Adaptive quantization event triggering control method and device for non-triangular nonlinear system

Abstract

The present invention discloses an adaptive quantization event-triggered control method and device for a non-triangular nonlinear system, which belongs to the field of automatic control technology and can control a non-triangular nonlinear system with quantized input. Through the improved dynamic gain technology, the limitations of the traditional scheme in processing quantized input errors and non-strict feedback structures are broken through, and the global practical tracking problem of a nonlinear system with both quantized input and triangular conditions can be solved. The designed controller does not depend on the quantizer parameters and can be applied to quantizers with different quantization densities, which enhances the versatility of the controller and eliminates the coupling relationship between the tracking error and the dynamic gain, ensuring that the system has a tracking solution. Finally, the dynamic gain is introduced into the control function and the event trigger threshold design, and an adaptive event trigger mechanism is constructed, so that the trigger threshold can be adaptively adjusted, thereby compensating for the unknown nonlinearity under the event trigger control framework.

Description

Technical Field

[0001] The present invention belongs to the technical field of automatic control, and relates to adaptive control of nonlinear systems, and in particular to an adaptive quantization event triggering control method and device for non-triangular nonlinear systems. Background Art

[0002] In modern control systems, adaptive control applications based on digitalization and network systems are gaining more and more attention. For example, intelligent manufacturing systems, autonomous driving control systems, flight control systems, etc. have all been upgraded from traditional automated control to networked control. Signal quantization and event triggering have become typical strategies for today's networked control because of their advantages in saving communication overhead and computing resources. However, signal quantization and event triggering inevitably bring about quantization errors and execution errors, which will lead to undesirable system performance deterioration or even instability. In addition, compared with lower triangular nonlinear systems, the nonlinear terms of non-triangular nonlinear systems actually contain all system states. Traditional design methods will lead to algebraic loop problems, so the existing quantized event triggering design methods will no longer be applicable.

[0003] There are two main control methods for non-triangular nonlinear systems: The first control method introduces a single dynamic gain to compensate for the unknown nonlinear term, thereby avoiding the algebraic loop problem. However, this method cannot avoid the coupling of quantization error and dynamic gain, and it is difficult to compensate for the quantization error. At the same time, it cannot guarantee the existence of a tracking solution for the system, that is, it cannot converge the tracking error to a controllable small enough interval, so it cannot be used to solve the adaptive quantization event-triggered tracking problem of non-triangular systems. Another control method uses a fuzzy logic system based on Gaussian functions or a radial basis neural network to approximate the unknown nonlinear term. Although it can effectively overcome the design difficulties brought by the non-triangular structure and ensure the existence of a tracking solution for the system, the system state is required to be restricted to a tight set, so it can only guarantee the stability of the system in a semi-global sense.

[0004] In addition, the controller in the current quantitative event triggered control method directly depends on the quantizer parameters or on the design constants of the quantizer parameters. When the quantizer parameters are unknown, the traditional quantitative event triggered control method will no longer be applicable. And when dynamic gain exists, how to design a reasonable event trigger mechanism so that the network control system remains stable is a technical problem in the industry.

[0005] In summary, designing a global adaptive quantization event-triggered tracking control method, device and system for non-triangular nonlinear systems that does not depend on quantizer parameters has important engineering application value for expanding the application scope of networked control systems and improving control performance. Summary of the invention

[0006] Taking into account the deficiencies of the prior art, the present invention proposes an improved dynamic gain technology for a type of non-triangular nonlinear system with quantized input, which relaxes the limitations of previous control methods in processing quantized input errors and non-triangular nonlinearities, and makes the controller independent of quantizer parameters, while eliminating the coupling relationship between tracking error and dynamic gain, which not only enhances the versatility of the controller but also ensures the tracking solution of the system. The dynamic gain is introduced into the control function and the event trigger threshold, so that the trigger threshold can be adaptively adjusted to compensate for the unknown nonlinearity under the event trigger control framework.

