Open-loop adaptive implementation method and system for state-dependent switched systems

Abstract

The application provides an open-loop adaptive implementation method and system of a state-dependent switching system, comprising the following steps: S1: based on a switching system dynamics model, using a boundary method vector and a vector field to judge the passability of a motion flow, and judging whether the current motion flow can be smoothly switched based on the passability of the motion flow; S2: when the motion flow cannot be smoothly switched, a full-drive dominant controller is selected based on a controller in the current switching system dynamics model; and S3: open-loop correction and open-loop compensation operations are sequentially performed on the current full-drive dominant controller, so that the motion flow is smoothly switched at the boundary.

Description

Technical Field

[0001] This invention relates to the field of switching system control, and more specifically, to an open-loop adaptive implementation method and system for state-dependent switching systems. Background Technology

[0002] In the nonlinear analysis and controller design of complex systems, the theory and research results of switching systems have been widely applied. For example, amphibious unmanned aerial vehicles (UAVs) with variable structure attitude control can simultaneously address abrupt changes in mechanical structure and operating environment. While shape memory alloy-based actuators leverage their high power-to-weight ratio and lightweight design, the highly nonlinear characteristics of hysteresis loops and constitutive models cannot be ignored. Improper control at the switching boundary can induce boundary flutter in the kinetic flow, adversely affecting the actuator and causing problems such as motor overheating and shape memory alloy aging. Significant challenges remain in state-dependent switching systems.

[0003] 1. Uncertainty of model parameters

[0004] Subsystems have numerous parameters, and some assumptions and simplifications may prevent the establishment of high-fidelity dynamic models. For example, motors are typically modeled as a relationship between current and output torque, but under long-term operation, gear clearance and fluctuations in operating temperature have a certain impact on output torque, and some parameters are time-varying, leading to modeling errors. By constructing an adaptive method, the influence of model parameter uncertainties on the switching system control method can be suppressed.

[0005] 2. The unpredictability of the external environment

[0006] For some real-time-critical switching systems, such as when a satellite tracks and acquires a non-cooperative target, the unpredictable changes in the external environment lead to the unpredictability of the desired trajectory, i.e., the lack of feedback signals. Consequently, some feedback-based control algorithms cannot be effectively applied. Open-loop correction and compensation methods can avoid the unpredictability of the desired trajectory caused by sudden changes in the external environment.

[0007] 3. The universality and transferability of control methods

[0008] In the control problem of state-dependent switching systems, for a specific dynamic model, the choice between model-based control, feedback-based control, or learning-based control may face the problem of reconstructing the controller or retraining data when transferring it to other models. Its generalization and transferability are affected by the model structure. Developing a universal control method that can be effectively transferred to state-dependent switching systems with different structures and parameters has become an urgent problem to be solved. Summary of the Invention

[0009] To address the shortcomings of existing technologies, the purpose of this invention is to provide an open-loop adaptive implementation method and system for state-dependent switching systems.

[0010] An open-loop adaptive implementation method for a state-dependent switching system provided by the present invention includes:

[0011] Step S1: Based on the switching system dynamics model, use the boundary normal vector and vector field to determine the passability of the motion flow, and based on the passability of the motion flow, determine whether the current motion flow can switch smoothly.

[0012] Step S2: When a smooth switch is not possible, select the full-drive dominant controller based on the controller in the current switching system dynamics model;

[0013] Step S3: Perform open-loop correction and open-loop compensation operations on the current fully driven dominant controller in sequence to achieve smooth switching of motion flow at the boundary.

