A data-driven fault-tolerant control method

Abstract

This invention discloses a data-driven fault-tolerant control method. This method analyzes historical data using machine learning algorithms to establish a fault characteristic model, enabling early identification of potential system faults. Control parameters are dynamically adjusted based on real-time data to adapt to system changes and fault conditions, ensuring optimal system performance. Compared to traditional control methods that require precise mathematical models, the control algorithm proposed in this invention is more novel and has simpler application conditions. This method can maintain optimal system performance in various complex and uncertain environments, effectively improving control accuracy and possessing significant engineering application value.

Description

Technical Field

[0001] This invention relates to a data-driven fault-tolerant control method, specifically a neural network-based fault-tolerant control method. Background Technology

[0002] The development of control theory: Traditional control theory relies on precise mathematical models to design controllers; this approach is known as model-based control. However, as system complexity increases, obtaining precise models becomes increasingly difficult, prompting researchers to explore control methods that do not rely on precise models, namely data-driven control. The advent of the big data era: With the development of information technology, especially the widespread adoption of the internet and the Internet of Things, massive amounts of data have been generated. This data provides new perspectives for system analysis and control, making it possible to directly extract system behavior and patterns from the data. Advances in artificial intelligence technology: The development of artificial intelligence, especially machine learning and deep learning technologies, provides powerful tools for data-driven control. These technologies can learn the dynamic characteristics of a system from large amounts of data and apply them to controller design. Challenges in practical applications: In many practical applications, the dynamic characteristics of a system are difficult to describe using traditional physical or mathematical models. For example, in fields such as autonomous driving and intelligent manufacturing, the uncertainty and complexity of the environment require control systems to adapt to rapidly changing conditions, making data-driven control an effective solution. Advantages of data-driven fault-tolerant control: Data-driven control does not rely on complex system models and can directly utilize the system's input / output data to design controllers.

[0003] Fault-tolerant control of systems is one of the core tasks in the research of data-driven fault-tolerant control. As modern systems become increasingly large-scale and complex, the requirements for system reliability and safety are becoming increasingly stringent. For example, failures in critical infrastructure such as aerospace, nuclear power plants, and chemical processes can cause enormous losses of life and property. Therefore, improving the fault tolerance of these systems has become an urgent need. The development of data-driven fault-tolerant control is closely related to neural network-based fault diagnosis technology. The development of fault detection and diagnosis technologies provides crucial support for fault-tolerant control, enabling systems to respond promptly when faults occur. Summary of the Invention

[0004] The purpose of this invention is to propose a data-driven fault-tolerant control method that can effectively solve the fault problems of complex systems and achieve good control results.

[0005] The specific technical solution of this invention is as follows: A data-driven fault-tolerant control method, comprising the following steps:

[0006] The system model for data-driven fault-tolerant control is shown below:

[0007] y(k+1)=f(y(k),y(k-1),...,y(kn y ),u(k)+p(k),u(k-1)+p(k-1),...,u(kn u )+p(kn u ))

[0008] In the formula, y(k)∈R represents the output, u(k)∈R represents the input, p(k)∈R represents an unknown actuator fault, k∈{0,1,...,} represents the sampling time, f(·) represents an unknown nonlinear function, and n y and n u Indicates the unknown order of the system;

[0009] The above nonlinear system is transformed into a linear input-output data model using the compact scheme dynamic linearization technique, as shown below:

[0010] y(k+1)=y(k)+Φ1(k)Δu(k)+Φ2(k)Δp(k)

[0011] In the formula, Δu(k)=u(k)-u(k-1), Δp(k)=p(k)-p(k-1), Φ1(k)∈R, Φ2(k)∈R are called pseudo-partial derivatives, which satisfy Φ1(k)≤b1, Φ2(k)≤b2, where b1 and b2 are positive constants.

