Preset time adaptive control method and system of high-order nonlinear MIMO system

Abstract

The invention discloses a preset time adaptive control method and system for a high-order nonlinear MIMO system, and relates to the technical field of industrial control. The method comprises the following steps: establishing a dynamic model of a high-order nonlinear MIMO system, and approaching an unknown nonlinear function in the dynamic model by using a neural network; determining a tracking error based on the dynamic model; constructing a virtual control law based on the tracking error and defining a virtual error; constructing a preset time filter to process the virtual control law, and determining a filtering error; the parameter of the preset time filter is configured to enable the filtering error to converge in the preset time; under a backstepping recursion framework, combining a tracking error, a virtual error and a filtering error, and adopting an improved weighted integral technology to design an actual control law; and setting an event triggering mechanism based on a relative threshold value to modulate the actual control law and then output a control signal. The system stabilization time can be directly preset without being influenced by the initial state, and meanwhile the updating frequency of the controller is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of industrial control, and particularly to a preset time adaptive control method and system for a high-order nonlinear MIMO system. BACKGROUND

[0002] With the continuous development of industrial systems towards intelligence and networking, unprecedented high requirements are put forward for the performance of control systems. High-order nonlinear multiple-input multiple-output (MIMO) systems are widely used in complex engineering fields such as robots, aerospace, power electronics, etc. and have become a research hotspot because they can more accurately describe the dynamic characteristics of the system. However, high-order systems need to handle multiple coupled state variables at the same time, which will lead to complex differential equations. Moreover, there are unknown nonlinear functions and disturbances in the system. In recent years, intelligent adaptive control methods based on fuzzy logic systems (FLSs) and neural networks (NNs) have been widely studied. Many domestic and foreign scholars have carried out in-depth exploration on nonlinear systems with unknown functions by using FLSs or NNs. The control design of high-order nonlinear MIMO systems has become an important and challenging topic in this field, among which the predefined time control method that can achieve stable tracking within a preset time has attracted widespread attention.

[0003] The goal of the preset time control is to make the system state or tracking error converge to the equilibrium point or its neighborhood within a preset time that is independent of the initial conditions. Existing control methods include asymptotic stability control, finite time control and fixed time control, which respectively guarantee the stability of the system within infinite time, finite time and fixed time. However, the existing technology still has significant limitations.

[0004] On one hand, for the control method of high-order nonlinear system, the existing control strategy can only guarantee the system to be asymptotically stable in infinite time, or can be stable in finite time but the convergence time is seriously dependent on the initial state, and the fixed time control can get rid of the initial value dependence, but the upper bound of the convergence time is determined by the controller parameters, and cannot be flexibly preset according to the task demand. In the face of high-order system control tasks with strict time constraints, the existing method is difficult to realize the preset time convergence in the true sense. On the other hand, the existing control mostly uses continuous time signals, resulting in high controller execution frequency and occupying a large amount of communication and calculation resources. In the networked control system, the bandwidth and calculation ability are often limited, and continuous control not only causes resource waste, but also may affect the system performance due to channel congestion. Although the event-triggered mechanism is introduced to alleviate the communication burden, the related researches are mostly concentrated on ordinary nonlinear systems or asymptotic, finite time stable framework, and the event-triggered control of high-order nonlinear MIMO system under the preset time stable framework is still blank. Therefore, it is urgent to develop a control method for high-order nonlinear MIMO system which can solve the problems of preset time convergence and resource saving. SUMMARY

[0005] To solve the problems in the prior art, the present application provides a preset time adaptive control method and system for high-order nonlinear MIMO system, which can directly preset the system stable time and is not affected by the initial state, and significantly reduces the controller update frequency and effectively prevents the control singularity problem.

