinear characteristics of TS fuzzy system. It effectively suppresses the combined effects of dynamic quantization error, SCP scheduling randomness, parameter uncertainty and external disturbance on the system, and significantly improves the anti-interference capability and control accuracy of the closed-loop system. 3. By adopting the synchronous mode dependency and fuzzy Lyapunov function method, compared with the general Lyapunov function, the conservatism of controller design is greatly reduced and it is easier to obtain relaxed system stability and performance conditions. At the same time, the design conditions of controller and dynamic quantization parameters are transformed into the problem of solving linear matrix inequalities (LMIs). With the help of mature LMIs solving tools, the design parameters can be obtained efficiently, reducing the difficulty of engineering implementation. 4. Through rigorous theoretical derivation, it is proven that the proposed control strategy can ensure the stability of the closed-loop system in a stochastic sense and satisfy the specified H. ∞ The performance indicators can effectively suppress the influence of external disturbances on the system output, enabling the system output to track the desired trajectory and maintain a small deviation. Its effectiveness has been verified in numerical simulation and mass-spring-damper mechanical system examples, providing reliable theoretical support and engineering solutions for the design of practical nonlinear networked control systems. Attached Figure Description

[0006] Figure 1 This is a state response curve diagram of the open-loop system in Example 2; Figure 2 The control system diagram with communication network provided in this application is as follows: Detailed Implementation Example 1: This example provides a fuzzy H-axis for implantable wearable medical devices. ∞ The closed-loop control method includes the following steps: A. Establishing a TS fuzzy model for nonlinear NCSs: For discrete-time nonlinear systems, TS fuzzy rules are used to describe the system dynamics; the TS fuzzy model's first... The rule is expressed as: if equal ,…,and equal The output equation is: (1); in, For discrete time, , For the number of fuzzy rules, Indicates the premise variable, Indicates inclusion fuzzy sets, For system status, For measurement output, To control the output, To control the input, As an external disturbance and belonging to ; , , , , , Given a constant matrix of appropriate dimension; , For norm-bounded parameter uncertainty, the following condition must be met: (2); in To meet The uncertainty matrix, , , Given a constant matrix; define the normalized membership function: (3); in ,and , Therefore, the TS fuzzy system is rewritten as follows: (4); in: And in subsequent derivations Abbreviated as ; B. Design of communication network mechanisms: Employ dynamic quantization strategies to measure output signals. Quantization, basic quantization function satisfy: (5); in 0 represents the quantization range. 0 represents the quantization error boundary; the dynamic quantizer output is: (6); in For dynamic quantization parameters, quantization error satisfy (when When ), and simultaneously using the Random Communication Protocol (SCP) for scheduling ( Transmission, SCP via Markov chains describe, Indicates time The transition probability of a sensor connected to the network is: (7); Post-scheduling quantization measurement output satisfy (8); Further rewritten as (9); in , The Kronecker delta function; C. Constructing the augmenting system: Defining augmenting states Combining equations (4), (6), and (9), the TS fuzzy system is reconstructed as follows: (10); in, , , , , , For the corresponding appropriate dimension matrix; D. Design of a dynamic output feedback controller: A mode-dependent and fuzzy-dependent dynamic output feedback controller is adopted, whose first... The rule is: If equal ,…,and equal The output equation is: (11); in The controller is in a certain state. , , , The controller gain matrix is ​​defined. Combining equations (10) and (11), we obtain the closed-loop system: (12); In the formula , , , ; Furthermore, this also includes: E. Definitions and Lemmas: Definition 1: A closed-loop system (12) is stochastically stable, that is, when At that time, for any initial conditions and If the corresponding stability criteria are met, then: (13); Definition 2: A closed-loop system (12) satisfies H ∞ Performance, i.e., for a given scalar γ>0, under zero initial conditions, satisfies the corresponding H∞ The performance determination criteria are as follows: (14); Lemma 1: Let matrix , and For an optimal dimension matrix, then for any matrix satisfying ... matrix ,