[0014] Preferably, step S1 employs:

[0015] Step S1.1: Initialize the switching system dynamics model and perform time-domain iteration;

[0016] The switching system dynamics model includes:

[0017]

[0018] in,

[0019] x is a switching system state vector of length N, where N≥2; f σ Describe the coupling relationships between switching system states; g σ Describe the relationship between the switching system state and the control input; u is the control input of the switching system; σ is the subspace domain in which the motion flow is located in the state space. When the motion flow crosses the boundary from one subspace domain to an adjacent subspace domain, the switching system completes the switching. σ With g σ Switch accordingly;

[0020] Step S1.2: Define the G function using the boundary normal vector and the vector field, as the moving flow approaches the boundary. Calculate the G function for each of two adjacent subspaces, and determine whether the motion flow can pass through based on the G function of the two adjacent subspaces;

[0021] Let Ω be any two adjacent subspaces. α and Ω β The intersection of two nonsets of subspaces is the boundary, denoted as . This boundary is defined by function l αβ () describes, when l αβWhen the sign of the parentheses changes, a system switch occurs; the switching set is the boundary. The tiny neighborhood in space is denoted as ∑αβ;

[0022] The boundary normal vector is denoted as From subspace domain Ω β Pointing to subspace Ω α :

[0023]

[0024] The boundary normal vector and the vector field pair G function, Define:

[0025]

[0026] When the flow of energy reaches the boundary If inequality (5) holds and the motion flow can switch smoothly, then the process ends; otherwise, if the motion flow cannot switch smoothly, then open-loop adaptive adjustment is performed.

[0027]

[0028] Preferably, step S2 employs: using the 2-norm ||·||2 and the infinity norm ||·|| ∞ Select the full-drive dominant controller based on the current switching system dynamics model;

[0029] Based on the 2-norm and the infinite norm ∞ Define the coefficient matrix H of the control input. αβ for:

[0030]

[0031] Select H αβ The two largest values ​​in the vector are represented by u. m and u n This is represented, and corresponds to controller u respectively. m and u n ;

[0032] When controller u m and u n China αm g βn ≠g αn g βm When, then the current controller u m and u n As the dominant controller for all drives.

[0033] Preferably, step S3 employs the following methods:

[0034] Step S3.1: Select control input u m and u n After establishing the dominant controller, keeping the other control inputs constant, open-loop compensation is performed on both, and the compensation values ​​are denoted as u. m1 and u n1 :

[0035]

[0036] Step S3.2: After the control input completes the open-loop correction, if there is no error in the switching system dynamics model, the impassable situation will disappear and the motion flow will not flutter at the boundary; if there is an error in the switching system dynamics model, the open-loop compensation module will be activated.

[0037] When errors exist in the switching system, an open-loop compensation is introduced to overcome the problem of vector field calculation distortion. Open-loop compensation is performed on the dominant controller, and the compensation value is denoted as u. m2 and u n2 :

[0038]

[0039] Where, γ αβ It is an adaptive operator.

[0040] Preferably, the adaptive operator γ can be adjusted through the adaptive algorithm module. αβ The system will be updated to further improve the effectiveness of open-loop control.

[0041] Adaptive operator γ αβ The initial value is γ αβ0 To select a constant value based on prior information about the switching system error, the adaptive operator γ... αβ The update method is shown in equation (9); where t αβ For the flow of motion at the boundary The duration of flutter; it begins when the self-flow enters the switching set ∑αβ and stops when the self-flow leaves the switching set ∑αβ;

[0042]

[0043] Where, λ αβ It is a positive number;

[0044] After open-loop correction, open-loop compensation, and adaptive algorithm, the proposed open-loop adaptive control input is... and for:

[0045]

[0046] An open-loop adaptive implementation system for a state-dependent switching system provided by the present invention includes:

[0047] Module M1: Based on the switching system dynamics model, it uses boundary normal vectors and vector fields to determine the passability of the motion flow, and based on the passability of the motion flow, it determines whether the current motion flow can switch smoothly.

[0048] Module M2: When a smooth switch is not possible, a fully driven dominant controller is selected based on the controller in the current switching system dynamics model;

[0049] Module M3: Performs open-loop correction and open-loop compensation operations on the current fully driven dominant controller in sequence to achieve smooth switching of motion flow at the boundary.

