Robust adaptive finite-time fault-tolerant control method and storage medium thereof

Abstract

This invention provides a robust adaptive finite-time fault-tolerant control method for T-S fuzzy systems with component faults and external disturbances. The method includes: modeling system component faults as multiplicative faults to establish a more general system fault model; constructing a fault-tolerant compensation controller using online estimation information provided by an adaptive mechanism to effectively handle faults, external disturbances, and input saturation; and introducing finite-time control based on the adaptive mechanism to ensure the finite-time convergence of the system trajectory tracking error. This invention establishes a system fault model, which is beneficial for describing system component faults, actuator faults, and uncertainties. It designs an adaptive fault-tolerant mechanism to estimate the upper bound of unknown parameters without needing to know the specific parameter information of the faults and disturbances. To improve fault tolerance performance and address saturated input nonlinearity, a finite-time control method is proposed to ensure the finite-time stability of the closed-loop fault-tolerant system and the finite-time convergence of the tracking error, thereby improving fault tolerance performance.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and to a robust adaptive finite-time fault-tolerant control method and its storage medium. More specifically, it relates to a robust adaptive finite-time fault-tolerant control method for a TS fuzzy system based on component failures and external disturbances. Background Technology

[0002] In pursuit of higher productivity, the complexity of today's industrial systems has increased dramatically, significantly raising the probability of failures in these complex systems. On the one hand, component failures, which can be described as multiplicative failures, can lead to unknown changes in system dynamics, resulting in severe performance degradation or even instability, ultimately causing catastrophic accidents. On the other hand, real-world systems almost always contain uncertainties and external disturbances, as well as the ubiquitous actuator saturation phenomenon, which presents even greater challenges to control systems. Adaptive fault-tolerant control strategies have become a popular technique due to their ability to handle variations in unknown parameters and the absence of explicit fault detection and diagnosis modules. Given the complexity, suddenness, and unpredictability of failures, researching robust adaptive finite-time fault-tolerant schemes for TS fuzzy systems with component failures and external disturbances is a challenging and significant topic in order to address uncertainties in the system and restore system performance to a certain extent in a timely manner.

[0003] Existing literature primarily considers actuator failures, focusing only on control channel matrix failures and uncertainties, with limited research on system component failures. System component failures can be described as multiplicative failures, encompassing both system matrix and control matrix failures. Therefore, their descriptions are more general. It should be noted that system component failures can lead to unknown changes in system dynamics, and even instability, thus warranting further investigation. Summary of the Invention

[0004] To address the aforementioned technical problems, a robust adaptive finite-time fault-tolerant control method is provided. This invention primarily targets TS fuzzy systems with system component faults and external disturbances, designing a robust adaptive finite-time fault-tolerant control method. System component faults are modeled as multiplicative faults, establishing a more general system fault model that can reasonably represent system component faults, actuator faults, and uncertainties. Utilizing online estimation information provided by the adaptive mechanism, a fault-tolerant compensation controller is constructed to effectively handle faults, external disturbances, and input saturation. Then, to improve the system's fault-tolerant transient performance, finite-time control is introduced based on the adaptive mechanism, ensuring the finite-time convergence property of the system trajectory tracking error.

[0005] The technical means employed in this invention are as follows:

[0006] A robust adaptive finite-time fault-tolerant control method includes:

[0007] S1. Model system component failures as multiplicative failures to establish a more general system failure model that can reasonably represent system component failures, actuator failures, and uncertainties.

[0008] S2. Utilize the online estimation information provided by the adaptive mechanism to construct a fault-tolerant compensation controller, which can effectively handle faults, external disturbances, and input saturation.

[0009] S3. Based on the adaptive mechanism, finite-time control is introduced to ensure the finite-time convergence property of the system trajectory tracking error.

