A control method based on tube-mpc predictive control

Abstract

This application relates to the field of aircraft control technology and provides a control method based on Tube-MPC predictive control, including: designing an adaptive recursive least squares algorithm to estimate the input time delay of the dynamic system and constructing an adaptive observer model including input time delay compensation; in the control law update decision, prioritizing whether the observation error meets the online judgment condition for entering the extended invariant set; in response to meeting the condition, triggering a first update to tighten the invariant set and update the nominal control gain; in response to not meeting the condition and the tracking error meeting the event triggering condition, triggering a second update and introducing a time constraint based on the reference trajectory change rate. This application reduces control conservatism and significantly reduces the online computational burden while ensuring robust stability.

Description

Technical Field

[0001] This application relates to the field of aircraft control technology, specifically to a control method based on Tube-MPC predictive control. Background Technology

[0002] In trajectory tracking control of complex dynamic systems, Tube Model Predictive Control (Tube-MPC) handles parameter uncertainties and external disturbances by constructing error tubes around the nominal trajectory. However, when the system state is unmeasurable or there is input time delay, existing technologies typically directly substitute the state estimate, which includes observation errors and time delay compensation errors, into the controller design. This leads to an excessive amplification of the control error invariant set, increasing the conservatism of the control and limiting the system's tracking accuracy. Furthermore, to adapt to time-varying reference trajectories, the controller often needs to update the nominal control gain online. However, traditional fixed-period update strategies waste computational resources when state changes are slow, while single event-triggered mechanisms are prone to high-frequency invalid updates or update lags due to improper threshold settings, making it difficult to effectively reduce the onboard computational burden while ensuring stability. Therefore, there is an urgent need for a Tube-MPC predictive control scheme that can reduce control conservatism while balancing computational efficiency and control performance. Summary of the Invention

[0003] To address the issues of high control conservatism and difficulty in balancing online computational burden and control performance in existing technologies, this application proposes a control method based on Tube-MPC predictive control, which achieves the reduction of control error boundaries while avoiding high-frequency invalid updates.

[0004] To achieve the above objectives, this application adopts the following technical solution: To obtain the observation state of a dynamic system, an adaptive recursive least squares algorithm is designed to estimate the input time delay of the dynamic system, and an adaptive observer model including input time delay compensation is constructed. Using existing methods, an alternative observation state is constructed based on boundary operations between the observation error invariant set and the control error invariant set. The control error invariant set is reconstructed based on the alternative observation state. In the control law update decision, it is prioritized to determine whether the observation error meets the online judgment condition for entering the expanded invariant set. In response to meeting the online judgment condition, a first update is triggered to tighten the control error invariant set and update the nominal control gain. In response to not meeting the online judgment condition and the tracking error meeting the event trigger condition, a second update is triggered to update the nominal control gain, and a transition time based on the reference trajectory change rate is introduced during the update process to avoid high-frequency invalid updates.

[0005] The above scheme geometrically reconstructs and reduces the control error invariant set by using alternative observation states instead of directly using the original output values ​​of the observer, thereby reducing the conservatism of the controller. At the same time, a dual update mechanism of online judgment and event triggering is established, which prioritizes the convergence characteristics of observation error to tighten the invariant set, updates the gain only when necessary through event triggering, and combines transition time to prevent Zeno's phenomenon, thereby significantly reducing the online computational burden while ensuring the robust stability of the system.

[0006] As one implementation method, the transfer function model of the dynamic system is approximated with all poles to approximate the input time delay, and then discretized using a bilinear transform. An adaptive recursive least squares algorithm is used to estimate the parameters of the discretized model to dynamically obtain the estimated value of the input time delay. This algorithm introduces adaptive regularization parameters and smooth update parameters to reduce abrupt gain changes. Based on the estimated input time delay, time delay compensation is performed on the control input, and an adaptive observer model incorporating time delay compensation is constructed. The observed state is then output through this adaptive observer model. This implementation method provides a high-precision online identification and compensation method for the specific disturbance source of input time delay, providing an accurate benchmark for the subsequent construction of alternative observed states and enhancing the adaptability of the entire control architecture to time-delay systems.

[0007] As one implementation method, an alternative observation state is constructed based on boundary operations between the observation error invariant set and the control error invariant set using existing methods; the control error invariant set is then reconstructed based on the alternative observation state. The offline-calculated and interpolated sequences of the observation error invariant set and the control error invariant set are obtained to determine the expanded invariant set; it is determined whether the observation error at the current moment enters the expanded invariant set; if it does, the online judgment condition is satisfied, and the first update is executed; if it does not enter the expanded invariant set, the online judgment condition is not satisfied, and it is further determined whether the tracking error satisfies the static event triggering condition or the dynamic event triggering condition to decide whether to execute the second update. This implementation method establishes a collaborative decision-making logic of "online judgment priority, event triggering as a fallback." When the observation error has converged to the expanded invariant set, the error control is actively tightened to improve accuracy; updates are only triggered by tracking error when convergence is not achieved, effectively avoiding redundant calculations caused by tracking error fluctuations when the system is stable.

