Trajectory tracking oriented key layer performance constraint structure simplification control method and system

Abstract

The application discloses a trajectory tracking-oriented key layer performance constraint structure simplification control method and system, relates to the technical field of nonlinear control and intelligent control, and constructs a state model of a dynamic trajectory tracking system and defines a reference trajectory and a tracking error. A first tracking error directly representing a control target is taken as a key tracking error layer, a preset performance boundary constraint is applied to the key tracking error layer, a shift transformation error and a barrier function are constructed, a regular control structure is maintained for a subsequent recursive layer, an actual control law and a parameter adaptive law are constructed, and continuous control input is generated. The continuous control input is taken as ideal control input, when a trigger condition is met, the control input is updated and applied to a controlled object, otherwise, the control input at the last moment is kept unchanged, and a closed-loop control process is formed. The application can reduce the complexity of a multilayer recursive control structure, reduce the number of control updates, ensure that the core tracking error meets the preset performance requirements, and improve the system operation efficiency.

Description

Technical Field

[0001] This invention relates to the field of nonlinear control and intelligent control technology, and in particular to a simplified control method and system for key layer performance constraint structures for trajectory tracking. Background Technology

[0002] Dynamic trajectory tracking control is an important area of ​​nonlinear system control and intelligent control, widely used in scenarios such as unmanned aerial vehicles (UAVs), mobile robots, intelligent vehicles, and electromechanical systems. To improve system tracking accuracy, response speed, and resource utilization efficiency, methods such as preset performance control, backstepping control, adaptive fuzzy control, and event-triggered control are widely adopted. However, traditional multi-level recursive control, when introducing performance constraints, often requires constructing error transformations and virtual control laws layer by layer, easily leading to structural complexity, parameter coupling, and increased computational burden. Therefore, how to reduce the complexity of the control structure while ensuring that the core tracking error is limited has become a key issue in the engineering application of dynamic trajectory tracking control.

[0003] In their paper "Adaptive Prescribed-Time Tracking Control for Strict-Feedback Nonlinear Systems: A Novel Full Errors Approach" published in IEEE Transactions on Systems, Man, and Cybernetics: Systems (IEEE Trans. Syst., Man, Cybern., Syst., 55(10), 6684–6695, 2025), Zhang et al. proposed a full-error prescribed-time tracking control method for strictly feedback nonlinear systems. This method combines an improved shift function with a barrier Lyapunov function to ensure that errors at each level of the system can enter a specified accuracy range within a preset time, and compensates for composite disturbances through a disturbance observer. However, this scheme still requires the introduction of error transformation, barrier Lyapunov function, virtual control law, and adaptive law in the multi-level recursive control process, resulting in a complex control structure and making it difficult to avoid the implementation burden caused by multi-level constraints.

[0004] In their paper "Prescribed-time event-triggered control of multi-agent systems based on continuous scaling function" (J. Franklin Inst., 362, 107399, 2025), Hou et al. proposed a multi-agent prescribed-time event-triggered control method based on a continuous scaling function. This method constructs a continuous bounded scaling function to avoid abrupt changes in control output that might be caused by discontinuous scaling functions, and combines an event-triggered mechanism to reduce the frequency of communication and control updates. However, this scheme mainly addresses the first-order multi-agent consensus problem and has not yet solved the problems of complex multi-layer recursive control structures and nested performance constraints in second-order dynamic trajectory tracking systems.

[0005] In their paper "Simplified adaptive backstepping control for uncertain nonlinear systems with unknown input saturation and its application" published in *Control Engineering Practice* (Control Eng. Pract., 139, 105639, 2023), Liu et al. proposed a simplified adaptive backstepping control method for uncertain nonlinear systems with unknown input saturation. This method eliminates the need for actual computation of the virtual stability function and its derivatives, and reduces the computational burden through a first-order compensation subsystem, adaptive control, and variable condensation techniques. However, this scheme primarily addresses the computational complexity and input saturation issues of backstepping control, and does not yet consider the selection of key error layers under pre-defined performance constraints or the simplification of multi-layer performance constraint structures.