[0050] Preferably, module M1 adopts:

[0051] Module M1.1: Initializes the switching system dynamics model and performs time-domain iteration;

[0052] The switching system dynamics model includes:

[0053]

[0054] in,

[0055] x is a switching system state vector of length N, where N≥2; f σ Describe the coupling relationships between switching system states; g σ Describe the relationship between the switching system state and the control input; u is the control input of the switching system; σ is the subspace domain in which the motion flow is located in the state space. When the motion flow crosses the boundary from one subspace domain to an adjacent subspace domain, the switching system completes the switching. σ With g σ Switch accordingly;

[0056] Module M1.2: Defines the G function using the boundary normal vector and the vector field, as the moving flow approaches the boundary. Calculate the G function for each of two adjacent subspaces, and determine whether the motion flow can pass through based on the G function of the two adjacent subspaces;

[0057] Let Ω be any two adjacent subspaces. α and Ω β The intersection of two nonsets of subspaces is the boundary, denoted as . This boundary is defined by function l αβ (x) describes, when l αβ (x) When the sign changes, the switching system switches; the switching set is the boundary. The tiny neighborhood in space is denoted as ∑αβ;

[0058] The boundary normal vector is denoted as From subspace domain Ωβ Pointing to subspace Ω α :

[0059]

[0060] The boundary normal vector and the vector field pair G function, Define:

[0061]

[0062] When the flow of energy reaches the boundary If inequality (5) holds and the motion flow can switch smoothly, then the process ends; otherwise, if the motion flow cannot switch smoothly, then open-loop adaptive adjustment is performed.

[0063]

[0064] Preferably, module M2 adopts the following approach: utilizing the 2-norm ||·||2 and the infinite norm ||·|| ∞ Select the full-drive dominant controller based on the current switching system dynamics model;

[0065] Based on the 2-norm and the infinite norm ∞ Define the coefficient matrix H of the control input. αβ for:

[0066]

[0067] Select H αβ The two largest values ​​in the vector are represented by u. m and u n This is represented, and corresponds to controller u respectively. m and u n ;

[0068] When controller u m and u n China αm g βn ≠g αn g βm When, then the current controller u m and u n As the dominant controller for all drives.

[0069] Preferably, the module M3 adopts:

[0070] Module M3.1: Selected control input u m and u n After establishing the dominant controller, keeping the other control inputs constant, open-loop compensation is performed on both, and the compensation values ​​are denoted as u. m1 and u n1 :

[0071]

[0072] Module M3.2: After the control input completes open-loop correction, if there is no error in the switching system dynamics model, the impassable situation will disappear and the motion flow will not flutter at the boundary; if there is an error in the switching system dynamics model, the open-loop compensation module will be activated.

[0073] When errors exist in the switching system, an open-loop compensation is introduced to overcome the problem of vector field calculation distortion. Open-loop compensation is performed on the dominant controller, and the compensation value is denoted as u. m2 and u n2 :

[0074]

[0075] Where, γ αβ It is an adaptive operator.

[0076] Preferably, the adaptive operator γ can be adjusted through the adaptive algorithm module. αβ The system will be updated to further improve the effectiveness of open-loop control.

[0077] Adaptive operator γ αβ The initial value is γ αβ0 To select a constant value based on prior information about the switching system error, the adaptive operator γ... αβ The update method is shown in equation (9); where t αβ For the flow of motion at the boundary The duration of flutter; it begins when the self-flow enters the switching set ∑αβ and stops when the self-flow leaves the switching set ∑αβ;

[0078]

[0079] Where, λ αβ It is a positive number;

[0080] After open-loop correction, open-loop compensation, and adaptive algorithm, the proposed open-loop adaptive control input is... and for:

[0081]

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] 1. The open-loop adaptive manipulation method proposed in this patent is universally applicable to state-dependent switching systems, requiring no closed-loop feedback or desired trajectory, and the switching system model to be manipulated is universal. Based on the passability law of motion flow at the boundary, the control input is designed to effectively avoid chattering near the boundary during motion, providing a theoretical reference for open-loop control of switching systems.

