A method for implementing feedforward nonlinear system sensor fault tolerance control based on switching observer
Patent Information
- Application Number
- CN202611505930.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-25
- Publication Date
- 2026-11-03
AI Technical Summary
Existing technologies struggle to effectively handle output sensor faults in feedforward nonlinear systems, leading to state estimation bias and control input errors. Furthermore, strict feedback fault-tolerant methods cannot be directly applied, and traditional methods may exhibit conservative performance in the fault-free phase or cause the system state to exceed compact set when fault detection is delayed.
A switching observer-controller structure is adopted, which switches the gain before and after fault detection. The first and second self-adjusting gains are used to drive the nominal and fault-tolerant modes respectively. The Lyapunov inequality ensures that the closed-loop signal is bounded, and the fault term and nonlinear term are compensated in the fault-tolerant mode to achieve global exponential convergence of the system state.
Before and after a fault occurs, the closed-loop signal is guaranteed to be bounded, and the global exponential convergence of the system state, observation state, and control input to the origin is provided, providing an explicit upper bound for the compact set of the trajectory, thus avoiding system instability and switching peaks during the detection delay period.
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Abstract
Description
Technical Field
[0001] This invention relates to the fields of nonlinear system control, output feedback control, and sensor fault tolerance, specifically to a sensor fault tolerance method for feedforward nonlinear systems based on a switched observer. This method is applicable to multi-input multi-output feedforward nonlinear systems where only the output is measurable, the internal state is not fully measurable, and the output measurement is affected by multiplicative sensor failures. Background Technology
[0002] Feedforward nonlinear systems exhibit an upper triangular state-dependent structure: lower-order state equations depend on higher-order states, and control inputs directly enter only the highest-order state equation. This structure can be observed in flexible spacecraft, cascaded electromechanical devices, and some industrial processes. Because the system's nonlinear terms propagate along the cascade direction, constructing a state observer and a stable controller solely based on output measurements is inherently challenging.
[0003] When the output sensor fails, the measurement deviation enters the observer error dynamics and propagates through cascaded structures and nonlinear coupling. The resulting state estimation deviation further affects the control input, potentially causing the closed-loop trajectory to deviate from the origin. Unlike strict feedback systems, feedforward systems lack recursive matching conditions that can be used to compensate for fault deviations at each stage; therefore, existing strict feedback fault-tolerant methods cannot be directly applied to such systems.
[0004] Existing passive fault-tolerant methods typically employ fixed-structure controllers according to predetermined fault categories, which can easily lead to conservative performance during fault-free phases. Active fault-tolerant methods can reconstruct the controller based on detection, diagnosis, or estimation results, but some methods require the system state and fault signals to be located in a pre-defined compact set, resulting in only semi-global stability conclusions. Furthermore, when there is a delay between fault occurrence and fault detection, the system state may exceed this compact set before the regulation mode is activated.
[0005] Furthermore, the output fault alters the structure of the nominal observation error equation, and the stability proof under fault-free conditions cannot be directly applied. It is necessary to characterize the closed-loop behavior separately for three stages: before the fault occurs, after the fault has occurred but not yet been detected, and after the fault-tolerant mode is activated, and to establish explicit upper bounds on the trajectory related to detection delay and control parameters. Summary of the Invention
[0006] This invention aims to provide an active sensor fault-tolerant method for feedforward nonlinear systems. Without designing the fault detection algorithm itself, this invention receives a finite detection time from an external detector, ensures that all closed-loop signals are bounded before detection by switching the observer-controller structure, and restores the global exponential convergence of the system state after the fault-tolerant mode is activated, while simultaneously providing a staged explicit upper bound on the compact set of the trajectory. In nominal mode, the method generates the control input using a first self-adjusting gain and the nominal observation state. In the interval where a fault occurs but has not yet been detected, the nominal observer-controller continues to operate, and the Lyapunov inequality is used to provide an upper bound on the trajectory growth related to the detection delay. At the detection time, the gain of the observer-controller is switched from the first self-adjusting gain to the second self-adjusting gain, and the fault-tolerant observer is reset according to the nominal observation state. In fault-tolerant mode, the state estimate and control input are reconstructed based on the output affected by the fault, and the second self-adjusting gain is used to compensate for the fault term and the unknown nonlinear term. By using phased dynamic gain coordinate transformation and Lyapunov analysis, we prove that the gain is bounded, the closed-loop signal is bounded, and the global exponential convergence of the system state after fault tolerance is achieved. We also calculate the compact set of the state trajectory.