[0006] The shortcomings of existing technologies are as follows:

[0007] Although the existing technology 1 (Zhang et al., 2025) has achieved full error predetermined time tracking control of strictly feedback nonlinear systems, its control design still requires constructing error transformation, barrier Lyapunov function, virtual control law and adaptive law along a multi-layer recursive structure, which makes the control structure more complex and the burden of parameter tuning and real-time implementation heavier.

[0008] While existing technology 2 (Hou et al., 2025) combines continuous scaling functions with event triggering mechanisms to reduce the frequency of control output mutations and trigger updates in multi-agent consensus control, it mainly addresses first-order consensus problems and fails to solve the problems of complex multi-layer recursive control structures and layer-by-layer nested performance constraints in second-order dynamic trajectory tracking systems.

[0009] While existing technology 3 (Liu et al., 2023) reduces the computational burden of the virtual stable function and its derivative by simplifying adaptive backstepping control, its focus is on dealing with the problems of unknown input saturation and complex backstepping calculations. It does not incorporate preset performance constraints into the structural simplification framework and lacks the design of key error layer selection and local performance constraint mechanisms.

[0010] Therefore, existing multi-layer performance-constrained recursive control methods suffer from problems such as nested error transformations, complex control law structures, heavy parameter tuning burdens, and significant online computational pressure. Summary of the Invention

[0011] To address the aforementioned technical problems, the main objective of this invention is to provide a simplified control method for key layer performance constraint structures in trajectory tracking. The core technical problem to be solved is how to apply performance constraints only to the key tracking error layer that directly represents the control objective in dynamic trajectory tracking control, while maintaining a relatively simple control structure for subsequent recursive layers. This reduces the controller design complexity, parameter coupling degree, and real-time implementation burden while ensuring that the core tracking error meets the preset performance requirements.

[0012] Another objective of this invention is to propose a simplified control system with a key layer performance constraint structure for trajectory tracking.

[0013] To achieve the above objectives, a first aspect of the present invention proposes a simplified control method for the key layer performance constraint structure in trajectory tracking, comprising: S101, Construct the state model of the dynamic trajectory tracking system and define the reference trajectory and tracking error; S102, the first layer of tracking error that directly represents the control target is taken as the key tracking error layer, a preset performance boundary constraint is applied to the key tracking error layer, and a shift transformation error and a barrier Lyapunov function are constructed to keep the key tracking error within the preset performance boundary. S103: After completing the performance constraint design at the critical layer, the conventional control structure is maintained for the subsequent recursive layers. The fuzzy logic system is used to approximate the unknown nonlinear terms. The actual control law and parameter adaptive law are constructed by combining the backstepping design idea to generate continuous control input. S104. Based on the relative threshold event triggering mechanism, the continuous control input is used as the ideal control input. When the triggering condition is met, the control input is updated and applied to the controlled object. Otherwise, the control input at the previous moment remains unchanged, forming a closed-loop control process.

[0014] In one embodiment of the present invention, the construction of the state model of the dynamic trajectory tracking system and the definition of the reference trajectory and tracking error include: Establish a second-order dynamic system model, where the position state and velocity state are denoted as , ... and The control input is denoted as The control gain is denoted as The unknown nonlinear term is denoted as Bounded perturbation terms are denoted as The system output is recorded as The second-order dynamic system model is expressed as: , , ; Define reference trajectory and based on the reference trajectory and the position state Define the first layer tracking error Based on the speed state First-level virtual control law and the derivative of the reference trajectory Define the second layer tracking error .

[0015] In one embodiment of the present invention, S102 includes: The first layer tracking error As a key tracking error layer, a time-varying displacement function is employed. Describe how the allowable error range changes over time; Constructing shift transformation error The original tracking error is mapped to the constrained space through a shift function; Constructing a key layer barrier Lyapunov function Based on this, the first-level virtual control law was designed. .

[0016] In one embodiment of the present invention, the Lyapunov function for constructing the critical layer barrier is:

[0017] in, To preset performance boundary parameters, The shift transformation error is denoted as .

[0018] In one embodiment of the present invention, S103 includes: Constructing the second-level Lyapunov function ,in For critical layer barriers, use the Lyapunov function. For the second layer tracking error, For adaptive gain, This represents the fuzzy weight estimation error. Using fuzzy logic systems to approximate unknown nonlinear terms ,in For the ideal weight vector, Its estimated value, For fuzzy basis function vectors, This is the fuzzy approximation error; Based on the backstepping design concept, and combined with the fuzzy approximation results, the actual control law and parameter adaptive law are designed to obtain the continuous control input.