[0006] To achieve the above-mentioned purpose, the present application provides a preset time adaptive control method for high-order nonlinear MIMO system, comprising: establishing a dynamic model of the high-order nonlinear MIMO system, and using a neural network to approximate unknown nonlinear functions in the dynamic model; determining a tracking error based on the dynamic model; constructing a virtual control law based on the tracking error and defining a virtual error; constructing a preset time filter to process the virtual control law and determining a filtering error; the parameters of the preset time filter are configured to make the filtering error converge within a preset time; under the framework of backstepping recursion, combining the tracking error, virtual error and filtering error, an improved weighted integral technique is used to design an actual control law; setting an event-triggered mechanism based on a relative threshold to modulate the actual control law and output a control signal.

[0007] Optionally, the equation expression of the dynamic model is: ; wherein, , the first The state vector of the system is represented as follows: , Represents the system state. Indicates the output. For an unknown nonlinear function, External disturbances It is a positive constant; Indicates the system status. Representing system dynamics, Representing system dynamics, Indicates control input, Represents an unknown function. Indicates interference. express 3D real vector space, express 3D real vector space, Indicates the number of states in the subsystem. This indicates the order of each subsystem.

[0008] Optionally, the mathematical expression of the neural network is: ; in, For the unknown function that needs to be approximated, , express 3D real vector space, Represents the estimated parameter vector, Indicates the number of neurons. Represents vector weights, express 3D real vector space, For Gaussian basis functions, Represents the basis functions.

[0009] Optionally, the equation expression for the preset time filter is: ; in, The filter design parameters are the second design parameters. The third and fourth design parameters are, in order. This is the fifth design parameter; For the first The first subsystem Auxiliary variables for filtering error in each state; This represents the filter output signal. Indicates time, The transformed value used for stability analysis represents the first... The first subsystem The filtering error for each state.

[0010] Optionally, the filtering error converges to a residual set within a preset time; an expression of the residual set is: ; wherein, is a filtering error auxiliary variable of a state of a subsystem, is a first design parameter, represents a lower Lyapunov function of a filtering signal, is a fifth design parameter; represents a third constant. Optionally, the event trigger mechanism is implemented as:

[0011] ; wherein, , , is a sixth design parameter, is a seventh design parameter, represents an order of a state; is a difference between a continuous control signal and an actual control input , is a time when a trigger condition is met, is a control signal, is a trigger time; represents a control input at a time , represents time.

[0012] Optionally, the control signal is generated by an event-triggered controller as follows: ; wherein, represents a designed event-triggered controller, and the output is a continuous control signal; is a first constant, is a second constant, , , is a virtual control input, is an error signal.

[0013] The application further provides a preset-time adaptive control system of a high-order nonlinear MIMO system, comprising: ​​The model building unit is used to establish a dynamic model of a high-order nonlinear MIMO system and to approximate the unknown nonlinear function in the dynamic model using a neural network. A tracking error generation unit is used to determine the tracking error based on the dynamic model; A virtual control law generation unit is used to construct a virtual control law and define a virtual error based on the tracking error; A filter unit is used to construct a preset time filter to process the virtual control law and determine the filtering error; the parameters of the preset time filter are configured to make the filtering error converge within a preset time. The actual control law generation unit is used to design the actual control law using an improved weighted integral technique, in combination with the tracking error, virtual error and filtering error, within the backstepping recursive framework. A control signal output unit is used to set an event triggering mechanism based on a relative threshold to output a control signal after modulating the actual control law.

[0014] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: The pre-set time adaptive control method for high-order nonlinear MIMO systems provided by this invention achieves direct pre-setting of the system's settling time, unaffected by the initial state, by constructing a pre-set time filter and ensuring that the filtering error converges within a pre-set time. This overcomes the limitations of existing finite-time control methods where the convergence time depends on the initial state, and fixed-time control methods where the upper bound of the convergence time is determined by controller parameters and cannot be flexibly set. By setting an event-triggered mechanism based on a relative threshold to modulate the control signal, and updating the control signal only when the triggering condition is met, the update frequency of the controller is significantly reduced. This effectively solves the problem of continuous control strategies consuming large amounts of communication and computing resources, achieving efficient resource utilization while maintaining control performance. Through the approximation of unknown nonlinear functions by neural networks, combined with the synergistic design of the pre-set time filter and the event-triggered mechanism, a complete control scheme is formed, ensuring that both the system tracking error and the filtering error converge to a small neighborhood near zero within a pre-set time, providing precise pre-set time control assurance for high-order nonlinear MIMO systems. Attached Figure Description

[0015] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same parts.

