Sensor fault compensation control method based on preset time adaptive neural network dynamic gain observer

Abstract

The invention belongs to the technical field of automatic control and fault tolerance, and particularly relates to a sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer. According to the method, an integrated framework integrating observer design, fault compensation and preset time control is provided for an uncertain nonlinear system which is unmeasurable in state and has unknown nonlinearity and sensor faults. The method comprises the following steps: constructing an uncertain nonlinear system model with unknown sensor sensitivity, and approaching unknown nonlinear dynamics by using a radial basis function neural network; a self-adaptive neural network state observer based on dynamic gain is designed, simultaneous estimation of the system state and unknown nonlinearity is achieved, and gain over-estimation is avoided; designing a preset time output feedback controller by adopting an inversion control method on the basis of an observer estimation value, and ensuring that all closed-loop signals converge to a neighborhood near an original point within a time predetermined by a user, and the convergence time is irrelevant to an initial condition; and obtaining design requirements of control parameters through Lyapunov stability analysis. According to the method, rapid and accurate trajectory tracking and fault compensation can still be realized under the conditions of sensor faults, model uncertainty and external interference.

Description

Technical Field

[0001] This invention belongs to the technical fields of automation control, fault tolerance and intelligent systems, and specifically relates to a preset time adaptive neural network control method for uncertain systems with sensor failure, unmeasurable state and unknown nonlinearity. Background Technology

[0002] Nonlinear system control is a key challenge in the field of automation, its core being the handling of strong nonlinearity and parameter uncertainty in systems. Existing methods are mainly based on fixed-gain design and asymptotic stability theory, which struggle to maintain robust performance in dynamically changing environments. In particular, traditional control strategies have significant limitations when facing sensor failures: most studies assume accurate and reliable sensor outputs, but in real systems, sensors are susceptible to aging, environmental interference, and other factors, leading to gain drift, deviations, or even complete failure, severely impacting state estimation accuracy and control stability. Current sensor failure compensation methods largely rely on fault detection and diagnosis mechanisms, which suffer from detection delays and the risk of misjudgment, and are often separated from controller design, lacking systematic collaborative optimization. More importantly, existing control schemes mostly focus on asymptotic convergence or finite-time stability, with convergence times heavily dependent on initial conditions, failing to meet the stringent response time requirements of modern highly dynamic systems. Although preset-time control theory has made progress in recent years, achieving convergence within a user-specified time, these methods typically assume fully measurable states or only consider ideal sensor conditions, making them difficult to directly apply to real-world situations with sensor failures.

[0003] To address the aforementioned challenges, an integrated control scheme capable of simultaneously handling unpredictable states, sensor failures, and preset time constraints is urgently needed. While existing dynamic gain observer methods can adapt to some uncertainties, observation errors are significantly amplified under sensor failures. Although neural networks possess powerful approximation capabilities, traditional static neural networks struggle to maintain stable learning under fault conditions. More critically, existing research lacks a systematic framework that organically combines dynamic gain mechanisms, neural network approximation, and preset time stability theory, resulting in limited performance when dealing with multiple challenges such as time-varying sensor failures, unknown nonlinear dynamics, and time constraints. This invention aims to fill this technological gap by constructing a collaborative architecture between a dynamic gain neural network observer and a preset time controller. This architecture enables adaptive compensation for sensor failures and ensures the system achieves the desired control accuracy within a user-specified time, providing an innovative solution for the reliable control of uncertain nonlinear systems. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a unified framework integrating a dynamic gain observer, sensor fault compensation, and preset time control. This method enables accurate estimation and rapid tracking of the system state even when the sensor exhibits unknown time-varying sensitivity faults, ensuring system stability within a user-defined timeframe and convergence of the tracking error to a bounded small neighborhood. The method mainly includes: S1: Establish an uncertain nonlinear system model with sensor faults, where the output signal contains unknown time-varying sensitivity; S2: The unknown nonlinear function in the system is approximated by the first radial basis function neural network vector to obtain the first nonlinear system model approximated by the first neural network; S3: Design an adaptive neural network dynamic gain state observer based on the second radial basis function neural network vector to simultaneously estimate the system state and unknown nonlinear functions; S4: Based on the state estimate and nonlinear function estimate output by the adaptive neural network dynamic gain state observer, define the coordinate transformation, adopt the inversion control method, design the Lyapunov function, and obtain the preset time output feedback controller. S5: Based on Lyapunov stability theory, obtain the design requirements of control parameters, design dynamic gain adaptive law, neural network weight update law and virtual control signal to ensure that all signals of the closed-loop system are consistent and bounded, and that the system tracking error converges to a bounded neighborhood near the origin within a fixed time preset by the user.