[0008] In one implementation, in response to the observation error entering the extended invariant set, an alternative observation set and a control error invariant set based on the alternative observation set are updated; a constrained optimization problem in the form of a first linear matrix inequality is constructed, the first linear matrix inequality constrained optimization problem being constrained by input constraints tightened by the updated control error invariant set, the initial error invariant set of the system state, and robust stability constraints for all vertices of the multicell; the first linear matrix inequality constrained optimization problem is solved to update the nominal control gain. This implementation couples the online tightening of the invariant set and the updating of the control gain within the same LMI optimization framework, ensuring that while tightening the error boundary, the new nominal control gain still meets the robust stability requirements of the system.

[0009] As one implementation, when the tracking error is greater than a preset static threshold, the static event triggering condition is determined to be met; when the tracking error is greater than a dynamic threshold dynamically adjusted based on historical error values, the dynamic event triggering condition is determined to be met; in response to meeting either the static or dynamic event triggering condition, a constraint optimization problem in the form of a second linear matrix inequality is constructed and solved to update the nominal control gain; after updating the nominal control gain, a transition time is introduced to limit the earliest time of the next trigger update, the transition time... satisfy: ,in, and It is a constant. Sampling time, This is the reference trajectory. This implementation adapts to tracking requirements under different operating conditions through static / dynamic dual thresholds, and designs a transition time inversely proportional to the rate of change of the reference trajectory. This mechanism eliminates high-frequency invalid updates caused by instantaneous error jitter (i.e., Zeno's phenomenon), ensuring the smoothness of control law updates and the rational allocation of computing resources.

[0010] In one implementation, the nominal control input, the auxiliary control input, and the time-delay compensation control input are superimposed to generate the final control input. The nominal control input is generated based on the nominal system tracking the reference trajectory. The auxiliary control input is generated using a robust feedback control law based on the error between the alternative observation state and the nominal state. The time-delay compensation control input is generated based on the estimated value of the input time delay. The final control input is applied to the dynamic system to achieve robust tracking control of the reference trajectory. This implementation clarifies the decoupling structure and superposition relationship of the three-channel control inputs, enabling the system to handle nominal tracking, lumped disturbance suppression, and time-delay compensation tasks respectively, thus improving the interpretability and modularity of the overall control performance.

[0011] Beneficial effects: This application, by employing alternative observation states and reconstructing the invariant set of control errors based on set operations, fundamentally eliminates the direct amplification effect of observation and compensation errors on the control error boundary. This ensures that the invariant set is determined solely by the permissible range of the alternative observations, significantly reducing the conservatism of the control and improving trajectory tracking accuracy. Simultaneously, by establishing a dual collaborative update mechanism with online judgment priority and event-triggered fallback, and introducing time constraints coupled with the rate of change of the reference trajectory, the incentive for high-frequency invalid updates is eliminated. This ensures that the control law is updated only when the system state undergoes a substantial deviation or the observation error converges significantly. While guaranteeing the robust stability of the closed-loop system, this greatly reduces the online computational burden and solves the technical challenge of high-precision real-time control of complex dynamic systems under resource-constrained environments. Attached Figure Description

[0012] Figure 1 This is a diagram of the control system architecture based on Tube-MPC predictive control according to an embodiment of this application; Figure 2 This is a flowchart of the control method based on Tube-MPC predictive control according to an embodiment of this application; Figure 3 This is a flowchart illustrating the integrated online update of the control law according to an embodiment of this application. Detailed Implementation

[0013] The following is in conjunction with the appendix Figure 1 -Appendix Figure 3 Provide a detailed explanation: To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0014] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0015] Example 1 This embodiment provides a control method based on Tube-MPC predictive control. This method addresses the problems of high control conservatism and uneven allocation of computational resources in traditional Tube-MPC predictive control when dealing with unmeasurable states and time-delayed disturbances by constructing alternative observed states and a dual collaborative update mechanism. It should be understood that although this embodiment may be described in conjunction with specific application scenarios later, this method is essentially applicable to various dynamic systems with input time delays, external disturbances, and unmeasurable or limited states, and is not limited to a specific type of controlled object, such as... Figure 2 As shown.

[0016] Step S100: Obtain the observed state of the dynamic system, design an adaptive recursive least squares algorithm to estimate the input time delay of the dynamic system, and construct an adaptive observer model that includes input time delay compensation. Specifically, in complex operating conditions with unknown time-varying input time delays, traditional observers, if they ignore the time delay effect or only use fixed time delay compensation, often lead to a significant phase deviation between the state estimate and the actual dynamic state. This causes the controller to make decisions based on incorrect state information, and in severe cases, even leads to system instability. This embodiment uses an adaptive recursive least squares algorithm, which, by introducing adaptive regularization parameters and a smooth update strategy, quickly tracks time delay changes while maintaining estimation stability, thereby obtaining accurate time delay estimates in real time. Based on this, the time delay estimation results are embedded into the observer structure to form an adaptive observer model that includes input time delay compensation, enabling the observed state to remain synchronized with the actual physical process containing time delays. This approach eliminates the interference of time delays on state observation from a mechanistic perspective, providing accurate and timely feedback signals for subsequent control law design, fundamentally improving the system's adaptability to time delays.