[0016] Figure 1 This is a schematic flowchart of a preset time adaptive control method for a high-order nonlinear MIMO system, as shown in an embodiment of the present invention. Figure 2 Command signals shown in embodiments of the present invention With output signal A schematic diagram of the trajectory; Figure 3 Errors shown in embodiments of the present invention and A schematic diagram of the trajectory; Figure 4 The filtering error shown in the embodiment of the present invention and A schematic diagram of the trajectory; Figure 5 Control input shown in the embodiment of the present invention and A schematic diagram of the trajectory; Figure 6 The signal response shown in the embodiment of the present invention Schematic diagram; Figure 7 The signal response shown in the embodiment of the present invention Schematic diagram; Figure 8 Event triggering as shown in the embodiments of the present invention and Images; Figure 9 Event triggering as shown in the embodiments of the present invention and Images; Figure 10 This is a schematic diagram of the module structure of the preset time adaptive control system of a high-order nonlinear MIMO system shown in an embodiment of the present invention; Figure 11 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0017] 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 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 are within the scope of protection of the present invention.

[0018] Please see Figure 1 , Figure 1 A schematic diagram of the method flow for a preset time adaptive control method for a high-order nonlinear MIMO system.

[0019] Preset time adaptive control methods for high-order nonlinear MIMO systems include: S101: Establish a dynamic model of a high-order nonlinear MIMO system and use a neural network to approximate the unknown nonlinear function in the dynamic model.

[0020] In applications, to achieve precise control of high-order nonlinear MIMO systems, a dynamic model is first established. This model is described by a set of differential equations, where each subsystem contains multiple coupled state variables. The system's dynamic characteristics are determined by unknown nonlinear functions and external disturbances. In the dynamic model, the state vector consists of multiple state variables, the control input is used to adjust the system dynamics, and the output is the physical quantity to be tracked. This dynamic model can accurately describe the dynamic behavior of high-order nonlinear MIMO systems under uncertainties and external disturbances.

[0021] For unknown nonlinear functions present in dynamic models, this invention employs neural networks for approximation. Neural networks, as an effective modeling tool for nonlinear systems, can approximate unknown nonlinear functions with arbitrary precision. Based on this neural network structure, a nonlinear approximator is designed to represent the unknown function as the sum of the neural network output and the approximation error, where the neural network output is calculated using the optimal weight vector, and the approximation error is a bounded constant. This approximation method transforms complex unknown nonlinear dynamics into a tractable parameterized form, providing a foundation for subsequent control design.

[0022] Specifically, the dynamic model of a high-order nonlinear MIMO system is described by the following differential equation: in, , No. The state vector of the system is represented as follows: , Represents the system state. Indicates the output. For an unknown nonlinear function, External disturbances It is a positive constant; Indicates the system status. Representing system dynamics, Representing system dynamics, Indicates control input, Represents an unknown function. Indicates interference. express 3D real vector space, express 3D real vector space, This indicates the number of states in the subsystem. This represents the order of each subsystem. The dynamic model contains an unknown smooth nonlinear function. Meet the conditions And subject to external disturbances Impact. These disturbances Restricted to a certain range, that is ,in It is a positive constant. and All are positive odd numbers.

[0023] in, Given an unknown nonlinear function, a neural network is used to approximate this unknown function; the mathematical expression of the neural network is: in, For the unknown function that needs to be approximated, , express 3D real vector space, Represents the estimated parameter vector, Indicates the number of neurons. Represents vector weights, express 3D real vector space, The basis functions are Gaussian, and their expressions are: in, and Indicates width, Indicates the central parameter, Indicates state, express A real vector space of dimension 1.

[0024] set up For set A continuous function in the form of a neural network. For any given positive constant Assume: Design the following nonlinear approximator: in, It is the optimal NN weight vector. It is a constant characterizing the NNN approximation error. This represents the unknown function that needs to be approximated. This represents Gaussian basis functions.