[0005] Preferably, the expression for the uncertain nonlinear system model with sensor fault described in step S1 is: , , , in, For system status, Given two system state vectors, , To represent unknown nonlinear continuous functions in the dynamics of a system, For input control signals, For output signal, Indicates the measurement sensitivity of an unknown time-varying sensor, and satisfies These are the known lower bound constant and the unknown upper bound constant, respectively.

[0006] Preferably, the approximation process using the first radial basis function neural network vector described in step S2 includes: S21: Definition ;in, State vector The estimated value, For unknown nonlinear continuous functions The estimated value, To estimate the error; S22: Assuming an unknown nonlinear continuous function Satisfying the Lipschitz condition, i.e. ,in It is the Lipschitz constant; S23: Employing a first radial basis function neural network to... To perform an approximate approximation, i.e. in, The ideal weight vector for the first radial basis function neural network vector. For radial basis function vectors, For a bounded neural network approximation error, satisfying in, For unknown positive constants; S24: Based on the output feedback requirements, the uncertain nonlinear system model is transformed into a first nonlinear system model. The expression of the transformed model is: , , , in, For system status, Given two system state vectors, Let be the system order. , These are the system state vectors. The estimated value, To estimate the error, For input control signals, This is the output signal.

[0007] Preferably, the expression for the adaptive neural network dynamic gain state observer described in step S3 is: , , in, This is the estimate of the state vector of the first nonlinear system model by the adaptive neural network dynamic gain state observer. For input control signals, For output signal, The second radial basis function neural network vector is the first... The element corresponds to the first radial basis function neural network vector. The estimated value of each element, The second radial basis function neural network vector is the first... A weight factor matrix with elements. For the second radial basis function neural network, the first Radial basis functions of elements, For dynamic gain, Set a fixed positive gain for the observer.

[0008] Prior to this, step S4, the process of designing a preset time output feedback controller based on the inversion control method, includes: S41: Define coordinate transformation: , , in, For dynamic system tracking error, This is the estimate of the state vector of the first nonlinear system model by the adaptive neural network dynamic gain state observer. This serves as the intermediate virtual control signal for the inversion control method; S42: Design Input Signal Control Rate for , in, For dynamic system tracking error, The second radial basis function neural network vector is the first... The element corresponds to the first radial basis function neural network vector. The estimated value of each element, The second radial basis function neural network vector is the first... A weight factor matrix with elements. For the second radial basis function neural network, the first Radial basis functions of elements, Set a fixed positive gain for the controller. To meet Design parameters, Virtual control signal The derivative, For dynamic gain, Set a fixed gain for the observer.

[0009] Furthermore, the aforementioned design dynamic gain The adaptive law is: , , in, Fix the gain vector for the observer. It is a positive integer and satisfies , , A positive definite matrix The maximum and minimum eigenvalues, For the positive constants that need to be designed, It is a positive integer and satisfies , For positive integers, The first state of the system The observation error, This refers to the tracking error of the dynamic system.

[0010] Furthermore, the intermediate virtual control signal satisfy: , , in, For dynamic system tracking error, For dynamic gain, Set the gain of the observer to a fixed value. Set a fixed positive gain for the controller. To meet Design parameters, Unknown positive constant The estimated value, intermediate virtual control signal The derivative, The second radial basis function neural network vector is the first... The element corresponds to the first radial basis function neural network vector. The estimated value of each element, The second radial basis function neural network vector is the first... A weight factor matrix with elements. For the second radial basis function neural network, the first Radial basis functions of elements.