[0019] In one embodiment of the present invention, the method of approximating the unknown nonlinear term using a fuzzy logic system is described. In the context, the fuzzy basis function vector Input This includes system state and control-related variables.

[0020] In one embodiment of the present invention, S104 includes: The relative threshold event trigger condition is designed as follows: ,in This represents the deviation between the ideal control input at the current moment and the actual control input at the previous trigger moment. and For trigger parameters; Based on the relative threshold event triggering condition, the continuous control input is taken as the ideal control input. When the triggering condition is met, the control input is updated and applied to the controlled object. When the triggering condition is not met, the control input at the previous moment remains unchanged.

[0021] In one embodiment of the present invention, the relative threshold event triggering condition In the context, the triggering parameters The triggering parameter is a relative threshold coefficient. This is the absolute threshold constant.

[0022] In one embodiment of the present invention, after S104, the system further includes: before the next event triggering time arrives, the control input remains the control value of the previous triggering time; when the triggering condition is met, the system re-executes S102 to S104 to update the key tracking error, fuzzy parameters and control input, forming a closed-loop control process.

[0023] To achieve the above objectives, a second aspect of the present invention proposes a simplified control system with key layer performance constraints for trajectory tracking, comprising: The state model building module is used to build the state model of the dynamic trajectory tracking system and define the reference trajectory and tracking error; The boundary constraint setting module is used to take the first layer of tracking error that directly represents the control target as the key tracking error layer, apply a preset performance boundary constraint to the key tracking error layer, and construct the shift transformation error and barrier Lyapunov function to keep the key tracking error within the preset performance boundary. The control input generation module is used to maintain the conventional control structure for subsequent recursive layers after the performance constraint design is completed at the critical layer. It also uses a fuzzy logic system to approximate unknown nonlinear terms, and combines the backstepping design idea to construct the actual control law and parameter adaptive law to generate continuous control input. The ideal control input determination module is used to take the continuous control input as the ideal control input based on the relative threshold event triggering mechanism. When the triggering condition is met, the control input is updated and applied to the controlled object; otherwise, the control input at the previous moment remains unchanged, forming a closed-loop control process.

[0024] The simplified control method and system for key layer performance constraint structure in trajectory tracking according to embodiments of the present invention reduces the complexity of multi-layer recursive control structure and the control update burden by concentrating performance constraints on the key tracking error layer and combining a fuzzy logic system and a relative threshold event triggering mechanism.

[0025] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0026] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 A flowchart of a simplified control method for key layer performance constraint structure for trajectory tracking provided in an embodiment of the present invention; Figure 2 A logic diagram of a simplified control method for key layer performance constraint structure in trajectory tracking, provided in an embodiment of the present invention; Figure 3 This is a performance comparison chart between the present invention and the traditional two-layer performance constraint control method; Figure 4 This is a structural diagram of a simplified control system for key layer performance constraints in trajectory tracking, provided as an embodiment of the present invention. Detailed Implementation

[0027] 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.

[0028] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0029] The following describes, with reference to the accompanying drawings, a simplified control method and system for key layer performance constraint structures in trajectory tracking, according to an embodiment of the present invention.

[0030] This embodiment provides a simplified control method for the key layer performance constraint structure in trajectory tracking. For example... Figure 1 As shown, it includes: S101, construct the state model of the dynamic trajectory tracking system, and define the reference trajectory and tracking error.

[0031] Constructing a state model for a dynamic trajectory tracking system is a fundamental step in implementing subsequent control methods. This step first establishes a mathematical model of the dynamic characteristics of the controlled object. This model must at least include state variables characterizing the system's motion state and their evolutionary relationships to describe the system's behavior in the time domain. Based on this, the desired motion trajectory is set as a reference signal; this reference trajectory is typically a time function or generated by external commands.