[0025] S102: Determine the tracking error based on the dynamic model.

[0026] After establishing a dynamic model and completing the neural network approximation of the unknown nonlinear function, it is necessary to determine the tracking error of the high-order nonlinear MIMO system based on this dynamic model. Tracking error, as a key indicator of system control performance, directly reflects the accuracy of the system output in tracking the desired trajectory. By calculating the difference between the output signal and the desired command in real time, an accurate tracking error signal is formed, thus providing a basis for the subsequent construction of virtual and actual control laws. By concretizing the system's control objective into an error adjustment problem, the entire control process gains clear direction.

[0027] S103: Construct a virtual control law based on the tracking error and define the virtual error.

[0028] After determining the tracking error, a virtual control law needs to be constructed based on this tracking error, and the virtual error itself needs to be defined. Unlike traditional methods that directly use state variables, this invention introduces an auxiliary function in the coordinate transformation, selecting the transformed auxiliary state variable to construct the virtual error. The virtual control law serves as an intermediate control variable, designing the desired dynamic characteristics for each subsystem, while the virtual error characterizes the deviation between the system state and the virtual control objective. This unique error definition not only provides a foundation for the design of the virtual control law but also effectively avoids the computational complexity and control singularities inherent in high-order systems under preset-time control, ensuring the smoothness and effectiveness of the control process.

[0029] S104: Construct a preset time filter to process the virtual control law and determine the filtering error.

[0030] The parameters of the preset time filter are configured to make the filtering error converge within a preset time.

[0031] Since continuous differentiation of the virtual control law in the backstep recursive framework leads to computational explosion, this invention constructs a nonlinear filter with preset time stability to process the virtual control law and determines the filtering error accordingly. This preset time filter performs differentiation operations on the virtual control law to generate the signals required for subsequent steps, while carefully configuring its design parameters to ensure that the dynamic behavior of the filtering error has preset time stability.

[0032] By selecting design parameters that meet specific conditions, such as ensuring that key filter design parameters are greater than or equal to half, it can be guaranteed that the filtering error will converge to a small set of residuals near the origin within a preset time. This effectively avoids the computational complexity caused by repeated differentiation in traditional backstepping recursive methods, significantly simplifying the implementation of the control law. Furthermore, by ensuring the filtering error converges within a preset time, a stable signal foundation is provided for the subsequent design of the actual control law. This convergence time is independent of the initial state and is directly set by the design parameters, laying the foundation for achieving the preset time stability of the entire control scheme.

[0033] Specifically, the equation for the preset time filter is as follows: in, The filter design parameters are the second design parameters, which affect the convergence behavior of the filtering error; For the first The first subsystem Auxiliary variables for filtering error in each state; Indicates the filter output signal; Indicates time; The transformed value used for stability analysis represents the first... The first subsystem The filtering error in each state; this transformation ensures that the Lyapunov derivative has a pre-defined time-convergent form, guaranteeing that the filtering error is within a certain time frame. Converging inwards to the set of residuals; The third and fourth design parameters, respectively, are used as adjustment parameters in the stabilization system and the control law. , , This is the eighth design parameter. Represents the system state dimension; This represents the fifth design parameter, a relative threshold parameter that affects the balance between triggering frequency and system performance. The method used to construct homogeneous convergence is key to achieving time stability.

[0034] When the filter input signal Meet the conditions hour, This is an unknown constant. For the preset time filter, select one that satisfies the condition... Suitable design parameters, Available at preset time The set of tiny residuals that converge to near the origin ;in, It is the primary design parameter that determines the system's convergence time. For the first The first subsystem Auxiliary variables for filtering error in each state. This represents the Lyapunov function for the filtered signal. This represents the third constant.

[0035] S105: Under the backstepping recursive framework, the actual control law is designed by combining tracking error, virtual error and filtering error using an improved weighted integral technique.

