Nonlinear system control method, device and equipment based on predetermined time convergence

Abstract

The present application relates to the nonlinear system control method, device and equipment based on predetermined time convergence, relate to system control technical field. Method includes: the general linearization processing to the time-varying physical system containing nonlinear factor, obtains small perturbation linearization state space equation;In actual time domain, the state feedback correlation is constructed, and the time-varying physical system realizes asymptotic stability convergence;Setting time-varying scaling function;Small perturbation linearization state space equation is converted into virtual time domain control equation;In virtual time domain, the state feedback correlation is again constructed, and the time-varying physical system realizes asymptotic stability convergence;According to the conversion relationship, the second control variable is converted to actual time domain in reverse, and the target control variable is obtained;The target control variable acts on small perturbation linearization state space equation, and the time-varying physical system realizes predetermined time convergence in actual time domain. The present application can guarantee that nonlinear system is based on predetermined time convergence, and engineering usability is strong.

Description

Technical Field

[0001] This invention relates to the field of system control technology, and in particular to a nonlinear system control method, apparatus, and device based on predetermined time convergence. Background Technology

[0002] Nonlinear systems are prevalent in modern industrial production, intelligent equipment control, and aerospace engineering fields. Their control performance directly determines the equipment's operational accuracy, task completion efficiency, and system reliability. For example, during high-speed trajectory tracking by industrial robotic arms, nonlinear factors such as joint friction and load changes make it difficult for traditional control methods to balance response speed and steady-state accuracy. In the attitude control of aircraft such as drones and spacecraft, nonlinear effects such as aerodynamic parameter perturbations and external airflow interference require the control system to converge rapidly within a finite time to ensure flight stability. In multi-agent collaborative operations, the coupling nonlinearity and communication delay between agents impose strict requirements on the timeliness and consistency of system convergence.

[0003] In current system convergence time control, there are mainly three categories: 1) Finite-time convergence: For a globally asymptotically stable system, if any solution of the system reaches equilibrium within a certain finite time, the system is called a finite-time convergent system. However, finite-time convergent control relies too much on the initial state of the system, and the convergence time of the system will change with the change of the initial state. Moreover, when the distance between the initial state and the system equilibrium point is large, the system convergence time will also increase. 2) Fixed-time convergence: Fixed-time convergence refers to a system with an arbitrary initial state that will converge to the equilibrium point within a finite time, and the convergence time is uniformly bounded. Compared with effective time convergence control, fixed-time convergence does not depend on the initial state of the system, and its convergence time is related to the control parameters. Although fixed-time convergence control can give an upper bound on the control error convergence time, it cannot give an exact error convergence time, and it does not have a good application effect in control systems with strict requirements for convergence time. 3) Predetermined-time convergence: If the system is stable for a fixed time, and the stabilization time is less than a predetermined time, the system is called a predetermined-time convergent system. However, there is currently a lack of research on control related to predetermined time convergence, and the determination of the relationship between system parameters and convergence time still requires extensive investigation. At the same time, the universality of the designed predetermined time convergence control method is also one of the important issues worthy of attention in the research.

[0004] In addition, most existing systems have certain requirements for convergence time control, which also have certain requirements for the system model. When the model changes, the control effect is difficult to guarantee, and the control method does not have good universality. Summary of the Invention

[0005] Therefore, it is necessary to provide a nonlinear system control method, device, and equipment based on predetermined time convergence that can solve the problems of inaccurately preset convergence time and weak adaptability to changes in operating conditions.

[0006] A control method for a nonlinear system based on predetermined time convergence, the method comprising:

[0007] Step 1: Perform general linearization on the time-varying physical system containing nonlinear factors to obtain the small-perturbation linearized state-space equation;

[0008] Step 2: In the actual time domain, based on the small-perturbation linearized state-space equation, construct the state feedback correlation between the first state variable and the first control variable, so that the time-varying physical system achieves asymptotically stable convergence.