[0007] It holds true if and only if a scalar exists. 0, such that: ; Lemma 2: For a matrix of appropriate dimension , , and and scalar ,like If , then the corresponding inequality holds; 3. Furthermore, this also includes: F, giving stochastic stability and H ∞ Sufficient condition for performance analysis (Theorem 1): For a T–S fuzzy system (10), given the controller (11) and its gain matrix, quantizer range and error bound If a matrix exists and ， For any , satisfy: (15); in, , , And parameters The online adjustment strategy is as follows: (16); If ≥1, then in the Markov chain defined by the transition probability (7) Under controlled SCP scheduling, the controller (11) and quantizer (6) can guarantee the stochastic stability and H of the closed-loop system (12). ∞ Performance γ>0; Constructing Lyapunov functions that depend on patterns and fuzziness: (17); among which, According to equations (5) and (16), the quantization error satisfy: (19); Combining system (4), equation (19) can be rewritten as with The relevant inequalities exist:

[0008]

[0009]

[0010] (twenty one);

[0011] (twenty two); ; (twenty four); ; ; (25); among which, , The Lyapunov function difference correlation matrix; For nonzero ,remember ,exist: (27); (30);

[0012] (31); (32); Furthermore, this also includes: G. Designing a dynamic output feedback controller: Theorem 2: For a T–S fuzzy system (10), given the controller (11) and its gain parameters, quantizer range and error bound If a matrix exists , and scalar and (for any) , )satisfy: (33); in, , , Under SCP scheduling, the controller and quantizer can guarantee that the closed-loop system (12) is stochastically stable and satisfies Performance γ>0; The proof of Theorem 2 depends on rewriting equation (15) as containing , The form is as follows: (34); And according to Lemma 1, we get: (35); Theorem 3: Given a scalar Transition probability Quantizer range and error bound If a matrix exists

[0013] , , and scalar , and (for any) , ),satisfy: (36); in, , , , ,

[0014] , ; is the dimension adjustment matrix ( ; ; hour, ) Then the closed-loop system (12) is stochastically stable and satisfies H ∞ Performance γ>0; The derivation of Theorem 3 depends on the definition. And combining with Lemma 2, we get: (37); in, ; Furthermore, in step A, the T-S fuzzy model approximates the nonlinear object with a set of linear models through the local linearization method, and combines the fuzzy membership function to smoothly connect and approximate the nonlinear object with arbitrary precision. Moreover, the norm bounded uncertainty in equation (2) exists in both the state and the measurement output. Furthermore, in step B, the dynamic quantizer is more general than the static quantization strategy, through... The dynamic adjustment (Equation (16)) increases the system's attraction domain and reduces the steady-state limit cycle. The SCP scheduling avoids data collisions through Markov chain transition probabilities and signal update rules. The T-S fuzzy system is reconstructed into Equation (10) to handle the time delay term introduced by SCP. Furthermore, in step C, the state dimension of the dynamic output feedback controller... and While maintaining the same dimensionality increases numerical complexity, it simplifies variable decoupling in controller design and ensures synchronization between the controller and the Markov pattern of SCP scheduling. Furthermore, in step E, conservatism is reduced by constructing a mode- and fuzzy Lyapunov function, and a matrix is ​​introduced. The relaxation method (Equation (22)) is used to treat The nonlinear terms, combined with the S-Procedure and Schur complement derivations (21), (25), (27), (30), and (32), ensure the stochastic stability of the closed-loop system and H. ∞ performance; Furthermore, in step F, Theorem 2 separates the uncertainty in equation (2) through Lemma 1. , Transform equation (15) into a form containing The matrix inequality (33); Theorem 3 is defined by... , The parameters, combined with Lemma 2, transform equation (37) into a solvable linear matrix inequality (36), and finally obtain the controller gain.

[0015] Furthermore, it also includes simulation verification steps: through numerical examples and examples of mass-elastic-damper mechanical systems, system parameters and disturbances are set. and uncertainty Solving the linear matrix inequality (36) of Theorem 3 yields the controller gain. Simulation results show that the closed-loop system is state-converged and stable, satisfying H. ∞ performance.

[0016] Example 2: This example verifies the proposed H through numerical calculation. ∞ The effectiveness of the fuzzy controller design scheme is considered in the form of the discrete-time TS fuzzy model (1), where The rules are as follows: Object Rule 1: If for ,but ; Object Rule 2: If for ,but ; in, , , , , , , , ; The disturbance in this example Set as and uncertainty parameters The corresponding membership functions are respectively and The initial conditions are set as follows: , Figure 1 The state response curve of the open-loop system is shown. As can be seen from the figure, if the influence of the controller is not considered, the system will be in an unstable state.