[0032] Subsequently, based on the deviation between the actual system state and the reference trajectory, a tracking error variable is defined to characterize the control objective. This tracking error directly reflects the degree to which the system output follows the desired trajectory and is the core variable upon which subsequent performance constraints and control law design are based. As one implementation method, a second-order dynamic system model including position and velocity states can be established. Its state equations describe the differential relationship between the two, and control inputs, unknown nonlinear terms, and bounded disturbance terms are introduced to reflect the actual characteristics of the system. Simultaneously, the position tracking error is defined as the difference between the system output and the reference trajectory, and the velocity tracking error is further defined as the difference between the velocity state and the derivatives of the virtual control law and the reference trajectory, thus forming an error hierarchy structure for recursive control design.

[0033] By constructing a system state model and clearly defining the tracking error, a clear mathematical foundation and control objective are provided for the application of performance constraints at the subsequent critical layer and the design of the recursive controller. This transforms the control problem into an adjustment problem that ensures the tracking error meets the preset performance requirements, thereby ensuring the pertinence and effectiveness of the control design.

[0034] S102, the first layer of tracking error that directly represents the controlled target is taken as the key tracking error layer, a preset performance boundary constraint is applied to the key tracking error layer, and a shift transformation error and a barrier Lyapunov function are constructed to keep the key tracking error within the preset performance boundary.

[0035] In dynamic trajectory tracking control, to reduce the complexity of the multi-layer recursive control structure while ensuring core tracking performance, this step designates the first-layer tracking error, which directly represents the control target, as the critical tracking error layer, and implements performance constraint design around this critical layer. Specifically, by setting a preset performance boundary for the critical tracking error layer, this boundary defines the allowable dynamic range of error variation, thereby ensuring that the tracking error does not exceed the set limit in both transient and steady-state phases.

[0036] Building upon this, a shift transformation error is constructed. This transformation maps the original tracking error to a constrained space, ensuring that the transformed error variable reflects the relative position of the original error with respect to the performance boundary. This provides the foundation for the subsequent design of the barrier Lyapunov function. The barrier Lyapunov function is constructed as a function of the shift transformation error, characterized by its tendency towards infinity as the shift transformation error approaches the performance boundary. Lyapunov stability analysis forces the error to remain within the preset boundary. Through this design, performance constraints are applied only to the critical error layer, eliminating the need to repeatedly construct similar constraint mechanisms in subsequent recursive layers. This significantly simplifies the control structure while ensuring that the core tracking error meets the preset performance requirements.

[0037] As one implementation method, a time-varying displacement function can be selected to describe the change process of the allowable error range over time, and a shift transformation error can be constructed based on this function. For example, the shift transformation error can be made into the product of the time-varying displacement function and the first-layer tracking error. Then, a critical layer barrier Lyapunov function can be constructed, and the first-layer virtual control law can be designed accordingly to achieve constraint control of the critical tracking error.

[0038] This step focuses performance constraints on the key tracking error layer, avoiding the nesting of performance constraints in multi-layer recursive control. While ensuring that the core tracking error meets the preset performance requirements, it significantly reduces the controller design complexity, parameter coupling degree and real-time implementation burden, achieving an effective balance between control performance and structural simplification.

[0039] S103, after completing the performance constraint design at the critical layer, maintains the conventional control structure for the subsequent recursive layers, and uses a fuzzy logic system to approximate the unknown nonlinear terms. Combined with the backstepping design idea, it constructs the actual control law and the parameter adaptive law to generate continuous control input.

[0040] After completing the performance constraint design at the critical layer, this method adopts a design strategy that maintains the conventional control structure for subsequent recursive layers. That is, it does not impose additional performance boundary constraints or construct shift transformation errors for the errors at this layer, but instead directly constructs a recursive control framework based on the system state and the virtual control law. Specifically, by constructing a composite Lyapunov function that includes the critical layer barrier Lyapunov function and the quadratic error term of the subsequent recursive layers, a stability analysis foundation is laid for the subsequent control law design.

[0041] Simultaneously, a fuzzy logic system is used to approximate the unknown nonlinear dynamics in the system online. The unknown nonlinear term is represented as the inner product of the ideal weight vector and the fuzzy basis function vector, plus the bounded approximation error. A weight estimation vector is introduced to update the approximation parameters in real time. Based on this, combined with the backstepping design concept and the derivative analysis results of the composite Lyapunov function, an actual control law and parameter adaptive law are designed to ensure that the system remains stable under the influence of unknown nonlinearities and bounded disturbances, and to generate continuous control input signals.