[0009] Step 3: Set the time-varying scaling function; based on the transformation relationship, convert the small-disturbance linearized state-space equation into a virtual time-domain control equation according to the time-varying scaling function.

[0010] Step 4: In the virtual time domain, based on the virtual time domain control equation, construct the state feedback correlation between the second state variable and the second control variable, so that the time-varying physical system achieves asymptotically stable convergence;

[0011] Step 5: Based on the transformation relationship between the small-disturbance linearized state-space equation and the virtual time-domain control equation, the second control variable is reverse-transformed to the actual time domain to obtain the target control variable;

[0012] Step 6: Apply the target control variable to the small-perturbation linearized state-space equation so that the time-varying physical system achieves convergence within a predetermined time in the actual time domain.

[0013] On the other hand, a nonlinear system control device based on predetermined time convergence is also provided, comprising:

[0014] The linearization module is used to perform general linearization on time-varying physical systems containing nonlinear factors to obtain small-perturbation linearized state-space equations.

[0015] The actual time-domain asymptotic convergence control module is used to construct a state feedback correlation between the first state variable and the first control variable based on the small-perturbation linearized state-space equation in the actual time domain, so that the time-varying physical system can achieve asymptotic stable convergence.

[0016] The time-domain transformation module is used to set the time-varying scaling function; based on the time-varying scaling function, the small-disturbance linearized state-space equation is transformed into a virtual time-domain control equation according to the transformation relationship.

[0017] The virtual time domain asymptotic convergence control module is used to construct a state feedback correlation between the second state variable and the second control variable based on the virtual time domain control equation within the virtual time domain, so that the time-varying physical system can achieve asymptotic stable convergence.

[0018] The control variable inverse transformation module is used to inversely transform the second control variable to the actual time domain according to the transformation relationship between the small disturbance linearized state space equation and the virtual time domain control equation, so as to obtain the target control variable;

[0019] The predetermined time convergence execution module is used to apply the target control variable to the small perturbation linearized state-space equation, so that the time-varying physical system achieves predetermined time convergence in the actual time domain.

[0020] In another aspect, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described nonlinear system control method based on predetermined time convergence.

[0021] Compared with existing technologies, the nonlinear system control method, apparatus, and device based on predetermined time convergence provided by this invention have the following beneficial effects:

[0022] 1. By establishing a mapping relationship between the actual time domain and the virtual time domain through a time-varying scaling function, and through the collaborative design of dual-time-domain asymptotic convergence control, the system convergence time is completely independent of the initial state, and the error can be strictly controlled to return to zero within a predetermined time, accurately meeting the rigid constraints on convergence time in engineering scenarios.

[0023] 2. A linear state feedback correlation between control variables and state variables is employed in both the actual and virtual time domains. Combined with small-disturbance linearization to effectively adapt to nonlinear factors, this accelerates system convergence and mitigates the effects of external disturbances and system parameter fluctuations. This significantly improves the reliability and robustness of nonlinear system control, avoiding the control effect degradation problem of existing methods under model changes or disturbances. Furthermore, the original system stability remains unchanged during the dual-time-domain transformation, ensuring control accuracy while simplifying the stability analysis process. The overall solution is rigorous and reliable.

[0024] 3. The method proposed in this invention does not depend on the model details of a specific nonlinear system. The unified state feedback control structure and modular time-domain transformation logic reduce the adaptation cost of cross-scenario applications. It has strong versatility, high portability, and is suitable for engineering applications in multiple scenarios. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention, and those skilled in the art can obtain other related drawings based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the nonlinear system control method based on predetermined time convergence in Example 1.

[0027] Figure 2 This is a schematic diagram illustrating the correspondence between the actual time domain and the virtual time domain in Example 1;

[0028] Figure 3 This is a structural block diagram of the nonlinear system control device based on predetermined time convergence in Example 2;

[0029] Figure 4 This is a diagram of the internal structure of the computer device in Example 3.