[0017] Step S200: Using existing methods, an alternative observation state is constructed based on boundary operations between the observation error invariant set and the control error invariant set; the control error invariant set is then reconstructed based on the alternative observation state. In the control law update decision, priority is given to determining whether the observation error meets the online judgment condition for entering the extended invariant set. Specifically, this is the first decision gate of the dual collaborative update mechanism in this embodiment. The extended invariant set represents a threshold region of the convergence degree of the observation error. When the observation error enters this region, it means that the current state estimation quality has been improved to a level sufficient to support more refined control. Placing this judgment with the highest priority reflects the design idea of ​​"actively seeking performance optimization when the system state stabilizes or the observation quality improves." This differs from the logic of traditional methods that is only passively triggered when the error exceeds the standard, allowing the controller to use the system's own convergence characteristics to improve control accuracy.

[0018] In step S300, in response to meeting the online judgment condition, a first update is triggered to tighten the control error invariant set and update the nominal control gain. Specifically, once it is confirmed that the observation error has entered the expanded invariant set, the system immediately executes the first update. This update operation includes two coupled actions: first, recalculating and tightening the control error invariant set based on the current better observation information, further compressing the pipe radius; second, simultaneously solving for the new nominal control gain to adapt to the reduced error constraints. This linked update ensures that while tightening the error boundary, the control law can still meet the stability requirements, avoiding the loss of feasibility caused by simply shrinking the invariant set. Through this mechanism, the system can dynamically "self-evolve" during operation, automatically releasing the overprotected performance potential as the observation accuracy improves.

[0019] In step S400, in response to the failure to meet the online judgment condition and the tracking error meeting the event triggering condition, a second update is triggered to update the nominal control gain. A transition time based on the reference trajectory change rate is introduced during the update process to avoid high-frequency invalid updates. Specifically, when the observation error has not yet converged to the extended invariant set, the system enters the second decision logic, namely the event triggering mechanism based on the tracking error. If the tracking error exceeds a preset threshold at this time, it indicates that external disturbances or model mismatch have affected the trajectory tracking performance, and a second update needs to be triggered to adjust the nominal control gain to correct the deviation. However, to prevent frequent recalculation of the controller due to noise or transient fluctuations at the threshold critical point (i.e., Zeno's phenomenon), this embodiment specifically introduces a transition time associated with the reference trajectory change rate. This transition time mandates a minimum interval between two updates, and this interval adaptively adjusts according to the drastic change of the reference trajectory: when the trajectory changes rapidly, the update frequency can be appropriately increased to ensure real-time tracking; when the trajectory is flat, the update interval is lengthened to save computing power. This design ensures timely system response under abnormal conditions and eliminates the ineffective consumption of computing resources from a mechanistic perspective, achieving a dynamic balance between control performance and computing efficiency.

[0020] Through the coordinated operation of steps S100 to S400, this embodiment constructs a complete, low-conservatism, high-efficiency Tube-MPC predictive control methodology. The reconstruction of alternative observation states solves the problem of "accurate observation," providing a geometric basis for tightening the error tube. The dual collaborative update mechanism resolves the contradiction between "economical calculation" and "good control," ensuring, through priority scheduling and time constraints, that control law updates always serve substantial performance improvement or stability maintenance, rather than falling into ineffective numerical oscillations.

[0021] Example 2 In this embodiment, the specific implementation method of the adaptive estimation of input time delay mentioned in Embodiment 1 is further described in detail. As a supporting step for the core control algorithm, this embodiment aims to provide a specific implementation basis for obtaining high-precision observation status.

[0022] Step S101 involves approximating the input time delay using an all-pole approximation of the transfer function model of the dynamic system, followed by discretization using a bilinear transform. Specifically, in practical engineering systems, the input time delay often manifests as a transcendental function, making direct processing extremely difficult. This application employs an all-pole approximation method to transform the time delay into a rational transfer function, thus enabling it to be processed within the framework of a standard linear system. Subsequently, a bilinear transform maps the continuous-time model to the discrete-time domain to accommodate the sampling characteristics of the digital controller.

[0023] Step S102 involves using an adaptive recursive least squares algorithm to estimate the parameters of the discretized model, dynamically obtaining the estimated input time delay. The adaptive recursive least squares algorithm introduces adaptive regularization parameters and smooth update parameters to reduce gain abrupt changes. Specifically, due to the complex operating environment and the often unknown input time delay, traditional fixed parameter identification algorithms struggle to balance tracking speed and estimation stability. The adaptive recursive least squares algorithm (ARLS) designed in this application addresses this problem through two key mechanisms. First, the adaptive regularization parameter is dynamically adjusted based on the magnitude of the real-time estimation error: when the error is large, the regularization strength is automatically increased to suppress noise; when the error is small, the regularization strength is decreased to avoid over-regularization. Second, the smooth update parameters constrain the rate of change of the gain matrix, effectively filtering out high-frequency gain jitter caused by instantaneous disturbances in the parameter update channel. This design, from a mechanistic perspective, avoids the observer divergence risk caused by gain abrupt changes, ensuring the stability and reliability of the reference signal relied upon when constructing alternative observation states.