[0042] As one implementation method, in a second-order dynamic trajectory tracking system, the second-layer Lyapunov function corresponding to the subsequent recursive layer can be constructed as follows: ,in For critical layer barriers, use the Lyapunov function. For the second level of error variables, For fuzzy weight estimation error; unknown nonlinear term Through fuzzy logic system An approximation is performed, and based on this, the actual control law and parameter adaptive law are designed to obtain continuous control input.

[0043] This step concentrates performance constraints on the critical layer, allowing subsequent recursive layers to maintain a conventional control structure. This avoids the repeated introduction of multi-layer performance constraints and the nesting of error transformations, significantly reducing the complexity of controller design and the degree of parameter coupling. At the same time, by combining the fuzzy logic system's ability to approximate unknown nonlinearities, the derivation process of the control law is simplified while ensuring system stability and tracking accuracy, thus improving the feasibility and efficiency of engineering implementation.

[0044] S104. Based on the relative threshold event triggering mechanism, the continuous control input is used as the ideal control input. When the triggering condition is met, the control input is updated and applied to the controlled object. Otherwise, the control input at the previous moment remains unchanged, forming a closed-loop control process.

[0045] Building upon the continuous control input generation based on a recursive control structure, an event-triggered mechanism is further introduced to optimize the control update strategy. The core of this mechanism lies in constructing a trigger condition based on a relative threshold. This condition determines whether the deviation between the ideal control input at the current moment and the actual control input applied to the controlled object at the previous moment exceeds a preset allowable range. Specifically, this trigger condition determines whether to trigger an update by comparing the absolute value of the deviation with a dynamic threshold consisting of a linear scaling term of the current control input amplitude plus a fixed offset. When the deviation exceeds this dynamic threshold, the system determines that the current control input has deviated from the ideal value to a degree requiring correction, and then updates the actual control input and applies it to the controlled object. Conversely, if the deviation does not exceed the threshold, the control input at the previous trigger moment remains unchanged, avoiding unnecessary control updates. In this way, the event-triggered mechanism only initiates updates when the system state changes significantly or the control requirements undergo substantial changes, thereby significantly reducing the calculation frequency of control inputs and the number of actuator actions while ensuring the stability and tracking performance of the closed-loop system.

[0046] As one implementation method, the relative threshold event triggering condition can be specifically constructed as follows: the next triggering time is defined as the minimum time point at which the absolute value of the deviation is greater than or equal to the control input amplitude multiplied by a proportional coefficient plus a positive offset, where both the proportional coefficient and the offset are adjustable parameters used to balance trigger sensitivity and update frequency. This mechanism works in conjunction with the aforementioned recursive control structure to form a closed-loop control process: during the non-triggered period, the system uses the control input from the previous moment, and once the triggering condition is met, it immediately updates using the currently generated ideal control input and restarts the next round of trigger judgment.

[0047] This step introduces a relative threshold event triggering mechanism to achieve adaptive adjustment of the control update frequency. While maintaining the key tracking error to meet preset performance constraints, it effectively reduces the number of unnecessary control updates, thereby reducing the online calculation burden of the controller, actuator wear and communication bandwidth occupation, and improving the resource utilization efficiency and engineering practicality of the system.

[0048] In this embodiment, after step S104, the system enters the specific execution stage of the closed-loop control process. Specifically, before the next event triggering time arrives, the control input remains the control value of the previous triggering time, that is, the system continuously applies this fixed control signal to the controlled object without performing any update operations. When the system operating state meets the constructed relative threshold event triggering condition, that is, when the absolute value of the control error reaches or exceeds the triggering boundary determined by the sum of the current absolute value of the control input and the fixed threshold, the system triggers the event. At this point, the system re-executes steps S102 to S104. First, based on the current system state and reference trajectory, it recalculates the first-layer tracking error, applies preset performance boundary constraints, constructs a shift transformation error and a barrier Lyapunov function, and then updates the first-layer virtual control law. Subsequently, in subsequent recursive layers, based on the updated virtual control law and the current system state, a fuzzy logic system is used to reapproximate the unknown nonlinear term, and the parameter adaptive law is updated, thereby generating a new continuous control input. Finally, based on this new continuous control input, combined with a relative threshold event triggering mechanism, it determines whether the triggering condition is met. If it is, the new continuous control input is applied to the controlled object as the actual control input; otherwise, the control value at the previous triggering moment remains unchanged. Through this process, the system synchronously updates the key tracking error, fuzzy parameters, and control input at each event triggering moment, forming a closed-loop control process. This effectively reduces the number of control updates, lowers the computational burden, and reduces the actuator update frequency while ensuring that the key tracking error always meets the preset performance requirements.