[0084] 2. The open-loop adaptive manipulation method proposed in this patent is robust, allowing for errors in the switching system model. By constructing an adaptive algorithm, the upper limit of error can be estimated in real time, and the open-loop compensation part can be corrected simultaneously to achieve the switching of motion flow at the boundary. That is, errors in the switching system model will not cause the manipulation method of this patent to fail.

[0085] 3. The open-loop adaptive control method designed in this patent sequentially performs open-loop correction, open-loop compensation, and an adaptive algorithm on the control input. Open-loop correction can eliminate impassable conditions in the motion flow, open-loop compensation can overcome vector field calculation distortion caused by model errors to a certain extent, and the adaptive algorithm can further improve the robustness of the system. The combination of these three can effectively avoid chatter and ensure the effectiveness of open-loop control.

[0086] 4. This patent provides guidance for practical engineering applications, particularly for power systems exhibiting switching phenomena. In actual engineering, repeated flutter near boundaries can negatively impact actuators, causing problems such as motor overheating and shape memory alloy aging, thus affecting the lifespan of products or systems. This patent eliminates the need for pre-defined desired trajectories and allows for model errors, demonstrating good transferability in practical engineering applications. This patent aims to enable smooth switching of motion flow, providing guidance for power systems exhibiting switching phenomena, such as variator drones and shape memory alloy actuators. Attached Figure Description

[0087] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0088] Figure 1 Flowchart of an open-loop adaptive implementation method for a state-dependent switching system. Detailed Implementation

[0089] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0090] This invention focuses on state-dependent switching systems, where the boundaries between subsystems are defined by functions composed of states. The state space is divided into several subspace domains. When the motion flow reaches the boundary, if the vector fields are opposite, the motion flow may flutter on both sides of the boundary. High-frequency flutter can negatively impact the actuator, causing problems such as motor overload and shape memory alloy aging. Given the unknown desired trajectory and the existence of errors in the system model, this invention proposes an open-loop control input design to achieve smooth switching of the motion flow at the boundary. Simultaneously, the design process also considers the problem of vector field calculation distortion caused by system errors.

[0091] Example 1

[0092] This invention provides an open-loop adaptive implementation system and method for state-dependent switching systems, relating to the field of switching system control technology. The method includes: determining the passability of the motion flow based on the subspace domain and boundary, using the boundary normal vector and vector field, and identifying boundaries where chatter may occur in real time; selecting a fully driven dominant controller using the 2-norm and infinite norm, referencing the concept of dominant poles; introducing open-loop correction to eliminate the impassable conditions of the motion flow at the boundary; introducing open-loop compensation to overcome the problem of vector field calculation distortion caused by system errors; and introducing an adaptive algorithm to further ensure the open-loop control effect and improve system robustness. This invention can effectively avoid chatter in the motion flow at the boundary in switching systems, thus preventing problems such as controller overheating. It can provide a theoretical reference for open-loop control of dynamic systems with switching phenomena, such as mutated UAVs and shape memory alloy actuators.

[0093] The open-loop adaptive implementation system of the state-dependent switching system, such as Figure 1 As shown, it includes:

[0094] Flow passability judgment module: For a general switching system dynamics model, a rule is given to judge whether the moving flow can pass based on the boundary normal vector and vector field;

[0095] Dominant Controller Selection Module: When the motion flow is not expected to complete a smooth transition, the control input needs to be designed. Referring to the concept of dominant poles, a fully driven dominant controller is selected based on the coefficient matrix.

[0096] Open-loop correction module: Performs open-loop correction on the control input to avoid vector field relativity;

[0097] Open-loop compensation module: Introducing open-loop compensation can overcome the problem of vector field calculation distortion caused by system errors;

[0098] Adaptive algorithm module: Combined with open-loop correction, it can further improve the robustness of open-loop manipulation schemes.