[0024] Step S103 involves compensating the control input for time delay based on the estimated input time delay, and constructing an adaptive observer model that includes time delay compensation. The observed state is then output through this adaptive observer model. Specifically, using the real-time time delay estimate obtained in step S601, known delay effects are compensated for in the control loop via feedforward, and the control input terms in the observer model are corrected to synchronize with the actual physical process. This adaptive observer corrects the input terms through time delay compensation, making the state estimate closer to the actual physical process with time delay, thereby outputting an enhanced observed state that incorporates time delay information. This high-quality observed state is the necessary input for using the alternative observed state in Example 1. Without the accurate benchmark provided by this step, subsequent geometric reconstruction and invariant set compaction would lose their physical foundation.

[0025] Example 3 In this embodiment, the first update path based on online judgment mentioned in Embodiment 1 is further described in detail. As the active optimization dimension in the dual collaborative update mechanism, this embodiment focuses on how to utilize the convergence characteristics of observation errors to dynamically improve control performance.

[0026] Using existing methods, we determine the invariant sets of observation and control errors for a dynamic system, and construct alternative observation states based on these sets. The invariant set of control errors is then reconstructed based on these alternative observation states. Specifically, the invariant set of control errors defines the maximum permissible range of deviation of the actual state from the nominal trajectory, i.e., the so-called "pipeline" thickness. Since the alternative observation states eliminate some redundant observation uncertainties, the reconstructed invariant set of control errors is more compact than that of traditional methods. Based on this, the control law is decoupled into three parts: the nominal control input drives the ideal model to track the reference trajectory, ensuring the steady-state performance of the system; the auxiliary control input pulls the actual state back and maintains it within the reconstructed compact invariant set, suppressing the influence of lumped disturbances; and the time-delay compensation control input is used to offset the input time-delay effect. This decoupled control strategy based on compact invariant sets enables the system to achieve a larger feasible control space and higher dynamic response capability while ensuring robust stability.

[0027] This paper obtains offline-calculated and interpolated sequences of observation error invariant sets and control error invariant sets to determine the extended invariant set. Specifically, in the actual engineering deployment of Tube-MPC predictive control, real-time online calculation of accurate robust positive invariant sets often involves complex iterative operations, posing a significant challenge to the computing power of onboard processors. Therefore, this application adopts an "offline pre-calculation + online interpolation" strategy. During the system design phase, a series of nested invariant sets are calculated offline for different error levels, and during runtime, a smoothly transitioning extended invariant set is generated in real-time using interpolation methods based on the current state. This extended invariant set geometrically represents a convergence target domain that is smaller than the current control error invariant set but sufficient to encompass the current observation error. It is not merely a mathematical boundary but also a "convergence marker" for improving the system's observation quality. When the observation error falls into this region, it indicates that the uncertainty of the state estimation has been reduced to a new level, providing a physical basis for further compressing the control pipeline radius.

[0028] The determination of whether the current observation error enters the extended invariant set is specifically the trigger threshold for the first update path. Unlike passive triggering based on a tracking error threshold, this determination is based on the observer's own performance metrics. This design embodies the control philosophy of "actively seeking performance breakthroughs when the system's state stabilizes." By monitoring the positional relationship of the observation error relative to the extended invariant set, the controller can accurately capture critical moments when the system transitions from transient to steady state or recovers from large disturbances to small disturbances, providing a reliable decision-making basis for subsequent invariant set tightening.

[0029] If the observation error enters the extended invariant set, the online judgment condition is met, and the first update is executed. Specifically, once it is confirmed that the observation error has entered the extended invariant set, the system immediately initiates the first update process. This priority setting is the key difference between this application and traditional event-triggered control. In actual control, even if the system has reached stable convergence, the tracking error may still hover around the threshold due to sensor noise or slight jitter in the reference trajectory. If the tracking error trigger condition is prioritized at this time, it is very easy for the controller to frequently recalculate the gain without adjustment, resulting in ineffective consumption of computing resources or even oscillation of the control law. By placing the online judgment with the highest priority, active optimization is only triggered when the observation quality is substantially improved, effectively shielding false trigger signals in steady state and achieving a dual guarantee of computational efficiency and control quality.

[0030] If the system fails to enter the extended invariant set, the online judgment condition is not met. Further checks are then made to determine whether the tracking error meets the static or dynamic event triggering conditions to decide whether to execute the second update. Specifically, this constitutes a fallback logic with a dual mechanism. When the observation error has not yet converged to the ideal range, it indicates that the system is still under considerable uncertainty, and it is not advisable to hastily tighten the invariant set. The controller instead relies on the tracking error to monitor the system's external performance, only passively intervening when the deviation exceeds the safety tolerance. This hierarchical decision-making structure allows the controller to both enjoy the performance benefits of convergence and maintain a stable baseline.