[0030] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0032] It should be noted that in this invention, the use of terms such as "first," "second," etc., is for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, 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.

[0033] It is understood that the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0034] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0035] Example 1

[0036] like Figure 1 As shown, this embodiment provides a nonlinear system control method based on predetermined time convergence, including the following steps:

[0037] Step 1: Perform general linearization on the time-varying physical system containing nonlinear factors to obtain the small-perturbation linearized state-space equation.

[0038] Step 2: In the actual time domain, based on the small-perturbation linearized state-space equation, construct the state feedback correlation between the first state variable and the first control variable, so that the time-varying physical system can achieve asymptotically stable convergence.

[0039] Step 3: Set the time-varying scaling function; based on the transformation relationship, transform the small-disturbance linearized state-space equations into virtual time-domain control equations according to the time-varying scaling function.

[0040] Step 4: In the virtual time domain, based on the virtual time domain control equations, construct the state feedback correlation between the second state variable and the second control variable, so that the time-varying physical system can achieve asymptotically stable convergence.

[0041] Step 5: Based on the transformation relationship between the linearized state-space equation with small disturbance and the virtual time domain control equation, the second control variable is transformed inversely to the actual time domain to obtain the target control variable.

[0042] Step 6: Apply the target control variable to the small-perturbation linearized state-space equation so that the time-varying physical system achieves convergence at a predetermined time in the actual time domain.

[0043] The nonlinear system control method based on predetermined time convergence provided by this invention solves the problems of inaccurate time preset, dependence on initial state, and weak versatility in existing convergence control by using the core logic of nonlinear system linearization, dual time-domain asymptotic convergence, time-varying scaling bidirectional conversion, and predetermined time convergence. It achieves stable convergence of nonlinear systems within a predetermined time, thereby improving control reliability and engineering applicability.

[0044] In step 1, the time-varying physical system containing nonlinear factors refers to a physical system existing in actual engineering where the state changes over time and includes nonlinear effects such as friction, load fluctuations, and parameter perturbations, such as robots, aircraft, and multi-agent systems. General linearization refers to the process of transforming nonlinear system equations into linear equations near the system's operating point or equilibrium point; the core of this method is the small-perturbation linearization method. The small-perturbation linearized state-space equation is the mathematical model used to describe the changes in the system's state after linearization.

[0045] Specifically, the state equation of the time-varying physical system containing nonlinear factors is first established, and its specific expression is as follows:

[0046] (1)

[0047] in:

[0048] (2)

[0049] In the formula, This represents the first derivative of the state variable with respect to time. Indicates the output vector; Represents the state vector; Represents the control vector; Represents time variables in the actual time domain; , Represents a function vector; Indicates the number of elements.

[0050] Subsequently, a general linearization process is performed on the time-varying physical system, transforming the aforementioned nonlinear function vector... and At work Expanding the domain into a Taylor series and neglecting terms of degree two and above, we obtain:

[0051] (3)

[0052] (4)

[0053] In the formula, and Therefore,

[0054] (5)

[0055] (6)

[0056] At the work point, the following conditions must be met:

[0057] (7)

[0058] (8)

[0059] Therefore, the linearized state-space equation with small perturbation can be obtained as follows:

[0060] (9)

[0061] (10)

[0062] In the formula, This represents the first derivative of the state variable with respect to time after linearization. , , , Represents the spatial state matrix; Indicates the output variable; Represents state variables; Indicates control variables; This represents the state vector at the operating point; This represents the control vector at the operating point; This represents the first derivative of the state variable at the operating point with respect to time. This represents the output vector at the operating point; Indicates the scheduled convergence time; Represents the time variable in the actual time domain.