[0007] The technical solution adopted in this invention is a method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer. This method includes the following steps:
[0008] Step 1: Obtain the model of the feedforward nonlinear system with only measurable output, and represent the measurable output affected by multiplicative sensor failure as follows:
[0009]
[0010] in, For the first Level system status, For the first The time derivative of the system state at level 1. To control the input, For measurable output, For an unknown time-varying nonlinear term, Δ The problem is a multiplicative output sensor malfunction. The time of the failure. express 3D real vector space, This represents the dimension of the system's inputs, outputs, and state variables at each level. express A set of 3D real matrices.
[0011] Step two, at the fault detection time Previously, the nominal operating mode was established, utilizing the first self-adjusting gain. Drive the nominal state observer and generate nominal control inputs based on the nominal observed state;
[0012] Step 3: Receive the fault detection signal output by the external fault detector, which is available within a finite time. A fault was detected; a detection delay was defined. ;
[0013] Step four, at time Switch the nominal operating mode to the fault-tolerant operating mode to keep the state of the controlled object continuous at the time of switching, and reset the fault-tolerant observer according to the nominal observation state.
[0014] Step 5: Utilize the second self-adjusting gain in fault-tolerant operating mode. Reconstruct the observer and controller gains, estimate the unmeasurable state based on the fault-affected output, and generate fault-tolerant control inputs;
[0015] Step 6: Construct dynamic gain coordinate transformation and Lyapunov function for the pre-detection stage and the post-detection stage respectively, so that all closed-loop signals before fault detection remain bounded, and the system state, fault-tolerant observation state and fault-tolerant control input global exponent after the fault-tolerant working mode is activated converge to the origin.
[0016] Step 7: Based on the Lyapunov function, give the upper bound of the compact set of the system state trajectory related to the initial dynamic gain, detection delay, and design parameters.
[0017] Furthermore, the fault of the multiplicative output sensor satisfies
[0018] ,
[0019]
[0020] in, Let α be the current time, and α be the unknown positive fault evolution rate. It is a time-varying diagonal fault function that is dependent on the system state. For the first A diagonal fault function, Let be a known upper bound of the positive constants of the fault function amplitude, and let each diagonal element satisfy | |≤ The fault function is not required to be differentiable with respect to time or output state.
[0021] Furthermore, the unknown time-varying nonlinear term and the output measurement satisfy...
[0022]
[0023] in, Given positive constants, the minimum singular value condition Used to rule out the complete loss of measurement information.
[0024] Furthermore, the nominal control input
[0025]
[0026] in, Composed of user-specified positive control gain, This refers to the observer system state.
[0027] First self-adjusting gain
[0028]
[0029] in Design functions for bounded non-increasing functions. This is the internal adjustment variable for the first self-adjusting gain. The update rate is...
[0030]
[0031] Its initial value is chosen as
[0032]
[0033] in, , , These are positive design parameters.
[0034] Nominal observer
[0035] ,
[0036] in, The time derivative of the system state. It is a dynamic matrix. Composed of the positive observer gain specified by the user, A , It is the first component of the nominal observation state. yes 3D identity matrix
[0037] Furthermore, the design function satisfy
[0038]
[0039] And allows the selection of constant values. = ,in It lies between the given positive lower bound and positive upper bound.
[0040] Furthermore, fault-tolerant control input
[0041]
[0042] in , For the fault-tolerant observer system state, It consists of a positive control gain specified by the user.
[0043] Second self-adjusting gain
[0044]
[0045] in, . The internal adjustment variable for the second self-adjusting gain has an update rate of
[0046]
[0047] Its initial value is chosen as
[0048]
[0049] in, , .
[0050] Fault-tolerant observer
[0051] ,
[0052] in, The time derivative of the system state. It is the first component of the fault-tolerant observation state.
[0053] Furthermore, to suppress the peak caused by mode switching, the fault-tolerant observer is reset as follows and a second self-adjusting gain initial value is selected:
[0054]
[0055] Furthermore, in the fault-free range [0, Within this range, the system state remains within the following computable compact set:
[0056]
[0057] After the fault-tolerant operating mode is activated, the system state remains within the following computable compact set:
[0058]
[0059] The sizes of the two compact sets are determined by the initial dynamic gains of the nominal mode and the fault-tolerant mode, respectively, as well as the initial values of the Lyapunov functions.