[0007] In a first aspect, the present invention provides an adaptive quantization event-triggered control method for a non-triangular nonlinear system, specifically comprising the following steps:

[0008] Step 1: Build a system model

[0009] For non-triangular nonlinear systems with quantized inputs Dimensional state space model:

[0010] (1)

[0011] in, for System status at all times, represents a set of n-dimensional vectors, , express Moment Maintain system status, express The first derivative of . , They are The system controls input and output at all times. Represents the set of real numbers. is the power of the system, represents the set of real numbers whose ratio of two positive odd numbers is greater than or equal to 1; represents a nonlinear function, is an unknown positive real number; is the control coefficient of the system, satisfying ,in are all positive real numbers and , It means to find the absolute value; For external disturbance, meet ,in is a positive real number. For control input quantized signal.

[0012] Preferably, the quantized signal adopts a log-uniform quantizer:

[0013] (2)

[0014] (3)

[0015] (4)

[0016] in, , , . , used to determine the logarithmic quantizer The quantization density of . Logarithmic Quantizer Dead zone size ,in . is a specified positive constant, indicating the switching threshold between the logarithmic quantizer and the uniform quantizer, Adjustable, Represents the set of all positive integers. Indicates less than or equal to The maximum integer. For the design parameters, the quantization density of the uniform quantizer is determined.

[0017] Defining quantization error , for any control input , there is always a normal number , so that , max{} means taking the maximum value. Due to the quantization error unknown, which means that the quantizer parameters , and is unknown.

[0018] Step 2: Introduce coordinate transformation

[0019] For the one established in step 1 The dimensional state space model makes the following assumptions:

[0020] (5)

[0021] in, , , Both Dynamic gain at all times, satisfying , , , , Respectively , The first derivative of . , is the power exponent of the dynamic gain, , ,and , , , , At the same time, the system's reference signal and its derivatives is bounded and continuous, satisfying ,in is a known positive constant.

[0022] Introduce a set of constructive coordinate transformation formulas , , , the The dimensional state space model can be rewritten as:

[0023] (6)

[0024] in, , , , , , ,when hour, ,when hour, . represents a diagonal matrix.

[0025] Defining virtual control laws and virtual error as follows:

[0026] (7)

[0027] in is the design parameter, Represents a symbolic function.

[0028] Step 3: Construction of adaptive quantization event-triggered controller based on improved dynamic gain

[0029] By combining improved dynamic gain technology, backstepping technology, power integral technology, sign function and hyperbolic tangent function, appropriate dynamic gain and Lyapunov function of tracking error and virtual error are selected, and the adaptive controller is recursively constructed. The specific steps are as follows:

[0030] s3.1. Select the first candidate Lyapunov function , and define the first virtual control law According to the definition of virtual control law and virtual error and the rewritten state space model, we can get:

[0031] (8)

[0032] in, and is a positive real number.

[0033] s3.2, for , assuming there exists a positive definite candidate Lyapunov function and a series of virtual controllers , virtual error , design parameters , , So that the following is true:

[0034] (9)

[0035] Select Candidate Lyapunov functions , , , according to formulas (7) and (9), and based on the power integration technique and inequality scaling, we can get:

[0036] (10)

[0037] S3.3, according to the recursive design steps in S3.2, combined with the quantization error ,definition , for the Candidate Lyapunov functions We can get:

[0038] (11)

[0039] Select the following auxiliary dynamic gain :

[0040] (12)

[0041] Substituting the auxiliary dynamic gain into The inequality of and scaling it yields:

[0042] (13)

[0043] in is an unknown parameter, , and are all positive real numbers.

[0044] s3.4. Selecting a Lyapunov-like function ,in , , Represent unknown parameters The estimated value and estimation error. , is the gain coefficient of the adaptive law. Define the adaptive law and adaptive dynamic gain They are:

[0045] (14)

[0046] (15)

[0047] in, Represents the correction parameter. According to the definition of adaptive law and adaptive dynamic gain, we can get:

[0048] (16)

[0049] s3.5. Design the following event triggering mechanism:

[0050] For the initial time , , Established, that is, the event triggering condition is not met.

[0051] If there is a moment ,satisfy , then trigger the event, let ; and before the next event triggers, the controller does not transmit a control signal to the actuator, that is, when When the control input In Keep constant, .in, represents the infimum of a set, , Respectively expressed as sequence The time when the event is triggered; is a continuous control function, Indicates the event trigger threshold, Trigger error for the event. Design parameters for event triggering mechanisms.

[0052] Based on the above event triggering mechanism, the following quantitative adaptive controller is designed:

[0053] (17)

[0054] in, and These are the design parameters of the event trigger mechanism and meet .