[0017] Example 3, referring to Figure 2 The main innovative points of this application can be summarized as follows: For the first time, dynamic quantization and SCP scheduling techniques are applied simultaneously in a communication network to model a TS fuzzy system with uncertainty and interference noise. To improve the control effect of Markov modes in closed-loop systems induced by SCP scheduling, a dynamic output feedback controller was designed, which has both mode-dependent and fuzzy-dependent characteristics.

[0018] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of protection of this application is limited to these examples; under the concept of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of one or more embodiments of this application as described above, which are not provided in detail for the sake of brevity; One or more embodiments in this application are intended to cover all such substitutions, modifications and variations that fall within the broad scope of this application; therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments in this application should be included within the protection scope of this application.

Claims

1. Fuzzy H for implantable wearable medical devices ∞ The closed-loop control method is characterized by, Includes the following steps: A. Establishing a TS fuzzy model for nonlinear NCSs: For discrete-time nonlinear systems, TS fuzzy rules are used to describe the system dynamics; the TS fuzzy model's first... The rule is expressed as: if equal ,…,and equal The output equation is: （1）； in, For discrete time, , For the number of fuzzy rules, Indicates the premise variable, Indicates inclusion fuzzy sets, For system status, For measurement output, To control the output, To control the input, As an external disturbance and belonging to ; , , , , , Given a constant matrix of appropriate dimension; , For norm-bounded parameter uncertainty, the following condition must be met: （2）； in To meet The uncertainty matrix, , , Given a constant matrix; define the normalized membership function: (3); in ,and , Therefore, the TS fuzzy system is rewritten as follows: （4）； in: And in subsequent derivations Abbreviated as ; B. Design of communication network mechanisms: Employ dynamic quantization strategies to measure output signals. Quantization, basic quantization function satisfy: （5）； in 0 represents the quantization range. 0 represents the quantization error boundary; the dynamic quantizer output is: （6）； in For dynamic quantization parameters, quantization error satisfy (when When ), and simultaneously using the Random Communication Protocol (SCP) for scheduling ( Transmission, SCP via Markov chains describe, Indicates time The transition probability of a sensor connected to the network is: （7）； Post-scheduling quantization measurement output satisfy (8); Further rewritten as (9); in , The Kronecker delta function; C. Constructing the augmenting system: Defining augmenting states Combining equations (4), (6), and (9), the TS fuzzy system is reconstructed as follows: (10); in, , , , , , For the corresponding appropriate dimension matrix; D. Design of a dynamic output feedback controller: A mode-dependent and fuzzy-dependent dynamic output feedback controller is adopted, whose first... The rule is: If equal ,…,and equal The output equation is: （11）； in The controller is in a certain state. , , , The controller gain matrix is ​​defined. Combining equations (10) and (11), we obtain the closed-loop system: （12）； In the formula , , , 。 2. The fuzzy H-shaped design for implantable wearable medical devices as described in claim 1 ∞ The closed-loop control method is characterized by, Also includes: E. Definitions and Lemmas: Definition 1: A closed-loop system (12) is stochastically stable, that is, when At that time, for any initial conditions and If the corresponding stability criteria are met, then: （13）； Definition 2: A closed-loop system (12) satisfies H ∞ Performance, i.e., for a given scalar γ>0, under zero initial conditions, satisfies the corresponding The performance determination criteria are as follows: （14）； Lemma 1: Let matrix , and For an optimal dimension matrix, then for any matrix satisfying ... matrix , It holds true if and only if a scalar exists. 0, such that: ; Lemma 2: For a matrix of appropriate dimension , , and and scalar ,like If , then the corresponding inequality holds.