[0060] Furthermore, the feedforward nonlinear system is a flexible spacecraft attitude control system, a cascaded industrial process system, or a nonlinear system with an upper triangular state-dependent structure in which only the highest-order state equation directly contains the control input.
[0061] Compared with the prior art, the present invention has the following beneficial effects:
[0062] 1. Only use the output measurements affected by the fault; it is not required that the entire system state be measurable.
[0063] 2. The fault function is allowed to change with time and output state, and differentiability of the fault function is not required.
[0064] 3. Clearly distinguish between the time of fault occurrence and the time of fault detection, and ensure that all closed-loop signals remain bounded during the detection delay period.
[0065] 4. After the fault-tolerant mode is activated, the global exponents of the system state, observation state, and control input converge to the origin.
[0066] 5. Provide explicit trajectory boundaries for the fault-free phase, detection delay phase, and fault-tolerant phase, and adjust the compact set size through initial gain and design parameters.
[0067] 6. By coordinating the dynamic gain before and after the switch, the scaling variable can be prevented from being amplified at the moment of switching, thereby reducing the switching peak. Attached Figure Description
[0068] Figure 1 This is a schematic diagram of the closed-loop signal flow between the nominal control mode and the fault-tolerant mode.
[0069] Figure 2 This is a schematic diagram illustrating the evolution of the system state.
[0070] Figure 3 This is a schematic diagram of the state evolution when the fault-tolerant controller is not enabled;
[0071] Figure 4 A schematic diagram of the control input signal;
[0072] Figure 5 This is a schematic diagram illustrating the evolution of the first and second self-adjusting gains. Detailed Implementation
[0073] The following provides a detailed description of the system modeling, nominal control, fault-tolerant control, and stability conclusions of this invention. The parameters and values below are for illustrative purposes only and do not limit the scope of protection of this invention.
[0074] System Model and Design Conditions
[0075] Consider a flexible spacecraft model:
[0076]
[0077] Nonlinear function The sensor malfunction is Time of failure =5s, fault detection time . For system status, It is a control input. Output.
[0078] Nominal control mode
[0079] exist Internally, the nominal controller uses the first self-adjusting gain. and nominal observation status The control input is:
[0080]
[0081] in , Positive control gain specified by the user. This represents the state of the nominal observer.
[0082] The first self-adjusting gain and its internal variable update law are:
[0083]
[0084] in , , , The initial value of the gain is chosen as follows: ,in , All are positive design parameters; P Q The chosen positive definite symmetric matrix is used; parameters are designed to ensure that the feasible interval of the corresponding quadratic equation is non-empty, and the matrix is selected within this interval. (0), function =1.65= .
[0085] The nominal state observer is:
[0086] ,
[0087] Where A This is the time derivative of the observer's state. This is the first observed state component. A fixed positive design gain is applied to the observer.
[0088] Nominal mode stability analysis
[0089] Define observation error and dynamic gain coordinates:
[0090]
[0091] in .
[0092] Choose a combination of Lyapunov functions:
[0093] ,
[0094] in and This is a positive definite symmetric matrix determined by the designer. Differentiating along the closed-loop system trajectory and using the upper bound of the nonlinear term and the first self-adjusting gain update law, the fractional-stage inequalities can be obtained:
[0095]
[0096]
[0097] in
[0098] Therefore, in the fault-free range [0, )Inside, Decays exponentially; First self-adjusting gain The system remains non-decreasing and bounded, with the system state, observed state, and control input all bounded. The system state is maintained within a computable compact set.
[0099]
[0100] exist[ , Within this range, a fault has occurred but has not yet been detected. Although the nominal controller cannot restore the expected exponential performance, the closed-loop signal remains bounded and satisfies:
[0101] .
[0102] Fault Tolerance Mode
[0103] At t= At this time, the control system switches from nominal mode to fault-tolerant mode. The fault-tolerant control input is:
[0104]
[0105] in and fault-tolerant observation status User-specified positive control gain
[0106] The second self-adjusting gain and its internal variable update law are as follows:
[0107]
[0108] in , , , ,and .
[0109] The fault-tolerant observer is:
[0110] ,
[0111] in , The time derivative of the observer state. This is the first observed state component.