[0011] Furthermore, the second radial basis function neural network... Weight factor matrix of elements , The adaptive update rate is: , in, For positive integers, For the second radial basis function neural network, the first Radial basis functions of elements, For dynamic system tracking error

[0012] Furthermore, the parameters The adaptive update rate is: , in, For positive integers, To meet Design parameters, This refers to the tracking error of the dynamic system.

[0013] Furthermore, the positive definite matrix normal numbers The observer has a fixed positive gain. and the sensitivity of sensors measuring unknown time-varying parameters satisfy: , in, .

[0014] Furthermore, the positive parameter , satisfy: , , in, For dynamic gain, A positive definite matrix The largest eigenvalue, To meet Design parameters, For positive integers, This is the preset time value.

[0015] Furthermore, the radial basis functions of the second radial basis function neural network vector are all the same Gaussian function: , , , in, Let be the system state vector. Here are the radial basis function vectors of the radial basis function neural network. For the first The first radial basis function neural network of the nth... Radial basis functions This represents the number of neurons in a neural network. Indicates the first The set of centers of the receiving domain, Indicates the first In the The center of the receiving domain of each input, This indicates the number of inputs to the neural network. Indicates the first The width of the Gaussian mode of the radial basis function.

[0016] This invention offers at least the following advantages: The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer proposed in this invention has significant advantages over traditional methods. Traditional methods often struggle to simultaneously handle sensor faults, unmeasurable states, and strict time constraints, and frequently rely on fault detection mechanisms, resulting in response delays and performance degradation. In contrast, this invention integrates a dynamic gain observer and a preset time controller, enabling accurate estimation of the system state and unknown nonlinearities even with unknown time-varying sensor faults. It also ensures that the tracking error converges to a bounded neighborhood within a user-specified timeframe, independent of initial conditions and fault severity. This method significantly improves the system's robustness and control accuracy under fault conditions, effectively suppressing control oscillations and energy loss by avoiding gain overestimation. It achieves a balance between stability, speed, and control efficiency, making it particularly suitable for highly dynamic systems such as autonomous driving and aerospace systems with extremely high safety and real-time requirements. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a tracking and estimation curve of the first state of the system in an embodiment of the present invention; Figure 3 This is a tracking and estimation curve of the second state of the system in an embodiment of the present invention; Figure 4 This is a graph showing the estimation error curves of the first and second states of the system in an embodiment of the present invention; Figure 5 This is a graph showing the change in the dynamic gain of the observer in an embodiment of the present invention. Figure 6 This is an estimation curve of the unknown continuous function of the system in an embodiment of the present invention; Figure 7 This is a graph of the control input signal in an embodiment of the present invention. Detailed Implementation

[0018] Next, the implementation details of the technical solution will be clearly and completely described with reference to the accompanying drawings of the embodiments of the present invention. It should be noted that the described embodiments are merely representative examples to facilitate understanding of the present invention and do not constitute a limitation on the scope of the present invention. Other reasonable implementation methods that can be derived by those skilled in the art based on the technical ideas and design principles of the present invention without creative effort should all be considered to fall within the protection scope of the present invention.

[0019] Example The method proposed in this invention was applied to a Van der Pol oscillator system to verify the effectiveness of the proposed control method. The Van der Pol oscillator nonlinear system, expressed in controllable canonical form, is described below: , , , Wherein, the unknown continuous function in the model is Sensor fault parameters All radial basis function neural networks (RBFNNs) contain activation functions that include Each node, its center Select as ,width Set to 1. The dynamic gain state observer based on RBFNN is constructed as follows: , , in, Therefore, the number of inputs to the neural network The initial system state is set to The initial weights are chosen as follows: The online weight update law, dynamic gain, and control law of the Radial Basis Function Neural Network (RBFNN) are as follows: , , , , , , , , The specific parameter selections are as follows: .