[0012] According to claim 1, a data-driven fault-tolerant control method is characterized by using a neural network to estimate actuator faults and providing a data-driven fault-tolerant controller. The specific steps are as follows:

[0013] In a neural network structure, the network input vector is:

[0014] X=[Δy(k),Δy(k-1),Δu(k-1),Δu(k-2)] T

[0015] The radial basis vectors of the neural network are L = [l1, l2, ... l1]. m ] T , where l i The Gaussian function is shown below:

[0016]

[0017] The center vector of the j-th node in the network is:

[0018] c j =[c j1 ,c j2 ,…c jm ]

[0019] The base width vector of the network is:

[0020] Q = [q1, q2, ... q m ] T ,

[0021] Where, q j The base width parameter of node j

[0022] The network's weight vector is:

[0023] W = [w1, w2, ... w m ] T ,

[0024] The output of the neural network is shown below:

[0025]

[0026] According to the gradient descent method, the iterative algorithm for output weights, node centers, and node base width parameters is as follows:

[0027]

[0028] q j (k)=q j (k-1)+η1Δq j +α1[q j (k-1)-q j (k-2)]

[0029]

[0030] c ji (k)=c ji (k-1)+η1Δc ji +α1[c ji (k-1)-c ji (k-2)]

[0031] Where η1 is the learning rate and α1 is the momentum factor;

[0032] In designing the tight-form dynamic linearized model, the estimated values ​​corresponding to Φ1(k) and Φ2(k) are... The update algorithm is as follows:

[0033]

[0034] In the formula, μ>0, γ>0, α+β=1, this algorithm can guarantee The estimation error is bounded;

[0035] Based on the existing control input u(k) update algorithm, a control input update algorithm including estimated fault information is obtained, as shown below:

[0036]

[0037] In the formula, Let ρ be the estimated values ​​of Φ1(k), Φ2(k), and Δp(k), where ρ is the step size sequence and λ is the weight factor.

[0038] According to claim 1, a data-driven fault-tolerant control method is characterized by providing a proof of the convergence of the data-driven fault-tolerant control method to ensure the consistent eventual boundedness of the closed-loop system. The specific steps are as follows:

[0039] When y * (k+1)=y * When the value is const, the system is convergent.

[0040] The systematic error is defined as follows:

[0041] e(k) = y * (k)-y(k)

[0042] Substituting the control algorithm into the system's dynamic linearization equations yields:

[0043]

[0044] Define the following function:

[0045]

[0046] Simplifying, we get the following formula:

[0047]

[0048] Subtract y from both sides of the above equation * We can obtain:

[0049]

[0050] because Both are bounded, therefore satisfying:

[0051]

[0052] In the formula, ξ1 is a small positive number.

[0053] Substituting the above equation into the equation, we get the following equation:

[0054] |e(k+1)|≤(1-d1)|e(k)|+ξ1

[0055] |e(k+1)|≤(1-d1) 2 |e(k-1)|+(1-d1)ξ1+ξ1

[0056] |e(k+1)|≤(1-d1) k |e(1)|+(1-d1) k-1 ξ1+...(1+d1)ξ1+ξ1

[0057] From B007, we can obtain the following formula:

[0058]

[0059] That is, the system's output error is convergent. Attached Figure Description

[0060] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0061] Figure 2 This is a tracking diagram of the system when there are no faults in this invention;

[0062] Figure 3 As an example, the output tracing graph for faults is added using the method proposed in this invention;

[0063] Figure 4 The output tracing graph after processing the corresponding fault was processed using the method proposed in this invention in the example embodiment; Detailed Implementation

[0064] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0065] like Figure 1 As shown, a data-driven fault-tolerant control method includes the following steps:

[0066] Step 1: Set initial parameter values;

[0067] Step 2: Update algorithm parameters;

[0068] Step 3: Generate control input u(k) in real time based on the updated algorithm parameters;

[0069] Step 4: Update the algorithm parameters synchronously based on the tracking error and compensation error generated by the control input u(k);

[0070] References

[0071] Z.Hou,R.Chi,and H.Gao,"An Overview of Dynamic-Linearization-BasedData-Driven Control and Applications,"IEEE Transactions on IndustrialElectronics,vol.64,no.5,pp.4076-4090,2017,doi:10.1109 / tie.2016.2636126.