[0010] Furthermore, the specific implementation process of step S1 includes:

[0011] S11. Based on a class of nonlinear continuous-time systems containing r fuzzy rules, infer the global fuzzy system;

[0012] S12. Considering the component failures in system matrices A and B, the following failure model is established:

[0013]

[0014] Where, ΔA fi ,ΔB fi This represents the changes in system components caused by faults and uncertainties, satisfying the following assumptions:

[0015]

[0016] in, It represents the unknown upper bound of component failure and uncertainty.

[0017] Furthermore, the specific implementation process of step S11 includes:

[0018] S111, Assumption The nonlinear continuous-time system is then represented as:

[0019]

[0020] in, It is the predecessor variable; symbol Used to represent fuzzy sets Let represent the number of fuzzy sets; i = 1, ..., r represent the number of fuzzy rules; ψ(t) represent a function of x(t), where Represents the system state vector; u s (t) represents the control signal affected by saturation nonlinearity, where the saturation nonlinearity is as follows:

[0021]

[0022] Where u(t) represents the command control signal generated by the designed control scheme, where u min ,u max Represents the known lower and upper bound constraints of the control input;

[0023] S112, Represent the external disturbance as Assume the external disturbance is unknown and bounded, i.e. in Given that is an unknown scalar, and assuming that all matrices in a nonlinear continuous-time system have rational dimensions for algebraic operations, the global fuzzy system is deduced as follows:

[0024]

[0025] in, α i ≥0, It is a fuzzy set The degree of membership.

[0026] Furthermore, step S1 also includes the step of introducing some necessary assumptions for the robust adaptive fault-tolerant tracking control problem, including:

[0027] Assumption 1: For the fault-tolerant method considered with input and control matrix faults, the matrix... It is the full order, that is

[0028] Lemma 1: The following inequalities hold:

[0029] x T (t)PBB T Px(t)≥τ‖x T (t)PB‖ 2

[0030] Lemma 2: For a constant ε > 0.5, the matrix And Then the following relationship holds:

[0031]

[0032] Lemma 3: For any positive real numbers m, n, w and any real variables φ, ψ, then:

[0033]

[0034] Lemma 4: For the variable χ l , If the constant 0 < a < 1, then the following equation holds:

[0035]

[0036] Lemma 5: For the system Assume it exists For a positive definite function V(ξ): D→R, with scalar c>0, 0<β<1, η>0, the following equation holds:

[0037]

[0038] Representation system The trajectory is stable in a finite time.

[0039] Furthermore, the specific implementation process of step S2 includes:

[0040] S21. Construct an adaptive finite-time fault-tolerant controller with a parallel distributed compensation control strategy, as follows:

[0041]

[0042] in, This represents a pre-designed model matching term inherited from classical reference tracking control to stabilize the system. This model matching term is assumed to be known beforehand and does not need to be designed in this way; K α,k This indicates additional control signals used to compensate for faults and other factors that may negatively impact the system;

[0043] S22. Define the state tracking error as follows:

[0044] e(t) = x(t) - x r (t)

[0045] S23, when the control signal K is given α,k Before that, we introduce the following variable definitions:

[0046]

[0047] Wherein, the parameter τ is selected according to the formula of Lemma 1;

[0048] S24. In order to handle system component failures, control signal K... α,1 Defined as:

[0049]

[0050]

[0051] S25. Considering the possibility of actuator failure, control signal K α,2 Defined as:

[0052]

[0053] Among them, the estimation of the unknown quantity k2 Its adaptive law is And γ2 > 0 indicates a constant adaptive gain;

[0054] S26. Considering the effect of input saturation, the control signal K... α,3 Defined as:

[0055]

[0056] Where, Δu=u s -u;

[0057] S27. Considering the influence of external disturbances, control signal K α,4 Defined as:

[0058]

[0059] Among them, the estimation of the unknown quantity k3 Its adaptive law is And γ3 > 0 indicates a constant adaptive gain;

[0060] S28. In order to achieve finite-time convergence, the control signal K... α,5 Defined as:

[0061]

[0062] Among them, the estimation of the unknown quantity k4 Its adaptive law is

[0063] Furthermore, the specific implementation process of step S3 includes: the stability of the tracking error system and the parameter estimation error system is guaranteed by the following theorem:

[0064] Theorem 1: Considering the faulty TS fuzzy system, the control law and the adaptive law, and the possible input saturation, the faulty TS fuzzy system is actually finite-time stable, and the state tracking error converges to a small region of the origin in finite time.