[0049] This specific implementation method, by clarifying the closed-loop update process after event triggering, realizes the coordinated operation of key layer performance constraint control and event triggering mechanism. While ensuring core tracking performance, it significantly reduces the online computing burden and implementation complexity of the controller, and improves the engineering application efficiency of the system.

[0050] Example 2 Figure 2 Here is a logic diagram of a simplified control method for key layer performance constraint structure in trajectory tracking according to the present invention, as shown below. Figure 2 As shown: Taking a second-order dynamic trajectory tracking task as an example, the technical solution of this invention mainly includes the following steps: S1. Construct a dynamic trajectory tracking system model; S2. Design of performance constraints for critical layers; S3. Simplified recursive controller design; S4. Design of relative threshold event triggering mechanism; S5. Control execution and closed-loop update.

[0051] Furthermore, step S1 specifically includes the following steps: S11. Establish a second-order dynamic system model:

[0052] in, and These represent the position state and velocity state, respectively. To control the input, To control the gain, For unknown nonlinear terms, For a bounded perturbation term, This is the system output.

[0053] S12. Define the reference trajectory and tracking error:

[0054] Furthermore, step S2 specifically includes the following steps: S21. The first layer of tracking error is taken as the key tracking error layer, and the time-varying displacement function is used. Used to describe how the allowable error range changes over time.

[0055] S22. Constructing shift transformation error: ； By using a shift function, the original tracking error is mapped to a constrained space, ensuring that the critical tracking error remains within the preset performance boundaries.

[0056] S23. Construct the Lyapunov function for the key layer:

[0057] Based on this, the first-level virtual control law was designed. .

[0058] Furthermore, step S3 specifically includes the following steps: S31. Construct the second layer of Lyapunov functions:

[0059] S32. Using a fuzzy logic system to approximate unknown nonlinear terms:

[0060] in, For the ideal weight vector, Its estimated value, For fuzzy basis function vectors, This represents the fuzzy approximation error.

[0061] S33. Construct a recursive controller; based on the backstepping design concept, design the actual control law and parameter adaptive law by combining the fuzzy approximation results, and obtain the continuous control input.

[0062] Furthermore, step S4 specifically includes the following steps: S41. The relative threshold event triggering condition is designed as follows:

[0063] S42. Generate actual control inputs: Based on the relative threshold event triggering condition constructed in step S41, the continuous control law designed in step S3 is used as the ideal control input. When the triggering condition is met, the control input is updated and applied to the controlled object; when the triggering condition is not met, the control input from the previous moment remains unchanged.

[0064] Furthermore, step S5 specifically includes the following steps: Before the next event trigger time arrives, the control input remains at the control value of the previous trigger time. When the trigger condition is met, the system re-executes steps S2 to S4, updates the key tracking error, fuzzy parameters, and control input, forming a closed-loop control process. This ensures that the key layer error meets the preset performance requirements while reducing the number of control updates and lowering the system implementation complexity.

[0065] In summary, this invention constructs a key-layer performance constraint control framework. In the multi-layer recursive control process, the first-layer tracking error, which directly represents the control objective, is taken as the key error layer. Performance boundaries, shift transformation errors, and barrier Lyapunov functions are constructed around this key error layer to ensure that the key tracking error remains within the preset performance boundaries. After completing the performance constraint design at the key layer, subsequent recursive layers maintain the conventional control structure and, combined with a fuzzy logic system, approximate unknown nonlinear terms to further design the actual control law and parameter adaptive law. This construction method concentrates performance constraints at the key error layer and nonlinear compensation and actual control input design at the subsequent recursive layers, achieving a structured division of labor among performance constraints, recursive control, and unknown nonlinear compensation. This invention combines the key-layer performance constraint control framework with a relative threshold event triggering mechanism. It generates actual control inputs based on continuous control laws and updates the control inputs when the event triggering conditions are met; otherwise, it keeps the control inputs unchanged from the previous triggering moment. This mechanism can reduce unnecessary control updates and lower the computational burden and actuator update frequency while ensuring that the key tracking error meets the preset performance requirements.