[0099] The flow passability determination module includes:

[0100] Considering the universality of this invention, a general switching system dynamics model is selected as follows:

[0101]

[0102] in,

[0103]

[0104] Where x is the switching system state vector of length N (N≥2); f σ Describe the coupling relationships between switching system states; g σ Describes the relationship between the state and control input of the switching system; u is the control input of the switching system; σ is the subspace domain in which the motion flow is located in the state space. When the motion flow crosses the boundary from one subspace domain to an adjacent subspace domain, the switching system is said to have completed the switching. σ With g σ Switch accordingly.

[0105] The G-function is defined by the boundary normal vector and the vector field, as the moving flow approaches the boundary. Calculate the G function for each of the two adjacent subspaces, and determine whether the motion flow can pass through based on the G function of the two adjacent subspaces; the motion flow approaching the boundary is determined by the distance from the motion flow to the boundary (the state of the motion flow is substituted into the boundary equation and the absolute value is calculated, and the distance can be judged by measuring the value). When the distance is continuously reduced, it is considered that the motion flow is approaching the boundary.

[0106] For the state-dependent switching system described by formula (1), arbitrarily choose two adjacent subspace domains denoted as Ω. α and Ω β The intersection of two nonsets of subspaces is the boundary, denoted as . This boundary can be defined by function l αβ () describes, when l αβ When the sign of the parentheses changes, a system switch is considered to have occurred. The switching set is the boundary. The tiny neighborhood in space is denoted as ∑αβ.

[0107] The boundary normal vector is denoted as From subspace domain Ω β Pointing to subspace Ω α It can be calculated by equation (3).

[0108]

[0109] The boundary normal vector and the vector field pair G function Define it as shown in formula (4).

[0110]

[0111] When the flow of energy reaches the boundary If inequality (5) holds and the motion flow can switch smoothly at the boundary, then the process ends; otherwise, if the motion flow cannot switch smoothly, then open-loop adaptive adjustment is performed.

[0112]

[0113] When the motion flow cannot be smoothly switched, it is necessary to combine the direction of the motion flow with the direction of the vector field. The sign of the product is changed to make it positive, and the transition is smooth, using the sign κ. αβ ( αβ =-1,1) identifier The expected positive or negative value.

[0114] This module provides the rules for whether the motion flow can pass through or not at the boundary. If inequality (5) is satisfied and the motion flow can switch smoothly, there is no need to design the control input; otherwise, the dominant controller selection module needs to be triggered.

[0115] The dominant controller selection module includes:

[0116] When the flowing flow is expected to flutter at the boundary, the control input needs to be designed to allow for passability. Referring to the concept of dominant poles, the closer a dominant pole is to the imaginary axis, the more significant its corresponding response component becomes in the system response. Therefore, in the controller of a switching system, the larger the controller coefficient, the stronger the dominant effect of the corresponding control input on the system response.

[0117] Based on the 2-norm and the infinite norm ∞ Define the coefficient matrix H of the control input. αβ for:

[0118]

[0119] Select H αβ The two largest values ​​in a vector (maximum and second largest) are represented by u. m and u n This is represented, and corresponds to controller u respectively. m and u n ;

[0120] When controller u m and u n China αm g βn ≠g αn g βm When, then the current controller u m and un As the dominant controller for all drives.

[0121] This module references the concept of dominant poles, performs L2 and L2 norm operations on the coefficient matrix, selects the dominant controller while satisfying the full drive constraints, and adjusts the control input u. m and u n Perform open-loop correction and open-loop compensation.

[0122] The open-loop calibration module includes:

[0123] Select control input u m and u n After establishing the dominant controller, keeping the other control inputs constant, open-loop compensation is performed on both, and the compensation values ​​are denoted as u. m1 and u n1 As shown in equation (7).

[0124]

[0125] After the module completes open-loop correction of the control input, if there is no error in the system model, the impassable situation disappears, and the motion flow will not flutter at the boundary. However, the existence of model error may trigger the error in equation (4). The computational distortion makes inequality (5) still not hold, and flutter is not avoided. The computational distortion problem introduced by the system uncertainty can be overcome to a certain extent by using the open-loop compensation module.