[0063] When the nonlinear system moves near the operating point, the linear system shown in formulas (9) and (10) can replace the nonlinear system shown in formula (1) with sufficient accuracy. , , , The element changes over time It changes with the operating point, which can be specifically represented as:

[0064] (11)

[0065] (12)

[0066] (13)

[0067] (14)

[0068] This step transforms the complex nonlinear system into an easily controllable linearized model through small perturbation linearization. This not only ensures the model's accuracy but also provides a foundation for the design of subsequent dual-time-domain control strategies. This enables the control method to be adapted to various time-varying physical systems containing nonlinear factors, thus improving the method's versatility.

[0069] In step 2, the actual time domain is the real time dimension, corresponding to the time variable. The first state variable refers to the state variable in the actual time domain, that is... The first control variable refers to the control variable in the actual time domain, i.e. State feedback correlation refers to the linear mapping relationship between control variables and state variables. Asymptotically stable convergence means that when... As time progresses, the system state gradually converges to the equilibrium point, and the control error approaches zero.

[0070] Specifically, based on the small-perturbation linearized state-space equation obtained in step 1, a state feedback correlation between the first state variable and the first control variable is designed, expressed as:

[0071] (15)

[0072] In the formula, This represents the first control variable in the actual time domain. Represents the state feedback gain matrix; This represents the first state variable in the actual time domain.

[0073] This step, through explicit linear state feedback correlation, ensures the asymptotic stability and convergence of the system in the actual time domain, providing a stable basic model for subsequent time-domain transformation; at the same time, the linear feedback structure is simple, easy to implement in engineering, and reduces the complexity of control law design.

[0074] In step 3, the time-varying scaling function is the core function used to establish the mapping relationship between the actual time domain and the virtual time domain, and it varies with the time variable of the actual time domain. Changes. The virtual time domain is a virtual time dimension constructed using a time-varying scaling function, corresponding to time variables. The transformation relationships include variable transformation relationships and differential transformation relationships between the actual time domain and the virtual time domain. The virtual time domain governing equations are equivalent expressions of the small-disturbance linearized state-space equations in the virtual time domain.

[0075] Specifically, it includes the following steps:

[0076] Step 3.1, for the time variables in the actual time domain Transformation is performed, introducing time variables from a virtual time domain. Suppose there exists a time-varying scaling function, expressed as:

[0077] (16)

[0078] In the formula, Indicates the time-varying scaling function; Represents time variables in the actual time domain; Indicates the scheduled convergence time; It is a constant greater than 0.

[0079] Step 3.2, adjust the time-varying scaling function with respect to the time variable. Taking the derivative, we obtain the expression for the derivative:

[0080] (17)

[0081] In the formula, This represents the first derivative of the time-varying scaling function; Time variables representing the virtual time domain, This represents the derivative mapping function.

[0082] remember Then there is ( (exists), and has Then the derivative expression can be further written as:

[0083] (18)

[0084] Step 3.3: Based on the time-varying scaling function and its derivative expression, establish the variable transformation equation and differential equation between the actual time domain and the virtual time domain. The expressions are as follows:

[0085] (19)

[0086] (20)

[0087] In the formula, Indicates the scaling function; Represents time variables in the virtual time domain.

[0088] Step 3.4: Based on the variable transformation equation and the differential equation, the linearized state-space equation for the small disturbance is transformed into the corresponding equation in the virtual time domain, resulting in the virtual time domain control equation, expressed as:

[0089] (twenty one)

[0090] (twenty two)

[0091] In the formula, This represents the first derivative of the state variable with respect to time after linearization in the virtual time domain. This represents the output variable within the virtual time domain.

[0092] This step establishes a strict mapping between the actual time domain and the virtual time domain using a time-varying scaling function, satisfying... hour The core condition provides key support for transforming the asymptotic convergence of the virtual time domain into the predetermined time convergence of the actual time domain. At the same time, the virtual time domain control equations maintain structural consistency with the actual time domain equations, which facilitates the reuse design of subsequent control strategies.

[0093] In step 4, the second state variable refers to the state variable within the virtual time domain, i.e. The second control variable refers to the control variable within the virtual time domain, i.e. .