[0072] J.Li,Z.Wang,T. and Y.Shen,“Unknown input observer design forlinear parameter-varying systems in a bounded error context,”IEEETrans.Autom.Control,vol.66,no.9,pp.4246–4251,Sep.2020.doi:10.1109 / TAC.2020.3027646.

Claims

1. A data-driven fault-tolerant control method, characterized in that, Includes the following steps: Establish an input / output data model containing fault signals, specifically as follows: The discrete mathematical expression of the data-driven system containing fault signals is as follows: y(k+1)=f(y(k),y(k-1),...,y(kn y ),u(k)+p(k),u(k-1)+p(k-1),...,u(kn u )+p(kn u In the formula, y(k)∈R represents the output, u(k)∈R represents the input, p(k)∈R represents an unknown actuator fault, k∈{0,1,...,} represents the sampling time, f(·) represents an unknown nonlinear function, and n y and n u Indicates the unknown order of the system; The above data-driven system is transformed into a linear input-output data model using a tight-format dynamic linearization technique, as shown below: y(k+1)=y(k)+Φ1(k)Δu(k)+Φ2(k)Δp(k) In the formula, Δu(k)=u(k)-u(k-1), Δp(k)=p(k)-p(k-1), Φ1(k)∈R, Φ2(k)∈R are called pseudo-partial derivatives, which satisfy Φ1(k)≤b1, Φ2(k)≤b2, where b1 and b2 are positive constants; Design a fault observer based on a neural network and construct a fault-tolerant controller, specifically as follows: In a neural network structure, the network input vector is: X=[Δy(k),Δy(k-1),Δu(k-1),Δu(k-2)] T The radial basis vectors of the neural network are L = [l1, l2, ... l1]. m ] T , where l j The Gaussian function is shown below: The center vector c of the j-th node in the network j for: c j =[c j1 ,c j2 ,…,c ji ,…,c jm ] T The base width vector of the network is: Q=[q1,q2,…q m ] T Where, q j Let be the base width parameter of node j; The network's weight vector is: In=[in1,in2,…in m ] T Among them, w j Let j be the weight; The output of the neural network is shown below: According to the gradient descent method, the iterative algorithm for outputting weights, node centers, and node base width parameters is as follows: q j (k)=q j (k-1)+η1Δq j +α1[q j (k-1)-q j (k-2)] c ji (k)=c ji (k-1)+η1Δc ji +α1[c ji (k-1)-c ji (k-2)] Where η1 is the learning rate and α1 is the momentum factor; In the design of the compact dynamic linearized model, the estimated values ​​of Φ1(k) and Φ2(k) are... The update algorithm is as follows: In the formula, μ>0, γ>0, α+β=1, this algorithm can guarantee The estimation error is bounded; Based on the existing control input u(k) update algorithm, a control input update algorithm including estimated fault information is obtained, as shown below: Where, Let ρ be the estimated values ​​of Φ1(k), Φ2(k), and Δp(k), where ρ is the step size sequence and λ is the weight factor. A proof of the convergence of a data-driven fault-tolerant control method to ensure the uniform eventual boundedness of the closed-loop system is given, specifically: B001: When y * (k+1)=y * When the constant is const, the system is convergent. B002: The definition of systematic error is as follows: e(k)=y * (k)-y(k); B003: Substituting the control algorithm into the system's dynamic linearization equations yields: B004: Define the following function: B005: Simplifying B003 yields the following formula: B006: Subtract y from both sides of the above equation. * We can obtain: B007: Due to Φ1(k), Φ2(k), Δp(k), Both are bounded, therefore satisfying: In the formula, ξ1 is a small positive number; B008: Substituting B006 into B007, we get the following formula: |e(k+1)|≤(1-d1)|e(k)|+ξ1 |e(k+1)|≤(1-d1) 2 |e(k-1)|+(1-d1)ξ1+ξ1 |e(k+1)|≤(1-d1) k |e(1)|+(1-d1) k-1 ξ1+...(1-d1)ξ1+ξ1 B009: From B008, we can obtain the following formula: That is, the system's output error is convergent.

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