[0065] prove:

[0066] S31. By applying the adaptive finite-time fault-tolerant controller constructed in step S21 to the fault model established in step S12, the error dynamic system is described as follows:

[0067]

[0068] S32. Consider the following Lyapunov function:

[0069]

[0070] in, It is the parameter estimation error;

[0071] The time derivatives of the S33 and Lyapunov functions are:

[0072]

[0073] S34. Based on Lemma 1 and control signal K α,1 Control signal K α,2 Control signal K α,3 Control signal K α,4 and control signal K α,5 This leads to the following inequality:

[0074]

[0075]

[0076]

[0077]

[0078] S35, when ||e T When PB(α)||≥0, then:

[0079]

[0080] S36. According to error dynamic analysis, we can obtain:

[0081]

[0082]

[0083]

[0084]

[0085] S37. Based on the above analysis, the following inequality can be obtained:

[0086]

[0087] S38. Substituting the adaptive update law into the inequality in step S37, we get the following equation:

[0088]

[0089] S39. According to the preset tracking controller, there exists a positive definite symmetric matrix Q such that the following equation satisfies

[0090] P(A(α)+B(α)F(α))+(A(α)+B(α)F(α)) T P = -Q

[0091] S40, then by the inequality Rewrite the inequality in step S38 as follows:

[0092]

[0093] S41. Based on Lemma 2, for any constant ε s If > 0.5, s = 1, 2, 3, 4, then:

[0094]

[0095] S42. Based on the above two inequalities, we can further obtain

[0096]

[0097] S43. Based on Lemma 3, the following inequality can be obtained:

[0098]

[0099] Among them,

[0100] S44. Based on the above analysis, we have:

[0101]

[0102] in,

[0103] S45. Based on the above analysis, we have the following formula:

[0104]

[0105] make Where ρ∈(0,1), V(0) is the initial condition of V, then according to Lemma 3, we have This means that the closed-loop system is stable in a practically finite time.

[0106] S46. According to the formula in step S45, we have This means that V is bounded, and the signal... It is also bounded, due to the ideal state trajectory x r Since x(t) is bounded, it can be deduced that the state x(t) is bounded.

[0107] The present invention also provides a storage medium storing a computer instruction set; when the computer instruction set is executed by a processor, it implements the robust adaptive finite-time fault-tolerant control method described above.

[0108] Compared with the prior art, the present invention has the following advantages:

[0109] 1. The robust adaptive finite-time fault-tolerant control method provided by this invention establishes a more general system fault model, which is beneficial for describing system component faults, actuator faults and uncertainties. Based on this, an adaptive fault-tolerant mechanism is designed to estimate the upper bound of unknown parameters without needing to know the specific parameter information of the fault and disturbance, and has better transient performance, applicability and disturbance attenuation capability.

[0110] 2. This invention proposes a finite-time control method to improve fault tolerance performance and address saturated input nonlinearity. This method ensures the finite-time stability of the closed-loop fault-tolerant system and the finite-time convergence of the tracking error, thereby improving fault tolerance performance.

[0111] 3. The robust adaptive finite-time fault-tolerant control method provided by the present invention has the advantage of improving the system control quality without changing the structure or parameters of the original controller.

[0112] Based on the above reasons, this invention can be widely applied in fields such as automatic control. Attached Figure Description

[0113] 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 based on these drawings without creative effort.

[0114] Figure 1 This is a flowchart of the method of the present invention.

[0115] Figure 2 The membership function of the fuzzy system provided in the embodiments of the present invention.