[0094] Specifically, based on the virtual time-domain control equations obtained in step 3, a state feedback correlation between the first state variable and the first control variable is designed, expressed as:

[0095] (twenty three)

[0096] In the formula, This represents the second control variable within the virtual time domain; Represents the state feedback gain matrix; This represents the second state variable within the virtual time domain.

[0097] This step continues the linear state feedback structure of the actual time domain, eliminating the need to redesign complex control laws and reducing the overall control scheme design difficulty. Simultaneously, by ensuring asymptotic convergence in the virtual time domain, it provides the necessary condition for the predetermined time convergence in the actual time domain after the subsequent inverse transformation.

[0098] In step 5, the reverse transformation refers to converting the second control variable within the virtual time domain. The process of converting control variables into actual time-domain control variables. The target control variable refers to the actual time-domain control variable obtained after the inverse transformation, used to achieve convergence at a predetermined time, denoted as... .

[0099] Specifically, firstly, based on formulas (21) and (22), the state variables in the virtual time domain are solved. .

[0100] Then, association based on status feedback. Solving the virtual time domain Control variables within .

[0101] Then, based on the variable transformation equation of formula (19), the actual time domain is obtained. Internal target control variables Among them, the time variable in the actual time domain and time variables in the virtual time domain See the correspondence. Figure 2 .

[0102] This step, through a rigorous reverse transformation, transfers the stable control logic of the virtual time domain to the actual time domain, achieving a closed-loop connection of the dual-time domain control strategy. The target control variable inherits the stability of asymptotic convergence in both time domains and possesses the timeliness of convergence at a predetermined time, providing a direct execution basis for achieving the final control objective.

[0103] In step 6, the predetermined time convergence refers to the convergence of the actual time... When the system state converges to the equilibrium point, the control error approaches zero, and the convergence time is independent of the initial state of the system.

[0104] Specifically, the target control variables obtained in step 5 Substituting the small-perturbation linearized state-space equations obtained in step 1, convergence within a predetermined time is achieved through the system's dynamic response.

[0105] The stability of this step can be verified by the Lyapunov stability criterion, specifically:

[0106] In step 2, the time-varying physical system in the actual time domain asymptotically converges, that is, when At that time, there exists a Lyapunov function. satisfy:

[0107] (twenty three)

[0108] In the formula, It represents the first derivative with respect to time.

[0109] To analyze the convergence of the system in the virtual time domain, the time variable is calculated on both sides of the Lyapunov function. The derivative of the derivative yields:

[0110] (twenty four)

[0111] because ,and ,therefore According to the Lyapunov stability criterion, the system also converges asymptotically in the virtual time domain. The time domain transformation process does not change the stability of the system, ensuring the stable convergence of the system in the actual time domain under the action of the target control variable.

[0112] After completing step 6, return to step 3 and repeat the transformation and optimization process from step 3 to step 6. Through iteration, further improve the control accuracy and convergence stability, enabling the system to converge within the predetermined time. It has smaller convergence error and stronger robustness.

[0113] This step directly achieves the predetermined time convergence of the nonlinear system in the actual time domain. The convergence time can be determined by the predetermined convergence time. Precise control, independent of the initial state, completely solves the shortcomings of existing finite-time convergence which depends on the initial state and fixed-time convergence which cannot determine the exact convergence time; at the same time, the verification of the stability criterion ensures the rigor of the control scheme, making it safer and more reliable in engineering applications.