[0126] The open-loop compensation module includes:

[0127] When system errors exist, the introduction of open-loop compensation can overcome the problem of vector field calculation distortion to a certain extent. Open-loop compensation is performed on the dominant controller, and the compensation value is denoted as u. m2 and u n2 As shown in equation (8).

[0128]

[0129] Where, γ αβ It is an adaptive operator.

[0130] This module, through open-loop compensation, can overcome the problem of inaccurate vector field calculation to a certain extent. If the prior information about system errors is inaccurately estimated, or if the system is subject to external disturbances, the initial value γ of the adaptive operator... αβ0 The compensation effect may be limited. The adaptive algorithm module can adjust the adaptive operator γ. αβ An update will be made to further improve the effectiveness of open-loop control.

[0131] The adaptive algorithm module includes the following steps: after open-loop compensation, if the motion flow can complete the switching, the process ends. If the motion flow cannot complete the switching, the adaptive algorithm module continues to execute.

[0132] Adaptive operator γ αβ The initial value is γ αβ0 To select a constant value based on prior information about system errors, the adaptive operator γ... αβ The update method is shown in equation (9), where t αβ For the flow of motion at the boundary The duration of flutter begins when the self-flow enters the switching set ∑αβ and stops when the self-flow leaves the switching set ∑αβ.

[0133]

[0134] Where λ αβ It is a positive number.

[0135] This module performs time-domain updates on the adaptive operator. If the flow exhibits chattering at the boundary, it prompts the adaptive operator γ... αβ The upper limit of the fitting error is calculated, the open-loop compensation is applied to the control input, and the adaptive operator γ in equation (9) is applied. αβ The estimated value is assigned the initial value γ. αβ0 This can reduce the occurrence of flutter in subsequent motion. In particular, when inequality (5) holds, if there is an error in the system, the motion flow may actually flutter at the boundary. In this case, it is still necessary to call the open-loop correction and open-loop compensation modules to achieve smooth switching of the motion flow.

[0136] After open-loop correction, open-loop compensation, and adaptive algorithm, the proposed open-loop adaptive control input is... and for:

[0137]

[0138] The open-loop adaptive implementation system for a state-dependent switching system provided by this invention can be implemented through the steps and flow of the open-loop adaptive implementation method for a state-dependent switching system provided by this invention. Those skilled in the art can understand the open-loop adaptive implementation method for a state-dependent switching system as a preferred example of the open-loop adaptive implementation system for a state-dependent switching system.

[0139] Example 2

[0140] Example 2 is a preferred example of Example 1.

[0141] An open-loop adaptive manipulation method for a state-dependent switching system provided by the present invention includes:

[0142] The system includes a flow passability judgment module, a dominant controller selection module, an open-loop correction module, an open-loop compensation module, and an adaptive algorithm module.

[0143] Step 1: Assign initial values ​​to the switching system dynamics model and perform time-domain iteration, then proceed to Step 2;

[0144] Step 2: Trigger the flow passability judgment module. If the motion flow approaches the boundary... Calculate the values ​​of two adjacent subspaces and

[0145] Step 2.1: Determine the symbol κ based on the direction of motion flow and the direction of vector field. αβ (κ αβ =-1,1).

[0146] Step 2.2: If If the result is negative, proceed to Step 3;

[0147] Step 2.3: If The result is positive, but the flow fails to switch smoothly at the boundary, proceeding to Step 3;

[0148] Step 2.4: If If the result is positive and the flow transitions smoothly at the boundary, return to Step 1;

[0149] Step 3: Execute the open-loop adaptive control scheme;

[0150] Step 3.1: Trigger the dominant controller selection module to calculate the coefficient matrix H. αβ The dominant controller u is selected based on the infinite norm and the full driving constraints. m and u n .

[0151] Step 3.2: Trigger the open-loop calibration module and calculate the open-loop calibration u. m1 with u n1 .