[0066] Furthermore, Figure 3This chart shows the performance comparison results between the present invention and the traditional two-layer performance constraint control method. The top left figure compares the root mean square error (RMSE) of tracking, the top right figure compares the settling time, the bottom left figure compares the total number of control updates (Total Triggers), and the bottom right figure compares the average computing time.

[0067] Furthermore, compared with the prior art, the simplified recursive control structure method based on key layer performance constraints proposed in this invention has the following beneficial effects: This invention achieves a synergistic design that balances performance constraints and structural simplification. Performance constraints are concentrated on the critical tracking error layer, which directly characterizes the control objective. Performance boundary constraints and error transformations are applied only to the critical layer error, while subsequent recursive layers maintain a conventional control structure. This design avoids the repeated introduction of performance constraints in multi-layer recursion processes. While ensuring that the critical tracking error meets preset performance requirements, it significantly reduces the controller's structural complexity, achieving an effective balance between control performance and structural simplification.

[0068] This invention reduces control design complexity and improves engineering implementation capabilities. It focuses performance constraint design around the critical tracking error layer, concentrating the main control objectives on the core error variables, thus making the controller design process clearer. By reducing the number of multi-layer performance function construction, multi-layer error transformation, and related parameter design steps, it lowers the difficulty of controller development, parameter tuning, and engineering deployment, improving the feasibility and implementation efficiency of the method in practical control systems.

[0069] This invention improves operational efficiency while maintaining tracking performance. Based on a simplified recursive control framework, it introduces a relative threshold event triggering mechanism, enabling control inputs to be updated on demand according to the system's operating state. This method reduces unnecessary control updates and computational resource consumption while keeping critical tracking errors limited and ensuring stable system operation, achieving a coordinated optimization between tracking performance and operational efficiency, and possesses significant engineering application value.

[0070] To implement the methods of the above embodiments, the present invention also provides a simplified control system 10 with key layer performance constraint structure for trajectory tracking, such as... Figure 4 As shown, it includes: The state model construction module 100 is used to construct the state model of the dynamic trajectory tracking system and define the reference trajectory and tracking error; The boundary constraint setting module 200 is used to take the first layer of tracking error that directly represents the control target as the key tracking error layer, apply a preset performance boundary constraint to the key tracking error layer, and construct the shift transformation error and barrier Lyapunov function so that the key tracking error is always kept within the preset performance boundary. The control input generation module 300 is used to maintain the conventional control structure for subsequent recursive layers after the performance constraint design is completed at the critical layer. It also uses a fuzzy logic system to approximate unknown nonlinear terms, and combines the backstepping design idea to construct the actual control law and parameter adaptive law to generate continuous control input. The ideal control input determination module 400 is used to take the continuous control input as the ideal control input based on the relative threshold event triggering mechanism. When the triggering condition is met, the control input is updated and applied to the controlled object; otherwise, the control input at the previous moment remains unchanged, forming a closed-loop control process.

[0071] The simplified control system based on the key layer performance constraint structure for trajectory tracking in this invention is designed for dynamic trajectory tracking control tasks. By concentrating performance constraints on the key error layer that directly characterizes the control objective, it reduces the complexity and implementation burden of multi-layer recursive control design while ensuring core tracking performance.

[0072] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0073] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0074] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A method for trajectory tracking oriented key layer performance constraint structure simplification control, characterized in that, include: S101, Construct the state model of the dynamic trajectory tracking system and define the reference trajectory and tracking error; S102, the first layer of tracking error that directly represents the control target is taken as the key tracking error layer, a preset performance boundary constraint is applied to the key tracking error layer, and a shift transformation error and a barrier Lyapunov function are constructed to keep the key tracking error within the preset performance boundary. S103: After completing the performance constraint design at the critical layer, the conventional control structure is maintained for the subsequent recursive layers. The fuzzy logic system is used to approximate the unknown nonlinear terms. The actual control law and parameter adaptive law are constructed by combining the backstepping design idea to generate continuous control input. S104. Based on the relative threshold event triggering mechanism, the continuous control input is used as the ideal control input. When the triggering condition is met, the control input is updated and applied to the controlled object. Otherwise, the control input at the previous moment remains unchanged, forming a closed-loop control process.