[0116] Figure 3 The fault system and fault tolerance result curves provided in the embodiments of the present invention.

[0117] Figure 4 The state trajectory tracking error curve provided in the embodiment of the present invention

[0118] Figure 5 The control input u(t) curve is provided for an embodiment of the present invention. Detailed Implementation

[0119] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0120] 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, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. 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.

[0121] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0122] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0123] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0124] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0125] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0126] like Figure 1 As shown, this invention provides a robust adaptive finite-time fault-tolerant control method, comprising:

[0127] S1. Model system component failures as multiplicative failures to establish a more general system failure model that can reasonably represent system component failures, actuator failures, and uncertainties.

[0128] S2. Utilize the online estimation information provided by the adaptive mechanism to construct a fault-tolerant compensation controller, which can effectively handle faults, external disturbances, and input saturation.

[0129] S3. Based on the adaptive mechanism, finite-time control is introduced to ensure the finite-time convergence property of the system trajectory tracking error.

[0130] In a specific implementation, as a preferred embodiment of the present invention, the specific implementation process of step S1 includes:

[0131] S11. Based on a class of nonlinear continuous-time systems containing r fuzzy rules, infer the global fuzzy system;

[0132] S111, Assumption The nonlinear continuous-time system is then represented as:

[0133]

[0134] in, It is the predecessor variable; symbol Used to represent fuzzy sets Let represent the number of fuzzy sets; i = 1, ..., r represent the number of fuzzy rules; ψ(t) represent a function of x(t), where Represents the system state vector; u s (t) represents the control signal affected by saturation nonlinearity, where the saturation nonlinearity is as follows:

[0135]

[0136] Where u(t) represents the command control signal generated by the designed control scheme, where u min ,u max Represents the known lower and upper bound constraints of the control input;

[0137] S112, Represent the external disturbance as Assume the external disturbance is unknown and bounded, i.e. in Given that is an unknown scalar, and assuming that all matrices in a nonlinear continuous-time system have rational dimensions for algebraic operations, the global fuzzy system is deduced as follows:

[0138]

[0139] in, α i ≥0, It is a fuzzy set The degree of membership.

[0140] S12. Considering the component failures in system matrices A and B, the following failure model is established:

[0141]

[0142] Where, ΔA fi ,ΔB fi This represents the changes in system components caused by faults and uncertainties, satisfying the following assumptions:

[0143]

[0144] in, This represents an unknown upper bound for component failures and uncertainties. In this embodiment, the possible failure types considered are those caused by A. fi B fi The system component failure represented has the same structure as the uncertainty. Consider the uncertainty ΔA. i ,ΔB i ΔA fi =ΔA i +A fi and ΔB fi =ΔB i +B fi It is worth noting that the "amplitude" of the fault is much greater than the uncertainty, and its impact on system performance is more severe. The fault model established in step S12 represents a type of multiplicative fault in the state matrix and input matrix, rather than considering only actuator faults. Many real-world faults and other negative impacts in real-world systems can be described by the fault model established in step S12, such as actuator faults, system disturbances, and component failures caused by vibration and aging. Therefore, theoretically, the system fault model established in this invention is more general but also more complex, making fault-tolerant controller design more challenging.

[0145] In a specific implementation, as a preferred embodiment of the present invention, step S1 further includes the step of introducing some necessary assumptions for the robust adaptive fault-tolerant tracking control problem, including:

[0146] Assumption 1: For the fault-tolerant method considered with input and control matrix faults, the matrix... It is the full order, that is In this embodiment, Assumption 1 concerns the redundancy of the system actuators, which is essential for fully compensating for component failures and disturbances. For the control problem under consideration, a more fundamental assumption is that the actuator under saturation constraints can still guarantee the feasibility of control performance.