[0036] In applications, complex nonlinear terms can lead to control singularities, a problem that traditional control methods struggle to address. To address this, this invention employs an improved weighted integral technique, combined with an auxiliary function previously introduced to construct virtual errors, effectively preventing control singularities. The designed actual control law, through weighted integration of various error signals, forms a continuous control signal that effectively coordinates the elimination of tracking errors, compensation for virtual errors, and convergence of filtering errors. This design ensures the actual control law remains smooth and effective throughout the control process, not only preventing control singularities but also providing a final guarantee for the stability of the entire control scheme within a preset time, enabling all error signals to reach a stable state in a coordinated manner within the preset time.

[0037] The error model is represented by the following equation: in, Indicates tracking error. For virtual error, where , This indicates the auxiliary virtual control input of the design. Indicates the system status. express State estimates under the power of 1 express State estimates under the power of 1 Indicates the filtered signal. Represents the estimated value of virtual control; , It is the auxiliary function to be designed. Indicates virtual control input. Represents the estimated value of virtual control; These represent the input and output signals of the filter to be designed later. It is the first The first subsystem Auxiliary variables for filtering error in each state. Definition , and , The power representing the system state. Represents the power of the system state. Definition .

[0038] Introduce auxiliary functions into coordinate transformations, and select... Instead To construct virtual errors, similarly, using Instead The filter error is defined using an auxiliary function. This invention avoids singularities in the PTC process by introducing an auxiliary function, a problem that traditional superposition power integrator techniques cannot solve.

[0039] S106: Set an event triggering mechanism based on a relative threshold to modulate the actual control law and output a control signal.

[0040] To address the limitations of communication and computing resources in networked control environments, this invention introduces an event-triggered mechanism based on a relative threshold. This mechanism modulates the continuous-time actual control law to output the final control signal. The core feature of this mechanism is that the control signal is updated only when a specific trigger condition is met, rather than through continuous updates as in traditional methods, thus significantly reducing the controller's update frequency. The trigger condition is determined by real-time comparison of the difference between the continuous control signal and the actual control input. When the absolute value of this difference exceeds a dynamic threshold composed of a relative threshold and a constant term, the trigger condition is met, and the controller immediately updates the output signal.

[0041] This relative threshold strategy allows the trigger sensitivity to be automatically adjusted according to the amplitude of the control signal, ensuring control accuracy while avoiding frequent triggering issues that may occur when the signal is too small. In actual operation, the continuous control signal, as the theoretically ideal control quantity, contains comprehensive information from all error signals; while the actual control input acting on the controlled object is represented as a piecewise constant signal. The value of the current continuous control signal is acquired at the trigger moment and kept constant until the next trigger condition is met, at which point it is updated. This design effectively alleviates resource consumption issues, significantly reducing communication transmission volume and computational burden while ensuring preset time control performance. It avoids channel congestion that may result from continuous control, providing a reliable guarantee for the practical application of high-order nonlinear multiple-input multiple-output systems in resource-constrained environments.

[0042] Specifically, the ETM implementation based on a relative threshold is as follows: in, , , This is the sixth design parameter. This is the seventh design parameter. The order of the state. It is a continuous control signal With actual control input The difference between them; express Control input at any given time, Indicates time; The control signal is triggered when the triggering condition is met. It remains constant thereafter until the next triggering time. occur.

[0043] control signals The controller is triggered by the following events: in, This indicates the design of an event-triggered controller, whose output is a continuous control signal triggered by the event; the control signal in It is triggered at a certain time and remains constant thereafter until the next trigger time. occur; This serves as the controller refresh time; prior to this, the control signal remains constant. When the conditions are met The time will be refreshed to [time]. and control value Applied to the system. , , It is the first constant. It is the second constant. For virtual control input, This is the error signal.

[0044] This invention first models a high-order nonlinear MIMO system, and then uses the unknown nonlinear function... By utilizing neural networks for approximation and introducing nonlinear filters to address computationally complex issues, an event-triggered mechanism with a relative threshold is established. Furthermore, a pre-designed time filter is incorporated into the backstepping recursive framework to develop an adaptive pre-time event-triggered control method. This method incorporates an improved weighted integral technique to prevent control singularities. Finally, the stability of the nonlinear system can be proven using Lyapunov functions.