[0020] like Figure 2 and Figure 3 As shown, the actual trajectory tracking curves of the system in the first and second states closely match the desired trajectory. The results demonstrate that the designed control strategy effectively suppresses the effects of unknown external disturbances and sensor malfunctions in the closed-loop system, achieving ideal tracking performance. Figure 4The estimation error curves of the dynamic gain neural network observer for the first and second states of the system are shown. It can be seen that the estimation error is always controlled within a very small range throughout the estimation process, which reflects the high precision characteristics of the observer. Figure 5 The evolution curve of the dynamic gain parameter in the observer is given. The curve shows that the dynamic gain tends to a stable value after adaptive adjustment in the initial stage, indicating that the observer structure has good convergence characteristics. Figure 6 The estimation performance of the observer for unknown disturbances in the system is further presented. The results show that the estimator based on the online dynamic gain neural network can accurately approximate the actual disturbance and continuously compensate for the disturbance effect in real time through a weight adaptive mechanism after the initial transient. This indicates that the proposed dynamic gain observer can adaptively adjust the gain according to the system state and error information, significantly enhancing its robustness to system uncertainties and external disturbances, thereby improving the overall estimation accuracy and stability. Figure 7 The simulation results demonstrate the change of the control input signal over time, showing that the input signal remains bounded and conforms to the physical constraints of actual execution. In summary, the simulation results show that the proposed method can still achieve fast and accurate trajectory tracking and effective fault compensation even under complex conditions involving sensor failures, model uncertainties, and external interference, verifying the effectiveness and engineering applicability of the invention.

[0021] The above embodiments further illustrate the purpose, technical means, and beneficial effects of the embodiments of the present invention. It should be understood that the embodiments described herein are merely preferred examples embodying the core ideas of the present invention and do not constitute a limitation thereof. Any reasonable changes, equivalent substitutions, or technical improvements made based on the design ideas and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sensor fault compensation control method based on a preset time-adaptive neural network dynamic gain observer, characterized in that, Includes the following steps: S1: Establish an uncertain nonlinear system model with sensor faults, where the output signal contains unknown time-varying sensitivity; S2: The unknown nonlinear function in the system is approximated by the first radial basis function neural network vector to obtain the first nonlinear system model approximated by the first neural network; S3: Design an adaptive neural network dynamic gain state observer based on the second radial basis function neural network vector to simultaneously estimate the system state and unknown nonlinear functions; S4: Based on the state estimate and nonlinear function estimate output by the adaptive neural network dynamic gain state observer, define the coordinate transformation, adopt the inversion control method, design the Lyapunov function, and obtain the preset time output feedback controller. S5: Based on Lyapunov stability theory, obtain the design requirements of control parameters, design dynamic gain adaptive law, neural network weight update law and virtual control signal to ensure that all signals of the closed-loop system are consistent and bounded, and that the system tracking error converges to a bounded neighborhood near the origin within a fixed time preset by the user.

2. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 1, characterized in that, The expression for the uncertain nonlinear system model with sensor fault described in S1 is as follows: ， ， ， in, For system status, Given two system state vectors, , To represent unknown nonlinear continuous functions in the dynamics of a system, For input control signals, For output signal, Indicates the measurement sensitivity of an unknown time-varying sensor, and satisfies These are the known lower bound constant and the unknown upper bound constant, respectively.

3. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 1, characterized in that, The approximation process using the first radial basis function neural network vector, as described in S2, includes: S21: Definition ;in, State vector The estimated value, For unknown nonlinear continuous functions The estimated value, To estimate the error; S22: Assuming an unknown nonlinear continuous function Satisfying the Lipschitz condition, i.e. ,in It is the Lipschitz constant; S23: Employing a first radial basis function neural network to... To perform an approximate approximation, i.e. in, The ideal weight vector for the first radial basis function neural network vector. Let them be radial basis function vectors. For a bounded neural network approximation error, satisfying in, For unknown positive constants; S24: Based on the output feedback requirements, the uncertain nonlinear system model is transformed into a first nonlinear system model. The expression of the transformed model is: ， ， ， in, For system status, Given two system state vectors, Let be the system order. , These are the system state vectors. The estimated value, To estimate the error, For input control signals, This is the output signal.

4. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 1, characterized in that, The expression for the adaptive neural network dynamic gain state observer described in S3 is: ， ， in, This is the estimate of the state vector of the first nonlinear system model by the adaptive neural network dynamic gain state observer. For input control signals, For output signal, The second radial basis function neural network vector is the first... The element corresponds to the first radial basis function neural network vector. The estimated value of each element, The second radial basis function neural network vector is the first... A weight factor matrix with elements. For the second radial basis function neural network, the first Radial basis functions of elements, For dynamic gain, Set a fixed positive gain for the observer.

5. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 1, characterized in that, The process of designing a preset time output feedback controller based on the inversion control method described in S4 includes: S41: Define coordinate transformation: ， ， in, For dynamic system tracking error, This is the estimate of the state vector of the first nonlinear system model by the adaptive neural network dynamic gain state observer. This serves as the intermediate virtual control signal for the inversion control method; S42: Design Input Signal Control Rate for ， in, For dynamic system tracking error, The second radial basis function neural network vector is the first... The element corresponds to the first radial basis function neural network vector. The estimated value of each element, The second radial basis function neural network vector is the first... A weight factor matrix with elements. For the second radial basis function neural network, the first Radial basis functions of elements, Set a fixed positive gain for the controller. To meet Design parameters, Virtual control signal The derivative, For dynamic gain, Set a fixed gain for the observer.

6. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 1 or 4, characterized in that, S5 describes the design dynamic gain The adaptive law is: , ， in, Fix the gain vector for the observer. It is a positive integer and satisfies , , A positive definite matrix Maximum and minimum eigenvalues, For the positive constants that need to be designed, It is a positive integer and satisfies , For positive integers, The first state of the system The observation error, This refers to the tracking error of the dynamic system.

7. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 1 or 5, characterized in that, S5 intermediate virtual control signal satisfy: ， ， in, For dynamic system tracking error, For dynamic gain, Set the gain of the observer to a fixed value. Set a fixed positive gain for the controller. To meet Design parameters, Unknown positive constant The estimated value, intermediate virtual control signal The derivative, The second radial basis function neural network vector is the first... The element corresponds to the first radial basis function neural network vector. The estimated value of each element, The second radial basis function neural network vector is the first... A weight factor matrix with elements. For the second radial basis function neural network, the first Radial basis functions of elements.

8. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 1, 4, 5 or 7, wherein the second radial basis function neural network described in S5... Weight factor matrix of elements , The adaptive update rate is: ， in, For positive integers, For the second radial basis function neural network, the first Radial basis functions of elements, This refers to the tracking error of the dynamic system.

9. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 7, characterized in that, The parameters The adaptive update rate is: ， in, For positive integers, To meet Design parameters, This refers to the tracking error of the dynamic system.

10. The sensor fault compensation control method based on a preset time adaptive neural network dynamic gain observer according to claim 6, characterized in that, The positive definite matrix normal numbers The observer has a fixed positive gain. and the sensitivity of sensors that measure unknown time-varying parameters satisfy: ， in, .

11. The sensor fault compensation control method based on a preset time-adaptive neural network dynamic gain observer according to claim 5, 6, 7, 8 or 9, characterized in that, The positive parameter , satisfy: ， ， in, For dynamic gain, A positive definite matrix The largest eigenvalue, To meet Design parameters, For positive integers, This is the preset time value.

12. The sensor fault compensation control method based on a preset time-adaptive neural network dynamic gain observer according to claim 3, 4, 5, 7 or 8, characterized in that, The radial basis functions of both the first and second radial basis function neural network vectors are the same Gaussian functions: ， ， ， in, Let be the system state vector. Here are the radial basis function vectors of the radial basis function neural network. For the first The first radial basis function neural network of the nth... Radial basis functions This represents the number of neurons in a neural network. Indicates the first The set of centers of the receiving domain, Indicates the first In the The center of the receiving domain of each input, This indicates the number of inputs to the neural network. Indicates the first The width of the Gaussian mode of the radial basis function.

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