[0147] Lemma 1: The following inequalities hold:

[0148] x T (t)PBB T Px(t)≥τ‖x T (t)PB‖ 2

[0149] Lemma 2: For a constant ε > 0.5, the matrix and Then the following relationship holds:

[0150]

[0151] Lemma 3: For any positive real numbers m, n, w and any real variables φ, ψ, then:

[0152]

[0153] Lemma 4: For variables If the constant 0 < a < 1, then the following equation holds:

[0154]

[0155] Lemma 5: For the system Assume it exists For a positive definite function V(ξ): D→R, with scalar c>0, 0<β<1, η>0, the following equation holds:

[0156]

[0157] Representation system The trajectory is stable in a finite time.

[0158] For a given target or reference x(t) = x r (t), under the influence of component failure, input saturation, and external interference, the goal of this embodiment is to construct an adaptive finite-time compensated fault-tolerant tracking controller to ensure that all closed-loop signals are uniformly bounded. Furthermore, after a finite time period, the tracking error remains within a small neighborhood of the bounded set. Specifically, as a preferred embodiment of the present invention, the specific implementation process of step S2 includes:

[0159] S21. Construct an adaptive finite-time fault-tolerant controller with a parallel distributed compensation control strategy, as follows:

[0160]

[0161] in, This represents a pre-designed model matching term inherited from classical reference tracking control to stabilize the system. This model matching term is assumed to be known beforehand and does not need to be designed in this way; K α,k This indicates additional control signals used to compensate for faults and other factors that may negatively impact the system;

[0162] S22. Define the state tracking error as follows:

[0163] e(t) = x(t) - x r (t)

[0164] S23, when the control signal K is given α,k Before that, we introduce the following variable definitions:

[0165]

[0166] The parameter τ is chosen according to the formula in Lemma 1; for simplicity, the time dependence represented by the symbol (t) can be ignored in the following description when there is no definition conflict.

[0167] S24. In order to handle system component failures, control signal K... α,1 Defined as:

[0168]

[0169]

[0170] S25. Considering the possibility of actuator failure, control signal K α,2 Defined as:

[0171]

[0172] Among them, the estimation of the unknown quantity k2 Its adaptive law is And γ2 > 0 indicates a constant adaptive gain;

[0173] S26. Considering the effect of input saturation, the control signal K... α,3 Defined as:

[0174]

[0175] Where, Δu=u s -u;

[0176] S27. Considering the influence of external disturbances, control signal K α,4 Defined as:

[0177]

[0178] Among them, the estimation of the unknown quantity k3 Its adaptive law is And γ3 > 0 indicates a constant adaptive gain;

[0179] S28. In order to achieve finite-time convergence, the control signal K... α,5 Defined as:

[0180]

[0181] Among them, the estimation of the unknown quantity k4 Its adaptive law is

[0182] In this embodiment, the designed active fault-tolerant controller has the advantage of improving system control quality without changing the structure or parameters of the original controller.

[0183] In a specific implementation, as a preferred embodiment of the present invention, the specific implementation process of step S3 includes: the stability of the tracking error system and the parameter estimation error system is guaranteed by the following theorem:

[0184] Theorem 1: Considering the faulty TS fuzzy system, the control law and the adaptive law, and the possible input saturation, the faulty TS fuzzy system is actually finite-time stable, and the state tracking error converges to a small region of the origin in finite time.

[0185] prove:

[0186] S31. By applying the adaptive finite-time fault-tolerant controller constructed in step S21 to the fault model established in step S12, the error dynamic system is described as follows:

[0187]

[0188] S32. Consider the following Lyapunov function:

[0189]

[0190] in, It is the parameter estimation error;

[0191] The time derivatives of the S33 and Lyapunov functions are:

[0192]

[0193] S34. Based on Lemma 1 and control signal K α,1 Control signal K α,2 Control signal K α,3 Control signal K α,4 and control signal K α,5 This leads to the following inequality:

[0194]

[0195]

[0196]

[0197]

[0198] S35, when ||e T When PB(α)||≥0, then:

[0199]

[0200] S36. According to error dynamic analysis, we can obtain:

[0201]

[0202]

[0203]

[0204]

[0205] S37. Based on the above analysis, the following inequality can be obtained:

[0206]

[0207] S38. Substituting the adaptive update law into the inequality in step S37, we get the following equation:

[0208]

[0209] S39. According to the preset tracking controller, there exists a positive definite symmetric matrix Q such that the following equation satisfies

[0210] P(A(α)+B(α)F(α))+(A(α)+B(α)F(α)) T P = -Q

[0211] S40, then by the inequality Rewrite the inequality in step S38 as follows:

[0212]

[0213] S41. Based on Lemma 2, for any constant ε s If > 0.5, s = 1, 2, 3, 4, then:

[0214]

[0215] S42. Based on the above two inequalities, we can further obtain

[0216]

[0217] S43. Based on Lemma 3, the following inequality can be obtained:

[0218]

[0219] in,

[0220] S44. Based on the above analysis, we have:

[0221]

[0222] in,

[0223] S45. Based on the above analysis, we have the following formula:

[0224]

[0225] make Where ρ∈(0,1), V(0) is the initial condition of V, then according to Lemma 3, we have This means that the closed-loop system is stable in a practically finite time.

[0226] S46. According to the formula in step S45, we have This means that V is bounded, and the signal... It is also bounded, due to the ideal state trajectory x r Since x(t) is bounded, it can be deduced that the state x(t) is bounded.

[0227] Example

[0228] This invention verifies the effectiveness of the proposed method through a numerical simulation example. The simulation results are as follows: Figure 2-5 As shown. Among them, as Figure 2 The figure shows the membership function of the fuzzy system. The fault curve and fault tolerance results are shown below. Figure 3 As shown in the figure, system component failures and actuator failures are introduced at times t=15s and t=30s, respectively. It can be seen from the figure that the fault-tolerant control scheme proposed in this invention can effectively handle multiplicative system failures, suppress noise, restore the stability of the faulty system, and achieve finite-time control. The curve of the tracking error e is shown in the figure. Figure 4 As shown, the fault-tolerant control strategy proposed in this invention can effectively handle faults, and the error converges within a finite time, achieving good trajectory tracking control. Figure 5 The control signal shown is a diagram, and it can be seen that it always satisfies the saturation constraint.