3. The fuzzy H-shaped design for implantable wearable medical devices as described in claim 2 ∞ The closed-loop control method is characterized by, Also includes: F. Given the stochastic stability and H ∞ Sufficient condition for performance analysis (Theorem 1): For a T–S fuzzy system (10), given the controller (11) and its gain matrix, quantizer range and error bound If a matrix exists and ， For any , satisfy: （15）； in, , , And parameters The online adjustment strategy is as follows: （16）； If ≥1, then in the Markov chain defined by the transition probability (7) Under controlled SCP scheduling, the controller (11) and quantizer (6) can guarantee the stochastic stability and H of the closed-loop system (12). ∞ Performance γ>0; Constructing Lyapunov functions that depend on patterns and fuzziness: (17); among which, According to equations (5) and (16), the quantization error satisfy: (19); Combining system (4), equation (19) can be rewritten as with The relevant inequalities exist: （21）； （22）； ； （24）； ； ； (25); among which, , The Lyapunov function difference correlation matrix; For nonzero ,remember ,exist: （27）； （30）； （31）； （32）。 4. The fuzzy H-type device for implantable wearable medical devices as described in claim 3 ∞ The closed-loop control method is characterized by, Also includes: G. Design a dynamic output feedback controller: Theorem 2: For a T–S fuzzy system (10), given the controller (11) and its gain parameters, quantizer range and error bound If a matrix exists , and scalar and (for any) , )satisfy: (33); in, , , Under SCP scheduling, the controller and quantizer can guarantee that the closed-loop system (12) is stochastically stable and satisfies H. ∞ Performance γ>0; The proof of Theorem 2 depends on rewriting equation (15) as containing , The form is as follows: （34）； And according to Lemma 1, we get: （35）； Theorem 3: Given a scalar Transition probability Quantizer range and error bound If a matrix exists , , and scalar , and (for any) , ),satisfy: （36）； in, , , , , , ; is the dimension adjustment matrix ( ; ; hour, Then the closed-loop system (12) is stochastically stable and satisfies Performance γ>0; The derivation of Theorem 3 depends on the definition. And combining with Lemma 2, we get: （37）； in, .

5. The fuzzy H-shaped design for implantable wearable medical devices as described in claim 1 ∞ The closed-loop control method is characterized by, In step A, the T-S fuzzy model approximates the nonlinear object with a set of linear models through the local linearization method, and combines the fuzzy membership function to smoothly connect and approximate the nonlinear object with arbitrary precision. Moreover, the norm bounded uncertainty in equation (2) exists in both the state and the measurement output.

6. The fuzzy H-shaped design for implantable wearable medical devices as described in claim 1 ∞ The closed-loop control method is characterized by, In step B, the dynamic quantizer is more general than the static quantization strategy, through... The dynamic adjustment (Equation (16)) increases the system's attraction domain and reduces the steady-state limit cycle. The SCP scheduling avoids data collisions through Markov chain transition probabilities and signal update rules. The T-S fuzzy system is reconstructed into Equation (10) to handle the time delay terms introduced by SCP.

7. The fuzzy H-shaped design for implantable wearable medical devices as described in claim 1 ∞ The closed-loop control method is characterized by, In step C, the state dimension of the dynamic output feedback controller and While maintaining the same dimensionality increases numerical complexity, it simplifies variable decoupling in controller design and ensures synchronization between the controller and the Markov pattern of SCP scheduling.

8. The fuzzy H-shaped design for implantable wearable medical devices as described in claim 2 ∞ The closed-loop control method is characterized by, In step E, conservatism is reduced by constructing a mode- and fuzzy Lyapunov function, which introduces a matrix. The relaxation method (Equation (22)) is used to treat The nonlinear terms, combined with the S-Procedure and Schur complement derivations (21), (25), (27), (30), and (32), ensure the stochastic stability of the closed-loop system and H. ∞ performance.

9. The fuzzy H-shaped design for implantable wearable medical devices as described in claim 3 ∞ The closed-loop control method is characterized by, In step F, Theorem 2 separates the uncertainty in equation (2) through Lemma 1. , Transform equation (15) into a form containing The matrix inequality (33); Theorem 3 is defined by... , The parameters, combined with Lemma 2, transform equation (37) into a solvable linear matrix inequality (36), and finally obtain the controller gain.

10. The fuzzy H-shaped design for implantable wearable medical devices as described in claim 1 ∞ The closed-loop control method is characterized by, It also includes simulation verification steps: setting system parameters and disturbances through numerical examples and examples of mass-elastic-damper mechanical systems. and uncertainty Solving the linear matrix inequality (36) of Theorem 3 yields the controller gain. Simulation results show that the closed-loop system is state-converged and stable, satisfying H ∞ performance.

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