[0152] Step 3.3: Trigger the open-loop compensation module to calculate the open-loop compensation u. m2 with u n2 .

[0153] Step 3.4: Integrating open-loop correction and open-loop compensation to obtain the open-loop adaptive control input. and

[0154] Step 3.4.1: If the flutter persists, trigger the adaptive algorithm module and update the adaptive operator γ. αβ and reset the initial value γ αβ0 Return to Step 3.3.

[0155] Step 3.4.2: If the flutter disappears, return to Step 1.

[0156] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0157] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. An open-loop adaptive implementation method for a state-dependent switching system, characterized in that, include: Step S1: Based on the switching system dynamics model, use the boundary normal vector and vector field to determine the passability of the motion flow, and based on the passability of the motion flow, determine whether the current motion flow can switch smoothly. Step S2: When a smooth switch is not possible, select the full-drive dominant controller based on the controller in the current switching system dynamics model; Step S3: Perform open-loop correction and open-loop compensation operations on the current fully driven dominant controller in sequence to achieve smooth switching of motion flow at the boundary; Step S3 employs the following: Step S3.1: Select control input and After establishing the dominant controller, keeping the other control inputs unchanged, open-loop calibration is performed on both, and the calibration values ​​are denoted as follows: and : （7）； Step S3.2: After the control input completes the open-loop correction, if there is no error in the switching system dynamics model, the impassable situation will disappear and the motion flow will not flutter at the boundary; if there is an error in the switching system dynamics model, the open-loop compensation module will be activated. When errors exist in the switching system, an open-loop compensation is introduced to overcome the distortion in vector field calculation. Open-loop compensation is applied to the dominant controller, and the compensation values ​​are denoted as follows: and : （8）； in, For adaptive operators; The adaptive algorithm module can be used to optimize adaptive operators. The system will be updated to further improve the effectiveness of open-loop control. Adaptive Operator The initial value is To select constant values ​​based on prior information about switching system errors, the adaptive operator... The update method is shown in equation (9); where, For the flow of motion at the boundary Duration of flutter; self-flow into the switching set Start, self-flow leaving switch set Stop at this time; （9）； in, It is a positive number; After open-loop correction, open-loop compensation, and adaptive algorithm, the proposed open-loop adaptive control input is... and for: （10）。 2. The open-loop adaptive implementation method for a state-dependent switching system according to claim 1, characterized in that, Step S1 adopts the following: Step S1.1: Initialize the switching system dynamics model and perform time-domain iteration; The switching system dynamics model includes: （1）； in, (2); Let N be the switching system state vector of length N, where N≥2; Describe the coupling relationships between switching system states; Describe the relationship between switching system states and control inputs; To switch the control input of the system; Let be the subspace domain in which the motion flow resides in the state space. When the motion flow crosses the boundary from one subspace domain to enter an adjacent subspace domain, the switching system completes the switching process. and Switch accordingly; Step S1.2: Define the G function using the boundary normal vector and the vector field, as the moving flow approaches the boundary. Calculate the G function of each of the two adjacent subspaces, and determine whether the motion flow can pass based on the G function of the two adjacent subspaces; Let any two adjacent subspaces be denoted as and The intersection of two nonsets of subspaces is the boundary, denoted as . The boundary is defined by the function Description, when When the sign changes, the switching system switches; the switching set is the boundary. A tiny neighborhood in space is denoted as ; The boundary normal vector is denoted as , by subspace domain Pointing to subspace : The boundary normal vector and the vector field pair G function, Define: （4）； When the flow of energy reaches the boundary If inequality (5) holds and the motion flow can switch smoothly, then the process ends; otherwise, if the motion flow cannot switch smoothly, then open-loop adaptive adjustment is performed. （5）。 3. The open-loop adaptive implementation method for a state-dependent switching system according to claim 1, characterized in that, Step S2 employs: using the L2 norm With the infinite norm Select the full-drive dominant controller based on the current switching system dynamics model; Based on L2 norm With the infinite norm Define the coefficient matrix of the control input. for: （6）； Select The two largest values ​​in the vector are respectively... and This indicates, and corresponds to the controller respectively. and ; When the controller and middle When that happens, the current controller will be... and As the dominant controller for all drives.