[0045] Simulation results are as follows Figures 2 to 9 As shown. From Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 It can be seen that, Able to track stably , It eventually stabilized within a small range. For example... Figure 5 The controller trajectory shown demonstrates that the preset time control scheme of the present invention can ensure that the preset time is met. It maintains internal stability and good performance. Figure 6 , Figure 7 , Figure 8 and Figure 9 This demonstrates the system's control execution frequency. It can be seen that the preset time control strategy affects the initial state. The changes exhibit strong robustness.

[0046] Corresponding to the aforementioned application function implementation method embodiments, the present invention also provides a preset time adaptive control system for a high-order nonlinear MIMO system and corresponding embodiments.

[0047] Please see Figure 10 , Figure 10 This is a schematic diagram of the module structure of a preset time adaptive control system for a high-order nonlinear MIMO system.

[0048] A preset time adaptive control system for a high-order nonlinear MIMO system includes: Model building unit 10 is used to build a dynamic model of a high-order nonlinear MIMO system and to approximate the unknown nonlinear function in the dynamic model using a neural network. Tracking error generation unit 11 is used to determine the tracking error based on the dynamic model; The virtual control law generation unit 12 is used to construct a virtual control law and define a virtual error based on the tracking error; Filter unit 13 is used to construct a preset time filter to process the virtual control law and determine the filtering error; the parameters of the preset time filter are configured to make the filtering error converge within a preset time. The actual control law generation unit 14 is used to design the actual control law by combining the tracking error, virtual error and filtering error under the backstepping recursion framework and using an improved weighted integration technique. The control signal output unit 15 is used to set an event triggering mechanism based on a relative threshold to output a control signal after modulating the actual control law.

[0049] Regarding the system in the above embodiments, the specific manner in which each unit module performs operations has been described in detail in the embodiments related to the method, and will not be elaborated further here.

[0050] Please see Figure 11 The electronic device 1100 includes a memory 1110 and a processor 1120.

[0051] The processor 1120 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0052] Memory 1110 may include various types of storage units, such as system memory, read-only memory (ROM), and permanent storage devices. ROM may store static data or instructions required by processor 1120 or other modules of the computer. Permanent storage devices may be read-write storage devices. Permanent storage devices may be non-volatile storage devices that retain stored instructions and data even when the computer is powered off. In some embodiments, permanent storage devices use mass storage devices (e.g., magnetic or optical disks, flash memory) as permanent storage devices. In other embodiments, permanent storage devices may be removable storage devices (e.g., floppy disks, optical drives). System memory may be a read-write storage device or a volatile read-write storage device, such as dynamic random access memory. System memory may store some or all of the instructions and data required by the processor during operation. Furthermore, memory 1110 may include any combination of computer-readable storage media, including various types of semiconductor memory chips (e.g., DRAM, SRAM, SDRAM, flash memory, programmable read-only memory), and disks and / or optical disks may also be used. In some embodiments, the memory 1110 may include a removable storage device that is readable and / or writable, such as a laser disc (CD), a read-only digital multifunction optical disc (e.g., DVD-ROM, dual-layer DVD-ROM), a read-only Blu-ray disc, an ultra-high density optical disc, a flash memory card (e.g., SD card, mini SD card, Micro-SD card, etc.), a magnetic floppy disk, etc. Computer-readable storage media do not contain carrier waves or transient electronic signals transmitted wirelessly or via wired connections.

[0053] The memory 1110 stores executable code, which, when processed by the processor 1120, can cause the processor 1120 to execute part or all of the methods described above.

[0054] Furthermore, the method according to the present invention can also be implemented as a computer program or computer program product, which includes computer program code instructions for performing some or all of the steps in the above-described method of the present invention.