[0229] 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 modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such 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 robust adaptive finite-time fault-tolerant control method, characterized in that, include: S1. Model system component failures as multiplicative failures, establish a system failure model to represent system component failures, actuator failures, and uncertainties. This also includes the step of introducing assumptions for the robust adaptive fault-tolerant tracking control problem, including: Assumption 1 : For the considered fault-tolerant method with input and control matrix faults, the matrices are row full rank, i.e. ; Lemma 1: The following inequalities hold: Lemma 2: For a constant , matrix , and , the following relation holds: Lemma 3: For any positive real number and any real variable then we have: Lemma 4: For variables , constants , the following holds: Lemma 5: For the system , assuming there exists a positive definite function , scalar , the following holds: Display system whose trajectories are actually finite-time stable; S2. Utilizing the online estimation information provided by the adaptive mechanism, a fault-tolerant compensation controller is constructed to effectively handle faults, external disturbances, and input saturation, including: S21. Construct an adaptive finite-time fault-tolerant controller with a parallel distributed compensation control strategy, as follows: in, This represents a pre-designed model matching term inherited from classical reference tracking control to stabilize the system. This model matching term is assumed to be known in advance and does not need to be designed in this way. This indicates additional control signals used to compensate for faults and other factors that may negatively impact the system; S22. Define the state tracking error as follows: S23, in response to the control signal Prior to, introduce the definition of the following variables: where the parameters According to the formula of the lemma 1 S24, in order to handle system component failure, a control signal is defined as: in, , For unknown quantities The estimate has an adaptive update law as follows: ,and Indicates constant adaptive gain; S25, taking into account possible actuator faults, the control signal is defined as: where the estimate of the unknown quantity is given by and its adaptive law is given by and denotes a constant adaptive gain; S26, considering the influence of input saturation, the control signal is defined as: wherein ; S27, taking into account the influence of external disturbances, the control signal is defined as: where the estimate of the unknown quantity is given by and its adaptive law is given by and denotes a constant adaptive gain; S28, in order to realize finite-time convergence, the control signal is defined as: Among them, the unknown quantity Estimate Its adaptive law is ; S3. Based on the adaptive mechanism, finite-time control is introduced to ensure the finite-time convergence property of the system trajectory tracking error. 2.The robust adaptive finite-time fault-tolerant control method according to claim 1, characterized in that, The specific implementation process of step S1 includes: S11. Based on a class of nonlinear continuous-time systems with fuzzy rules, a global fuzzy system is inferred. S12, taking into account component failures in the system matrix A , B , a failure model is established as follows: wherein, represents the change in system components due to faults and uncertainties, satisfying the following assumptions: in, It represents the unknown upper bound of component failure and uncertainty. 3.The robust adaptive finite-time fault-tolerant control method according to claim 2, characterized in that, The specific implementation process of step S11 includes: S111, assume = = = then the nonlinear continuous-time system is represented as​​​​​​ in, It is the predecessor variable; symbol Used to represent fuzzy sets Indicates the number of fuzzy sets; Indicates the number of fuzzy rules; Indicates about The function, where Represents the system state vector; The control signal is affected by saturation nonlinearity, where the saturation nonlinearity is as follows: in, This represents the command control signal generated by the designed control scheme, where Represents the known lower and upper bound constraints of the control input; S112, Represent the external disturbance as Assuming the external disturbance is unknown and bounded, i.e. ,in Given that is an unknown scalar, and assuming that all matrices in a nonlinear continuous-time system have a rational dimension for algebraic operations, the global fuzzy system is deduced as follows: wherein , , ; is the membership of the fuzzy set . 4.The robust adaptive finite-time fault-tolerant control method according to claim 2, characterized in that, The specific implementation process of step S3 includes: the stability of the tracking error system and the parameter estimation error system is guaranteed by the following theorem: Theorem 1: Considering the faulty TS fuzzy system, the control law and the adaptive law, and the possible input saturation, the faulty TS fuzzy system is actually finite-time stable, and the state tracking error converges to a small region of the origin in finite time. prove: S31. By applying the adaptive finite-time fault-tolerant controller constructed in step S21 to the fault model established in step S12, the error dynamic system is described as follows: S32. Consider the following Lyapunov function: in, It is the parameter estimation error; The time derivatives of the S33 and Lyapunov functions are: S34、According to the lemma 1 and the control signal , the control signal , the control signal , the control signal and the control signal , the following inequality is obtained: S35、when then: S36. According to error dynamic analysis, we can obtain: S37. Based on the above analysis, the following inequality can be obtained: S38. Substituting the adaptive update law into the inequality in step S37, we get the following equation: S39. According to the preset tracking controller, there is a positive definite symmetric matrix such that the following formula is satisfied S40, then by the inequality Rewrite the inequality in step S38 as follows: S41、based on the lemma 2, for any constant then there is: S42. Based on the above two inequalities, we can further obtain S43. Based on Lemma 3, the following inequality can be obtained: wherein ; S44. Based on the above analysis, we have: wherein , ; S45. Based on the above analysis, we have the following formula: Let where, , is the initial condition, then according to the lemma 3, we have which means that the closed-loop system is practically finite-time stable. S46. According to the formula in step S45, we have ,mean It is bounded, the signal It is also bounded, due to the ideal state trajectory. It is bounded, therefore the state can be deduced. Bounded.

5. A storage medium, characterized by The storage medium stores a computer instruction set; when the computer instruction set is executed by the processor, it implements the robust adaptive finite-time fault-tolerant control method as described in any one of claims 1-4.

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