[0031] During the first update, in response to the observation error entering the extended invariant set, the alternative observation set and the control error invariant set based on the alternative observation set are updated. Specifically, this step uses the more accurate current observation information to recalculate the admissible set of the alternative observation state, and derives a new, smaller control error invariant set. This new invariant set will become the hard constraint boundary of the subsequent optimization problem, ensuring that the adjustment of the control strategy is always based on the latest system knowledge.

[0032] A constrained optimization problem in the form of a first linear matrix inequality is constructed, with the system state and control input weight matrices, the updated control error invariant set, and the multicell vertex matrix as constraints. Specifically, to obtain the optimal nominal control gain while ensuring stability, this application constructs the following optimization problem: in, The upper bound scalar for the performance to be optimized; and As an auxiliary matrix variable, used to linearize the feedback gain. ; The geometry of the new pipeline is determined by the symmetric positive definite matrix that is directly related to the updated control error invariant set. and A multicell vertex matrix to describe the uncertainty of system parameters; and These are weight matrices for the system state and control input, respectively, used to balance tracking accuracy and energy consumption; This represents the error state between the nominal system and the reference system at the current moment. It is the maximum permissible auxiliary control input amplitude determined by the updated control error invariant set.

[0033] The logic behind constructing the optimization problem described above has profound physical implications. First, the first matrix inequality encompasses all possible vertices of model uncertainty, ensuring the robust stability of the new gain across the entire envelope. Second, the second matrix inequality forces the current nominal error state to be constrained to a new ellipsoidally invariant set. Internally, this ensures the continuity of the state during the transition. The most crucial element is the third matrix inequality, in which... It is not a fixed constant, but rather changes dynamically as the invariant set of the control error shrinks. This means that when the invariant set shrinks, the input margin left for the auxiliary controller will also be adjusted accordingly, and the optimization problem must find a feasible solution under stricter constraints. This coupling mechanism mathematically guarantees the "stability of the shrinking process itself," that is, no matter how the invariant set shrinks, the solved nominal control gain can ensure that the actual state does not escape the new pipeline boundary.

[0034] Solve the constrained optimization problem in the form of the first linear matrix inequality to update the nominal control gain. Specifically, solve the LMI problem using a convex optimization algorithm to obtain the optimal... and The matrix is ​​then used to calculate the new nominal control gain. This gain not only adapts to the reduced error constraints but also minimizes the upper bound of the infinite time-domain performance index while satisfying robust stability. Compared to fixed gain or gain based solely on tracking error updates, this gain update strategy driven by observation convergence can maximize the performance potential of the controller at the moment when the system state is clearest and uncertainty is minimal, achieving a balance between high accuracy and low conservatism.

[0035] It should be understood that although this embodiment is illustrated using a specific LMI form as an example, other equivalent convex optimization forms or nonlinear optimization methods can be used to solve for the nominal control gain in other embodiments. As long as the constraints include the updated control error invariant set information and can guarantee the robust stability of the closed-loop system, they all fall within the scope of protection of this application. Furthermore, the frequency of online judgment can be synchronized with the control cycle or executed asynchronously, depending on the processor's scheduling capabilities and the required control precision.

[0036] Example 4 In this embodiment, the event-triggered second update path and the mechanism for preventing high-frequency invalid updates mentioned in Embodiment 1 are further described in detail. As the passive response dimension in the dual collaborative update mechanism, this embodiment mainly addresses the control law adjustment problem when the observation error does not meet the convergence condition but the system tracking performance shows a significant deviation, and focuses on how to ensure the computational stability of the system through a time constraint mechanism. Figure 3 As shown, this process constitutes a safety net and security layer for the update of the control law.

[0037] Step S401: When the tracking error exceeds a preset static threshold, the static event triggering condition is determined to be met. Specifically, the static threshold is a pre-set fixed constant applicable to situations where the system is in steady-state cruise or the reference trajectory changes gently. In such scenarios, the system's dynamic characteristics are relatively stable, and any tracking error exceeding this fixed threshold usually indicates the presence of continuous external disturbances or model parameter drift, rather than transient noise. By setting the static threshold, the controller can maintain a defined error tolerance band during the steady-state phase, avoiding frequent false triggers caused by sensor noise floor, while ensuring timely intervention and correction before the deviation accumulates to the point of affecting task accuracy.

[0038] Step S402: When the tracking error exceeds a dynamic threshold dynamically adjusted based on historical error values, the dynamic event triggering condition is deemed met. Specifically, unlike the static threshold, the dynamic threshold is calculated in real-time based on the tracking error sequence over a past period. This design is specifically for transient conditions involving severe maneuvers, mode switching, or sudden strong disturbances. During transients, the tracking error itself fluctuates significantly. If a fixed static threshold is still used, the controller is easily triggered repeatedly during normal dynamic responses, causing unnecessary computational overhead and even control signal jitter. The dynamic threshold can adaptively "breathe" with the historical error level: it automatically widens the trigger threshold during transient phases when errors are generally large, triggering updates only when the error deviates abnormally from the current dynamic trend; and it automatically tightens the threshold as the error gradually converges, smoothly transitioning back to steady-state monitoring mode. This dual-threshold complementary mechanism allows the second update path to both keenly capture minor anomalies in steady-state conditions and readily cope with large fluctuations in transient conditions, significantly improving the environmental adaptability of the event triggering strategy.