[0112] Fault-tolerant mode stability analysis
[0113] Define the observation error and scaling coordinates for the fault-tolerant phase:
[0114]
[0115] in .
[0116] Constructing Lyapunov functions
[0117]
[0118] By differentiating along the fault-tolerant closed-loop trajectory, we can obtain:
[0119] ,
[0120] in
[0121] because Bounded, the above formula gives the following from Initial exponential decay estimation. In fault-tolerant mode, the system state, observed state, and control input are all bounded and converge to the origin. The system state remains within the following compact set:
[0122]
[0123] This conclusion is global and does not require the system's initial state to belong to a given compact set beforehand. The size of the compact set is explicitly determined by the Lyapunov function value at the switching time, the initial value of the second self-adjusting gain, and the design parameters.
[0124] Example
[0125] The initial state and the initial value of the observer are x. The initial value of the gain is chosen as follows: The control gain parameter and the observer fixed gain are respectively Switch the initial value to .
[0126] Simulation results are as follows Figures 2 to 5 As shown. Figure 2 The system state is shown; under the same initial conditions, the proposed method achieves fault tolerance and has good performance. Figure 3 The state evolution process without a fault-adaptive controller is described: before the fault occurs, the state decays rapidly under the action of the nominal controller; after the fault occurs, the nominal controller cannot compensate for the fault effect, resulting in the accumulation of deviations, the state gradually deviates from the origin and eventually diverges. Figure 4 The control input is given. Figure 5 The trajectory of the dynamic gain is shown.
[0127] The technical features of this invention are as follows: For multi-input multi-output feedforward nonlinear systems where only the output is measurable, the internal state is not fully measurable, and the output measurement is affected by multiplicative sensor failures, an active fault-tolerant control structure that switches between a "nominal observer-controller" and a "fault-tolerant observer-controller" is employed. This method does not require the design of the fault detection algorithm itself, but rather receives finite detection times from external detectors and drives the nominal mode and fault-tolerant mode respectively through a first self-adjusting gain and a second self-adjusting gain. Its core features include: allowing the fault function to change with time and output state without requiring differentiability; clearly distinguishing between the fault occurrence time and the fault detection time; ensuring that all closed-loop signals are bounded during the detection delay; causing the system state, observation state, and control input to converge globally exponentially to the origin after the fault-tolerant mode is activated; and providing an explicit upper bound of the compact set of the trajectory related to the initial dynamic gain, detection delay, and design parameters.
[0128] To address the problem that fault deviations propagate along the cascade direction due to the upper triangular state-dependent structure of feedforward nonlinear systems, rendering strict feedback fault-tolerant methods inapplicable, this invention generates a nominal control input using a first self-adjusting gain and the nominal observed state before a fault occurs. During the interval where a fault occurs but has not yet been detected, the nominal observer-controller system continues to operate, and Lyapunov inequalities are used to provide an upper bound on the trajectory growth related to the detection delay. At the detection time, the observer-controller gain is switched from the first self-adjusting gain to the second self-adjusting gain, and the fault-tolerant observer is reset according to the nominal observed state, ensuring the controlled object's state remains continuous at the switching time. In fault-tolerant mode, the state estimate and control input are reconstructed based on the output affected by the fault, and the second self-adjusting gain is used to compensate for the fault term and unknown nonlinear term. Through staged dynamic gain coordinate transformation and Lyapunov analysis, the closed-loop behavior is characterized in three stages: before a fault occurs, after a fault has occurred but not yet been detected, and after the fault-tolerant mode is activated. This demonstrates that the gain is bounded, the closed-loop signal is bounded, and the system state after fault tolerance converges globally exponentially.
[0129] In summary, compared with existing technologies, firstly, it only uses output measurements affected by faults, without requiring all system states to be measurable; secondly, it allows the fault function to change with time and output state, and does not require the fault function to be differentiable; thirdly, it clearly distinguishes between the fault occurrence time and the fault detection time, ensuring that all closed-loop signals remain bounded during the detection delay; fourthly, after the fault-tolerant mode is activated, the system state, observed state, and control input converge globally to the origin; fifthly, it provides explicit trajectory boundaries for the fault-free stage, the detection delay stage, and the fault-tolerant stage, and the compact set size can be adjusted through the initial gain value and design parameters; sixthly, by coordinating the dynamic gain before and after switching, it can avoid the scaling variable being amplified at the moment of switching, thereby reducing the switching peak.