[0114] It should be understood that, although this embodiment Figure 1The steps are shown sequentially as indicated by the arrows, but they are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order in which these steps are performed; they can be executed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0115] Example 2

[0116] Based on the nonlinear system control method based on predetermined time convergence in Embodiment 1, this embodiment discloses a nonlinear system control device based on predetermined time convergence, such as... Figure 3 As shown, the nonlinear system control device based on predetermined time convergence includes: a linearization processing module 701, an actual time-domain asymptotic convergence control module 702, a time-domain transformation module 703, a virtual time-domain asymptotic convergence control module 704, a control variable inverse transformation module 705, and a predetermined time convergence execution module 706, wherein:

[0117] The linearization module 701 is used to perform general linearization on time-varying physical systems containing nonlinear factors to obtain small-perturbation linearized state-space equations.

[0118] The actual time-domain asymptotic convergence control module 702 is used to construct a state feedback correlation between the first state variable and the first control variable in the actual time domain based on the small-perturbation linearized state-space equation, so that the time-varying physical system can achieve asymptotic stable convergence.

[0119] The time-domain transformation module 703 is used to set the time-varying scaling function; based on the time-varying scaling function, the small-disturbance linearized state-space equation is transformed into a virtual time-domain control equation based on the transformation relationship.

[0120] The virtual time-domain asymptotic convergence control module 704 is used to construct a state feedback correlation between the second state variable and the second control variable in the virtual time domain based on the virtual time-domain control equation, so that the time-varying physical system can achieve asymptotic stable convergence.

[0121] The control variable inverse transformation module 705 is used to inversely transform the second control variable to the actual time domain according to the transformation relationship between the small disturbance linearized state-space equation and the virtual time domain control equation, so as to obtain the target control variable.

[0122] The predetermined time convergence execution module 706 is used to apply the target control variable to the small perturbation linearized state space equation, so that the time-varying physical system can achieve predetermined time convergence in the actual time domain.

[0123] In this embodiment, the specific working process and working principle of the linearization processing module 701, the actual time-domain asymptotic convergence control module 702, the time-domain transformation module 703, the virtual time-domain asymptotic convergence control module 704, the control variable inverse transformation module 705, and the predetermined time convergence execution module 706 are the same as those in Embodiment 1, and therefore will not be described again in this embodiment. Each unit module can be implemented entirely or partially through software, hardware, or a combination thereof. Each unit module can be embedded in or independent of the processor in the computer device in hardware form, or it can be stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above unit modules.

[0124] Example 3

[0125] like Figure 4 The diagram illustrates a terminal device disclosed in this embodiment, comprising a transmitter, a receiver, a memory, and a processor. The transmitter transmits instructions and data, the receiver receives instructions and data, the memory stores computer-executed instructions, and the processor executes the computer-executed instructions stored in the memory to implement the method described in Embodiment 1 above.

[0126] It is important to note that the aforementioned memory can be either standalone or integrated with the processor. When the memory is set up independently, the terminal device also includes a bus for connecting the memory and the processor.

[0127] Example 4

[0128] This embodiment discloses a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the method in Embodiment 1 above.

[0129] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0130] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0131] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A control method for a nonlinear system based on predetermined time convergence, characterized in that, include: Step 1: Perform general linearization on the time-varying physical system containing nonlinear factors to obtain the small-perturbation linearized state-space equation; Step 2: In the actual time domain, based on the small-perturbation linearized state-space equation, construct the state feedback correlation between the first state variable and the first control variable, so that the time-varying physical system achieves asymptotically stable convergence. Step 3: Set the time-varying scaling function; based on the transformation relationship, convert the small-disturbance linearized state-space equation into a virtual time-domain control equation according to the time-varying scaling function. Step 4: In the virtual time domain, based on the virtual time domain control equation, construct the state feedback correlation between the second state variable and the second control variable, so that the time-varying physical system achieves asymptotically stable convergence; Step 5: Based on the transformation relationship between the small-disturbance linearized state-space equation and the virtual time-domain control equation, the second control variable is reverse-transformed to the actual time domain to obtain the target control variable; Step 6: Apply the target control variable to the small-perturbation linearized state-space equation so that the time-varying physical system achieves convergence at a predetermined time in the actual time domain; In step 3, based on the time-varying scaling function and the transformation relationship, the small-perturbation linearized state-space equation is converted into a virtual time-domain control equation, including: Step 3.1, define the time-varying scaling function; Step 3.2, adjust the time-varying scaling function with respect to the time variable. Differentiate to obtain the derivative expression; Step 3.3: Based on the time-varying scaling function and derivative expression, establish the variable transformation relationship equation and differential relationship equation between the actual time domain and the virtual time domain; Step 3.4: Based on the variable transformation relationship equation and the differential relationship equation, the small perturbation linearized state space equation is converted into the corresponding equation in the virtual time domain to obtain the virtual time domain control equation; In step 3.1, the expression for the time-varying scaling function is: ； In the formula, Indicates the time-varying scaling function; Represents time variables in the actual time domain; Indicates the scheduled convergence time; It is a constant greater than 0.