4. An open-loop adaptive implementation system for a state-dependent switching system, characterized in that, include: Module M1: Based on the switching system dynamics model, it uses boundary normal vectors and vector fields to determine the passability of the motion flow, and based on the passability of the motion flow, it determines whether the current motion flow can switch smoothly. Module M2: When a smooth switch is not possible, a fully driven dominant controller is selected based on the controller in the current switching system dynamics model; Module M3: Performs open-loop correction and open-loop compensation operations sequentially on the current fully driven dominant controller to achieve smooth switching of motion flow at the boundary; The module M3 adopts: Module M3.1: Selected control input and After establishing the dominant controller, keeping the other control inputs unchanged, open-loop calibration is performed on both, and the calibration values ​​are denoted as follows: and : （7）； Module M3.2: After the control input completes open-loop correction, if there is no error in the switching system dynamics model, the impassable situation will disappear and the motion flow will not flutter at the boundary; if there is an error in the switching system dynamics model, the open-loop compensation module will be activated. When errors exist in the switching system, an open-loop compensation is introduced to overcome the distortion in vector field calculation. Open-loop compensation is applied to the dominant controller, and the compensation values ​​are denoted as follows: and : （8）； in, For adaptive operators; The adaptive algorithm module can be used to optimize adaptive operators. The system will be updated to further improve the effectiveness of open-loop control. Adaptive Operator The initial value is To select constant values ​​based on prior information about switching system errors, the adaptive operator... The update method is shown in equation (9); where, For the flow of motion at the boundary Duration of flutter; self-flow into the switching set Start, self-flow leaving switch set Stop at this time; （9）； in, It is a positive number; After open-loop correction, open-loop compensation, and adaptive algorithm, the proposed open-loop adaptive control input is... and for: （10）。 5. The open-loop adaptive implementation system of the state-dependent switching system according to claim 4, characterized in that, The module M1 adopts: Module M1.1: Initializes the switching system dynamics model and performs time-domain iteration; The switching system dynamics model includes: （1）； in, (2); Let N be the switching system state vector of length N, where N≥2; Describe the coupling relationships between switching system states; Describe the relationship between switching system states and control inputs; To switch the control input of the system; Let be the subspace domain in which the motion flow resides in the state space. When the motion flow crosses the boundary from one subspace domain to enter an adjacent subspace domain, the switching system completes the switching process. and Switch accordingly; Module M1.2: Defines the G function using the boundary normal vector and the vector field, as the moving flow approaches the boundary. Calculate the G function of each of the two adjacent subspaces, and determine whether the motion flow can pass based on the G function of the two adjacent subspaces; Let any two adjacent subspaces be denoted as and The intersection of two nonsets of subspaces is the boundary, denoted as . The boundary is defined by the function Description, when When the sign changes, the switching system switches; the switching set is the boundary. A tiny neighborhood in space is denoted as ; The boundary normal vector is denoted as , by subspace domain Pointing to subspace : The boundary normal vector and the vector field pair G function, Define: （4）； When the flow of energy reaches the boundary If inequality (5) holds and the motion flow can switch smoothly, then the process ends; otherwise, if the motion flow cannot switch smoothly, then open-loop adaptive adjustment is performed. （5）。 6. The open-loop adaptive implementation system of the state-dependent switching system according to claim 4, characterized in that, Module M2 adopts: using the L2 norm With the infinite norm Select the full-drive dominant controller based on the current switching system dynamics model; Based on L2 norm With the infinite norm Define the coefficient matrix of the control input. for: （6）； Select The two largest values ​​in the vector are respectively... and This indicates, and corresponds to the controller respectively. and ; When the controller and middle When that happens, the current controller will be... and As the dominant controller for all drives.

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