[0055] Alternatively, the present invention may also be implemented as a computer-readable storage medium (or a non-transitory machine-readable storage medium or a machine-readable storage medium) storing executable code (or computer program or computer instruction code) thereon, which, when executed by a processor of an electronic device (or server, etc.), causes the processor to perform part or all of the steps of the methods described above according to the present application.

[0056] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or improvement of the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A preset time adaptive control method of a high-order nonlinear MIMO system, characterized by, The application relates to a method for designing a control law of a high-order nonlinear MIMO system. A dynamic model of the high-order nonlinear MIMO system is established, and a neural network is used to approximate unknown nonlinear functions in the dynamic model. A tracking error is determined based on the dynamic model. A virtual control law is constructed based on the tracking error, and a virtual error is defined. A preset time filter is constructed to process the virtual control law, and a filtering error is determined. In a backstepping recursive framework, an improved weighted integral technique is used to design an actual control law in combination with the tracking error, the virtual error and the filtering error. An event-triggered mechanism based on a relative threshold is set to modulate the actual control law and output a control signal.

2. The pre-set time adaptive control method of a high-order nonlinear MIMO system according to claim 1, characterized in that, An equation expression of the dynamic model is as follows: ； wherein, , the state vector of the represents the system state, represents the output, is an unknown nonlinear function, is an external disturbance, is a positive constant; represents the system state, represents the system dynamics, represents the system dynamics, represents the control input, represents an unknown function, represents a disturbance, represents a n-dimensional real vector space, represents a n-dimensional real vector space, represents the number of states of the subsystem, represents the order of each subsystem.​​ 3. The method of claim 1, wherein, A mathematical expression of the neural network is as follows: ； wherein, is an unknown function to be approximated, , denotes a d-dimensional real vector space, denotes an estimated parameter vector, denotes the number of neurons, denotes a vector weight, denotes a d-dimensional real vector space, is a Gaussian-type basis function, denotes a basis function.

4. The method of claim 1, wherein, An equation expression of the preset time filter is as follows: ； in, The filter design parameters are the second design parameters. The third and fourth design parameters are, in order. This is the fifth design parameter; For the first The first subsystem Auxiliary variables for filtering error in each state; This represents the filter output signal. Indicates time, The transformed value used for stability analysis represents the first... The first subsystem The filtering error for each state.

5. The method of claim 1, wherein, The filtering error converges to a residual set within a preset time, and an expression of the residual set is as follows: ； wherein is a first design parameter, is a first design parameter, is a first design parameter, is a first design parameter, represents a lower bound of the filtered signal, is a fifth design parameter; represents a third constant.

6. The method of claim 1, wherein, An implementation mode of the event-triggered mechanism is as follows: ； wherein , , is a sixth design parameter, is a seventh design parameter, denotes the order of the state; is a continuous control signal and the difference between the actual control input , is the time instant when the trigger condition is fulfilled, is a control signal, is the trigger time instant; denotes the control input at the time instant, denotes time.

7. The method of claim 6, wherein the method is a pre-set time adaptive control method for a high order nonlinear MIMO system. Control signals The controller is triggered by the following events: ； wherein, represents a designed event-triggered controller with output as continuous control signal; is a first constant, is a second constant, , , is a virtual control input, is an error signal.

8. A pre-set time adaptive control system for a high order nonlinear MIMO system, characterized by, The application relates to a method for designing a control law of a high-order nonlinear MIMO system. A model construction unit is used to establish a dynamic model of the high-order nonlinear MIMO system, and a neural network is used to approximate unknown nonlinear functions in the dynamic model. A tracking error generation unit is used to determine a tracking error based on the dynamic model. A virtual control law generation unit is used to construct a virtual control law based on the tracking error, and a virtual error is defined. A filter unit is used to construct a preset time filter to process the virtual control law, and a filtering error is determined. The parameters of the preset time filter are configured to make the filtering error converge within a preset time. An actual control law generation unit is used to design an actual control law in a backstepping recursive framework in combination with the tracking error, the virtual error and the filtering error. An improved weighted integral technique is used. A control signal output unit is used to set an event-triggered mechanism based on a relative threshold to modulate the actual control law and output a control signal.

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