Claims
1. A method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer, characterized in that, The method includes the following steps: Step 1: Obtain the model of the feedforward nonlinear system with only measurable output, and represent the measurable output affected by multiplicative sensor failure as follows: ； in, For the first Level system status, For the first The time derivative of the system state at level 1. To control the input, For measurable output, For an unknown time-varying nonlinear term, Δ The problem is a multiplicative output sensor malfunction. The time of the failure. express 3D real vector space, This represents the dimension of the system's inputs, outputs, and state variables at each level. express A set of 3D real matrices; Step two, at the fault detection time Previously, the nominal operating mode was established, utilizing the first self-adjusting gain. Drive the nominal state observer and generate nominal control inputs based on the nominal observed state; Step 3: Receive the fault detection signal output by the external fault detector, which is available within a finite time. A fault was detected; a detection delay was defined. ; Step four, at time Switch the nominal operating mode to the fault-tolerant operating mode to keep the state of the controlled object continuous at the time of switching, and reset the fault-tolerant observer according to the nominal observation state. Step 5: Utilize the second self-adjusting gain in fault-tolerant operating mode. Reconstruct the observer and controller gains, estimate the unmeasurable state based on the fault-affected output, and generate fault-tolerant control inputs; Step 6: Construct dynamic gain coordinate transformation and Lyapunov function for the pre-detection stage and the post-detection stage respectively, so that all closed-loop signals before fault detection remain bounded, and the system state, fault-tolerant observation state and fault-tolerant control input global exponent after the fault-tolerant working mode is activated converge to the origin. Step 7: Based on the Lyapunov function, give the upper bound of the compact set of the system state trajectory related to the initial dynamic gain, detection delay, and design parameters.
2. The method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer as described in claim 1, characterized in that, The multiplicative output sensor fault satisfies ， ； in, Let α be the current time, and α be the unknown positive fault evolution rate. It is a time-varying diagonal fault function that is dependent on the system state. For the first A diagonal fault function, Let be a known upper bound of the positive constants of the fault function amplitude, and let each diagonal element satisfy | |≤ The fault function is not required to be differentiable with respect to time or output state.
3. The method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer as described in claim 1, characterized in that, The unknown time-varying nonlinear term and the output measurement satisfy ； in, Given positive constants, the minimum singular value condition Used to rule out the complete loss of measurement information.
4. The method for sensor fault-tolerant control of a feedforward nonlinear system based on a switching observer as described in claim 1, characterized in that... The nominal control input ； in, Composed of user-specified positive control gain, The observer system state; First self-adjusting gain ； in Design functions for bounded non-increasing functions. This is the internal adjustment variable for the first self-adjusting gain. The update rate is... ； Its initial value is chosen as ； in, , , Positive design parameters; Nominal observer , in, The time derivative of the system state. It is a dynamic matrix. Composed of the user-specified positive observer gain, A , It is the first component of the nominal observation state. yes 3D identity matrix .
5. The method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer according to claim 4, characterized in that, The design function satisfy ； And allows the selection of constant values. = ,in It lies between the given positive lower bound and positive upper bound.
6. The method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer according to claim 1, characterized in that... Fault-tolerant control input ； in , For the fault-tolerant observer system state, Composed of a positive control gain specified by the user; Second self-adjusting gain ； in, . The internal adjustment variable for the second self-adjusting gain has an update rate of ； Its initial value is chosen as ； in, , ; Fault-tolerant observer ， in, The time derivative of the system state. It is the first component of the fault-tolerant observation state.
7. The method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer according to claim 1, characterized in that, To suppress peak values caused by mode switching, reset the fault-tolerant observer using the following formula and select the second self-adjusting gain initial value: 。 8. The method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer according to claim 1, characterized in that, In the fault-free range [0, Within this range, the system state remains within the following computable compact set: ； After the fault-tolerant operating mode is activated, the system state remains within the following computable compact set: ； The sizes of the two compact sets are determined by the initial dynamic gains of the nominal mode and the fault-tolerant mode, respectively, as well as the initial values of the Lyapunov functions.
9. The method for sensor fault-tolerant control of a feedforward nonlinear system based on a switched observer according to any one of claims 1 to 8, characterized in that, The feedforward nonlinear system is a flexible spacecraft attitude control system, a cascaded industrial process system, or a nonlinear system with an upper triangular state-dependent structure in which only the highest-order state equation directly contains the control input.