[0039] Step S403: In response to satisfying either a static or dynamic event triggering condition, a constraint optimization problem in the form of a second linear matrix inequality is constructed and solved to update the nominal control gain. Specifically, when any triggering condition is activated, it indicates that the current nominal control gain is insufficient to maintain the desired tracking performance, and the optimization problem needs to be solved again. The constraint optimization problem in the form of the second linear matrix inequality constructed here is structurally similar to the first optimization problem in Example 3, but the error state vector in its constraints is replaced with the actual tracking error at the current triggering moment, and the boundary of the invariant set may be adjusted accordingly based on the current triggering type. The new nominal control gain obtained by solving this problem can pull the current state that has deviated from the nominal trajectory back into the feasible region and provide a corrected control benchmark for subsequent trajectory tracking. It should be understood that although this embodiment uses a linear matrix inequality as an example, in other embodiments, nonlinear programming or other convex optimization methods can also be used, as long as they can generate a new gain that guarantees closed-loop stability based on the current triggering information.

[0040] Step S404: After updating the nominal control gain, a transition time is introduced to limit the earliest time of the next triggered update. Specifically, this is the core technical means of this application to prevent high-frequency invalid updates (i.e., Zeno's phenomenon in control theory). In event-triggered control systems, if there is a lack of effective time interval constraints, when the system state oscillates around the trigger threshold, theoretically an infinite number of updates may be triggered within a finite time, which will lead to instantaneous saturation of the onboard processor's computing power or even system crash. To solve this problem, this application designs the following transition time calculation formula: in, and As a preset constant, Sampling time, For reference trajectory, It represents the rate of change of the reference trajectory at the current moment.

[0041] This formula contains profound physical mechanisms and control wisdom. Transition time It is inversely proportional to the rate of change of the reference trajectory: when the reference trajectory changes drastically, the denominator increases, and the calculated... The corresponding decrease means the system can perform more frequent control law updates per unit time to adapt to rapidly changing tracking requirements and avoid performance degradation due to update lag; conversely, when the reference trajectory is flat, the denominator decreases. Automatic stretching forces the controller into a "cooling-off period," during which it does not respond even if the tracking error touches the threshold again, effectively filtering out false trigger signals caused by measurement noise or unmodeled high-frequency dynamics. (Constant term) This provides a minimum base time interval, ensuring that even in extreme cases where the reference trajectory changes abruptly (the denominator approaches zero), the update frequency will not exceed the processor's physical limits.

[0042] To illustrate the necessity of this feature more intuitively, consider a counterexample: If the aforementioned transition time constraint is removed, and only threshold judgment is relied upon, during the cruise phase of a hypersonic vehicle, the frequency of structural elastic vibration caused by aerodynamic heating happens to couple with the sensor sampling frequency, causing the tracking error to repeatedly oscillate around the static threshold at extremely high frequencies. Without time constraints, the controller will trigger LMI solving in every sampling cycle, and the LMI solving time far exceeds the sampling cycle time. This will directly lead to control loop blockage, command accumulation, and ultimately, vehicle instability. However, with the introduction of the transition time mechanism of this application, even if the error signal has high-frequency jitter, the calculated error will be significantly reduced due to the extremely low rate of change of the reference trajectory during the cruise phase. The frequency will be much larger than the jitter period, forcibly suppressing the update frequency within a safe range. This ensures both macroscopic trajectory tracking accuracy and completely avoids microscopic computational disasters. This design is not a simple choice based on engineering experience, but a theoretical solution based on the coupling relationship between the dynamic characteristics of the system and the constraints of computing resources. It constitutes an indispensable and necessary technical feature of the technical solution in this application.

[0043] It should be understood that although this embodiment provides a specific analytical expression for the transition time, in other embodiments, methods such as lookup tables, fuzzy inference, or neural network prediction can also be used to determine the time interval negatively correlated with the rate of change of the reference trajectory. As long as it can achieve the adaptive adjustment function of "more frequent updates when the trajectory changes quickly, and less frequent updates when the trajectory changes slowly," it falls within the protection scope of this application. In addition, the calculation of the transition time can be performed synchronously with the control cycle, or it can be calculated asynchronously after each triggered update and the next allowed update time is locked, depending on the scheduling architecture of the embedded system.

[0044] Example 5 In this embodiment, the specific implementation of the multi-channel control law synthesis mentioned in Embodiment 1 is further described in detail. As a post-execution stage of the core control algorithm, this embodiment aims to provide a specific implementation basis for generating robust final control inputs.

[0045] Step S500 involves superimposing the nominal control input, auxiliary control input, and time-delay compensation control input to generate the final control input. Specifically, this application employs a functionally decoupled multi-channel control architecture, rather than coupling all control objectives into a complex optimization problem for unified solution. This superposition relationship can be expressed as: in, This is the final control input applied to the controlled object; For nominal control input; For auxiliary control input; This is the input for time-delay compensation control.