2. The method as described in claim 1, characterized in that, The state model for constructing the dynamic trajectory tracking system, and the definition of the reference trajectory and tracking error, includes: Establish a second-order dynamic system model, where the position state and velocity state are denoted as , ... and The control input is denoted as The control gain is denoted as The unknown nonlinear term is denoted as Bounded perturbation terms are denoted as The system output is recorded as The second-order dynamic system model is expressed as: , , ; Define reference trajectory and based on the reference trajectory and the position state Define the first layer tracking error Based on the speed state First-level virtual control law and the derivative of the reference trajectory Define the second layer tracking error .

3. The method as described in claim 1, characterized in that, S102 includes: The first layer tracking error As a key tracking error layer, a time-varying displacement function is employed. Describe how the allowable error range changes over time; Constructing shift transformation error The original tracking error is mapped to the constrained space through a shift function; Constructing a key layer barrier Lyapunov function Based on this, the first-level virtual control law was designed. .

4. The method as described in claim 3, characterized in that, The Lyapunov function for constructing the key layer barrier is as follows: in, To preset performance boundary parameters, The shift transformation error is denoted as .

5. The method as described in claim 1, characterized in that, S103 includes: Constructing the second-level Lyapunov function ,in For critical layer barriers, use the Lyapunov function. For the second layer tracking error, For adaptive gain, This represents the fuzzy weight estimation error. Using fuzzy logic systems to approximate unknown nonlinear terms ,in For the ideal weight vector, Its estimated value, For fuzzy basis function vectors, This is the fuzzy approximation error; Based on the backstepping design concept, and combined with the fuzzy approximation results, the actual control law and parameter adaptive law are designed to obtain the continuous control input.

6. The method as described in claim 5, characterized in that, The fuzzy logic system is used to approximate the unknown nonlinear term. In the context, the fuzzy basis function vector Input This includes system state and control-related variables.

7. The method as described in claim 1, characterized in that, S104 includes: The relative threshold event trigger condition is designed as follows: ,in This represents the deviation between the ideal control input at the current moment and the actual control input at the previous trigger moment. and For trigger parameters; Based on the relative threshold event triggering condition, the continuous control input is taken as the ideal control input. When the triggering condition is met, the control input is updated and applied to the controlled object. When the triggering condition is not met, the control input at the previous moment remains unchanged.

8. The method as described in claim 7, characterized in that, The relative threshold event triggering condition In the context, the triggering parameters The triggering parameter is a relative threshold coefficient. This is the absolute threshold constant.

9. The method as described in claim 1, characterized in that, Following S104, the system further includes: before the next event triggering time arrives, the control input remains the control value of the previous triggering time; when the triggering condition is met, the system re-executes S102 to S104, updates the key tracking error, fuzzy parameters and control input, and forms a closed-loop control process.

10. A simplified control system with key-layer performance constraints for trajectory tracking, characterized in that, include: The state model building module is used to build the state model of the dynamic trajectory tracking system and define the reference trajectory and tracking error; The boundary constraint setting module is used to take the first layer of tracking error that directly represents the control target as the key tracking error layer, apply a preset performance boundary constraint to the key tracking error layer, and construct the shift transformation error and barrier Lyapunov function to keep the key tracking error within the preset performance boundary. The control input generation module is used to maintain the conventional control structure for subsequent recursive layers after the performance constraint design is completed at the critical layer. It also uses a fuzzy logic system to approximate unknown nonlinear terms, and combines the backstepping design idea to construct the actual control law and parameter adaptive law to generate continuous control input. The ideal control input determination module is used to take the continuous control input as the ideal control input based on the relative threshold event triggering mechanism. When the triggering condition is met, the control input is updated and applied to the controlled object; otherwise, the control input at the previous moment remains unchanged, forming a closed-loop control process.

Images