2. The nonlinear system control method based on predetermined time convergence according to claim 1, characterized in that, In step 1, the expression for the linearized state-space equation with small perturbation is: ； In the formula, This represents the first derivative of the state variable with respect to time after linearization. , , , Represents the spatial state matrix; Indicates the output variable; Represents state variables; Indicates a control variable.

3. The nonlinear system control method based on predetermined time convergence according to claim 1, characterized in that, In step 2, the state feedback correlation expression between the first state variable and the first control variable is: ； In the formula, This represents the first control variable in the actual time domain. Represents the state feedback gain matrix; This represents the first state variable in the actual time domain.

4. The nonlinear system control method based on predetermined time convergence according to any one of claims 1 to 3, characterized in that, In step 3.3, the expressions for the variable transformation equation and the differential equation are respectively: ； ； In the formula, Indicates the time-varying scaling function; Represents the time variable in the virtual time domain.

5. The nonlinear system control method based on predetermined time convergence according to claim 4, characterized in that, In step 3.4, the expression for the virtual time domain control equation is: ； ； In the formula, This represents the first derivative of the state variable with respect to time after linearization in the virtual time domain. This represents the output variable within the virtual time domain; Represents state variables; Indicates the output variable; Indicates control variables; , , , Represents the spatial state matrix.

6. The nonlinear system control method based on predetermined time convergence according to any one of claims 1 to 3, characterized in that, In step 4, the state feedback correlation expression between the second state variable and the second control variable is: ； In the formula, This represents the second control variable within the virtual time domain; Represents the state feedback gain matrix; This represents the second state variable within the virtual time domain.

7. A control device for a nonlinear system based on predetermined time convergence, characterized in that, The apparatus employing the nonlinear system control method based on predetermined time convergence according to any one of claims 1 to 6 comprises: The linearization module is used to perform general linearization on time-varying physical systems containing nonlinear factors to obtain small-perturbation linearized state-space equations. The actual time-domain asymptotic convergence control module is used to construct a state feedback correlation between the first state variable and the first control variable based on the small-perturbation linearized state-space equation in the actual time domain, so that the time-varying physical system can achieve asymptotic stable convergence. The time-domain transformation module is used to set the time-varying scaling function; based on the time-varying scaling function, the small-disturbance linearized state-space equation is transformed into a virtual time-domain control equation according to the transformation relationship. The virtual time domain asymptotic convergence control module is used to construct a state feedback correlation between the second state variable and the second control variable based on the virtual time domain control equation within the virtual time domain, so that the time-varying physical system can achieve asymptotic stable convergence. The control variable inverse transformation module is used to inversely transform the second control variable to the actual time domain according to the transformation relationship between the small disturbance linearized state space equation and the virtual time domain control equation, so as to obtain the target control variable; The predetermined time convergence execution module is used to apply the target control variable to the small perturbation linearized state-space equation, so that the time-varying physical system achieves predetermined time convergence in the actual time domain.

8. A computer device, comprising a memory and a processor, characterized in that, The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the nonlinear system control method based on predetermined time convergence as described in any one of claims 1 to 6.

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