[0046] In this architecture, each channel has a clearly defined and independent function. The nominal control input is generated based on the nominal system tracking reference trajectory, and its design goal is to pursue ideal dynamic performance and steady-state accuracy, without considering the effects of uncertainties and disturbances. The auxiliary control input is generated through a robust feedback control law based on the error between the alternative observed state and the nominal state. Its sole responsibility is to constrain the actual state within the channel centered on the nominal trajectory, suppressing lumped disturbances caused by external disturbances and model mismatch. The time-delay compensation control input is specifically generated based on the estimated input time delay, and is used to offset the pure time delay effect introduced by the actuator or transmission link.

[0047] This decoupled structure brings significant technical advantages and scalability. On the one hand, it decomposes the complex robust tracking problem into three relatively simple sub-problems, reducing the dimensionality and complexity of online computation. On the other hand, it enables modular replacement of the core invention. For example, when it is necessary to upgrade the construction algorithm for replacing the observation state or improve the dual update mechanism, only the internal logic of the auxiliary control channel or the nominal control channel needs to be adjusted, without reconstructing the entire controller architecture or affecting the independent operation of the time delay compensation channel. Similarly, if a more advanced time delay identification algorithm is introduced in the future, it can be directly replaced. The generation module is independent and does not affect other parts. This design not only improves the engineering practicality of the current solution, but also reserves sufficient interface space for subsequent technology iterations, reflecting the defensive layout of the technical solution at a deeper level.

[0048] It should be understood that although this embodiment uses the superposition of three signals as an example, in other embodiments, feedforward disturbance suppression channels or nonlinear compensation channels can be added according to the needs of specific application scenarios. As long as the logical independence of each functional module is maintained and the final robust tracking target is met, they all fall within the protection scope of this application. In addition, the generation order of the control inputs of each channel can be parallel or serial, depending on the scheduling strategy and real-time requirements of the embedded processor.

[0049] Specific procedures: Step S501: Establish a multicellular LPV model of an elastic hypersonic vehicle with input time delay by using Jacobi linearization and tensor product transformation methods. Step S502: The input time delay term is approximated as an additional perturbation between state inputs using a first-order Taylor expansion, and the all-pole approximation method is introduced to represent the time delay term as a finite-dimensional system; on this basis, an adaptive recursive least squares algorithm (ARLS) is designed to achieve dynamic estimation of the input time delay; Step S503: Based on the obtained time delay estimate, construct an adaptive observer model that includes input compensation, and use offline optimization to obtain the observer gain matrix; Step S504: By constructing an invariant set of observation error and control error, the actual observation state is replaced with a substitute observation value located in the safety set, thereby improving control accuracy and robustness.

[0050] Step S505: Calculate the invariant set sequence offline and design an online judgment mechanism. If the online judgment condition is met, calculate the new invariant set and update the nominal control gain. If the online judgment condition is not met, proceed to step S506. Step S506: To reduce computational burden and resource consumption, static and dynamic trigger thresholds are introduced. When the error growth condition is met, the control law is updated. Static event triggering uses a fixed threshold for judgment, which is suitable for slowly changing operating conditions. Dynamic triggering adjusts the threshold according to the historical error value, which is suitable for drastic dynamic changes. Step S507: Based on the nominal system and the error system, construct a constrained optimization problem in the form of a linear matrix inequality and solve it to obtain the nominal control gain; through the Schur complement lemma and Lyapunov function stability analysis, it is proved that the system can always stably converge to the inside of the error invariant set under the triggering condition.

[0051] Step S508: Integrate the adaptive observer, alternative observation feedback, Tube-MPC controller, and dynamic and static event triggering mechanism to construct the final control law and achieve robust tracking control of the reference trajectory.

[0052] In this application scenario, the control system of this application plays a crucial role. Facing the unpredictable state problem caused by elastic effects, the control system utilizes an adaptive observer and an alternative observation state construction mechanism. Without directly relying on expensive or unreliable elastic modal sensors, it uses geometric reconstruction to remove redundant components from the observation error, generating a more compact set of control error invariants. This means that under the same actuator deflection constraints, the aircraft can achieve greater attitude adjustment margin, or significantly reduce the frequency of control surface movements under the same tracking accuracy requirements, thereby mitigating fatigue wear on the thermal protection system. Addressing the phase lag risk caused by input time delay, the control system uses an adaptive recursive least squares algorithm to identify time delay parameters in real time and integrates them into the synthesis process of the multi-channel control law, achieving a shift from "passively tolerating time delay" to "actively compensating for time delay." More importantly, considering the difficulty of heat dissipation for airborne computers under high-speed flight conditions and the extreme scarcity of computing resources, the dual collaborative update mechanism and transition time constraint design of this application ensure that the control law is only recalculated when the observation quality substantially improves or the tracking error truly exceeds the limit, avoiding processor overheating or task blocking caused by high-frequency invalid updates.

[0053] It is particularly important to emphasize that although this embodiment uses a hypersonic vehicle as a specific application carrier for detailed description, this is only to more clearly illustrate the implementation effect and technical advantages of the technical solution of this application under extreme conditions, and is by no means a limitation on the scope of protection of this application. Those skilled in the art should understand that any dynamic system with characteristics such as input time delay, limited state observation, bounded external disturbances, and limited computing resources, such as deep-sea submersibles, flexible robotic arms, satellite attitude control systems, or autonomous vehicles, can be applied to the control system and control method provided in this application. Therefore, any equivalent substitutions or modifications that do not depart from the core technical concept of this application should be included within the scope of protection of this application.

[0054] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. For example, the geometric construction method for alternative observation states, the triggering logic of the dual collaborative update mechanism, the specific form of the linear matrix inequality, and the calculation expression for the transition time in the foregoing embodiments can all be adaptively adjusted or equivalently replaced according to the dynamic characteristics of the actual controlled object and the constraints of computing resources; the technical features described between the various embodiments can also be arbitrarily combined or rearranged without departing from the inventive concept of this application. Furthermore, although this application has described in detail with hypersonic vehicles as a preferred application scenario, this control method and system are also applicable to other complex dynamic systems with input time delays, unmeasurable states, or limited computing resources. Therefore, the scope of protection of this application should be determined by the scope of protection of the claims.

Claims

1. A control method based on Tube-MPC predictive control, characterized in that, include: To obtain the observed state of a dynamic system, an adaptive recursive least squares algorithm is designed to estimate the input time delay of the dynamic system, and an adaptive observer model including input time delay compensation is constructed. In the decision-making process for updating the control law, priority is given to determining whether the observation error meets the online judgment condition for entering the extended invariant set; In response to the satisfaction of the online judgment condition, a first update is triggered to tighten the control error invariant set and update the nominal control gain; In response to the failure to meet the online judgment condition and the tracking error meeting the event trigger condition, a second update is triggered to update the nominal control gain, and a transition time based on the reference trajectory change rate is introduced during the update process to avoid high-frequency invalid updates.

2. The control method according to claim 1, characterized in that, The method for estimating the input time delay of a dynamic system and constructing an adaptive observer model that includes input time delay compensation includes: The transfer function model of the dynamic system is approximated by all poles to approximate the input time delay, and then discretized by combining the bilinear transform. An adaptive recursive least squares algorithm is used to estimate the parameters of the discretized model in order to dynamically obtain the estimated value of the input time delay. The adaptive recursive least squares algorithm introduces adaptive regularization parameters and smooth update parameters to reduce abrupt changes in gain. Based on the estimated input time delay, time delay compensation is performed on the control input, and an adaptive observer model containing time delay compensation is constructed. The observation state is then output through the adaptive observer model.

3. The control method according to claim 1, characterized in that, In the control law update decision, priority is given to determining whether the observation error meets the online judgment condition for entering the extended invariant set, including: Using existing methods, an alternative observation state is constructed based on boundary operations between the observation error invariant set and the control error invariant set; the control error invariant set is then reconstructed based on the alternative observation state. Obtain the offline calculated and interpolated sequence of observation error invariant set and control error invariant set to determine the extended invariant set; Determine whether the observation error at the current moment enters the extended invariant set; If the extended invariant set is entered, it is determined that the online judgment condition is met, and the first update is executed; If the extended invariant set is not entered, it is determined that the online judgment condition is not met, and it is further determined whether the tracking error meets the static event triggering condition or the dynamic event triggering condition, so as to decide whether to execute the second update.

4. The control method according to claim 3, characterized in that, Performing the first update includes: In response to the observation error entering the extended invariant set, update the alternative observation set and the control error invariant set based on the alternative observation set; A first linear matrix inequality form of constrained optimization problem is constructed. The first linear matrix inequality form of constrained optimization problem contains three constraints, namely the input constraint of the tightened control error invariant set, the initial error invariant set constraint of the system state, and the robust stability constraint for all multicell vertices. Solve the constrained optimization problem in the form of the first linear matrix inequality to update the nominal control gain.

5. The control method according to claim 3, characterized in that, Determining whether the tracking error meets the static event triggering condition or the dynamic event triggering condition to decide whether to execute the second update includes: When the tracking error is greater than a preset static threshold, it is determined that the static event triggering condition is met; When the tracking error is greater than the dynamic threshold that is dynamically adjusted based on the error history value, it is determined that the dynamic event triggering condition is met. In response to the satisfaction of the static event triggering condition or the dynamic event triggering condition, a constraint optimization problem in the form of a second linear matrix inequality is constructed and solved to update the nominal control gain; After updating the nominal control gain, a transition time is introduced to limit the earliest time when the next update will be triggered. satisfy: in, and It is a constant. Sampling time, This is the reference trajectory.

6. The control method according to claim 1, characterized in that, The method further includes: The nominal control input, auxiliary control input, and time-delay compensation control input are superimposed to generate the final control input. The nominal control input is generated based on the nominal system tracking the reference trajectory; The auxiliary control input is generated by a robust feedback control law based on the error between the alternative observed state and the nominal state. The time delay compensation control input is generated based on the estimated value of the input time delay; The final control input is applied to the dynamic system to achieve robust tracking control of the reference trajectory.

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