[0055] At this point, the network controller design is completed.

[0056] In a second aspect, the present invention provides an adaptive quantization event-triggered control device for a non-triangular nonlinear system, the device comprising a system modeling module, a parameter estimation module, a dynamic gain design module, a controller module, an event triggering module and a quantization module.

[0057] The system modeling module is used to select the state variables and control inputs of the system according to the differential equations of the non-triangular nonlinear system with uncertain parameters, and to construct accurate dynamic system equations, so as to provide a basis for subsequent analysis and controller design.

[0058] The parameter estimation module is used to construct an adaptive control law according to the state value of the actual system, and gradually approach the unknown dynamic parameters and unknown quantizer parameters in the system by adjusting the parameter estimation strategy in real time, thereby improving the system's adaptability and robustness, and ensuring the stability and performance optimization of the system in complex environments.

[0059] The dynamic gain design module is used to compensate for the quantization error introduced by the quantizer and the unknown nonlinear influence in the system, and ensures that the system can maintain stable tracking performance under different operating conditions by decoupling the relationship between tracking error and dynamic gain.

[0060] The controller module is used to construct a Lyapunov function containing tracking error and virtual error, and recursively design an adaptive controller to achieve precise adjustment of the system output so that it can effectively track the reference signal. The design of the Lyapunov function ensures the stability of the system, while the adaptive mechanism corrects the controller parameters in real time to cope with system dynamic changes and external interference, ensuring that the system output matches the reference signal quickly and accurately.

[0061] The event trigger module is used to construct an adaptive continuous control function according to the dynamic gain, and to design an event trigger threshold. By comparing the event trigger error with the set trigger threshold in real time, it is determined whether to activate the event trigger mechanism. The event trigger module can dynamically adjust the execution frequency of the controller under the premise of ensuring system performance and stability, reduce unnecessary calculation burden, and thus improve the response efficiency and resource utilization of the system.

[0062] The quantization module is used to design the quantizer density according to system requirements and performance indicators to accurately quantize the control input signal calculated by the controller module, ensuring that the control input signal optimizes the use of signal transmission and computing resources while meeting system stability and response speed, avoiding information loss due to over-quantization or control accuracy problems due to under-quantization.

[0063] In a third aspect, the present invention provides an adaptive quantization event-triggered control system for a non-triangular nonlinear system, comprising a memory for storing a computer program / instruction for network control, and a processor for executing the computer program / instruction in the memory to implement the global adaptive quantization event-triggered tracking control method for the above-mentioned nonlinear system.

[0064] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the above-mentioned adaptive quantization event-triggered control method for non-triangular nonlinear systems.

[0065] In a fifth aspect, the present invention provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, can implement the steps of the above-mentioned adaptive quantization event-triggered control method for a non-triangular nonlinear system.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] 1. The present invention can compensate for quantization error and nonlinearity at the same time by carefully designing and improving dynamic gain technology. In particular, the proposed controller is independent of the quantizer parameters and can be used for quantizers with different quantization densities without redesigning the controller, which has better versatility. In addition, while effectively avoiding the algebraic loop problem, the tracking solution of the system is also guaranteed; specifically, the coupling relationship between the tracking error and the dynamic gain is eliminated, so that the tracking error can be adjusted to any preset range.

[0068] 2. The present invention develops an adaptive event trigger mechanism by incorporating dynamic gain into the control function and event trigger threshold design. Unknown nonlinearity is compensated under the event trigger control framework, and the event trigger threshold is changed with the online adjustment of dynamic gain, avoiding the need for offline adjustment of the event trigger threshold to cope with severe system uncertainty. In addition, the proposed control method can ensure that the non-triangular nonlinear system has Lyapunov stability, the system output can track the reference signal with satisfactory tracking accuracy, and the Zeno phenomenon will not occur.

[0069] 3. The present invention constructs a global adaptive quantized event-triggered tracking control method, device and system for nonlinear systems, which can be used for global adaptive quantized event-triggered tracking control of non-triangular nonlinear networked control systems in different engineering application fields, including but not limited to permanent magnet brushed DC motor systems, gear transmission systems, and chemical reactor systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 A flow chart of an adaptive quantized event-triggered control method for a non-triangular nonlinear system;

[0071] Figure 2 A mapping diagram of a logarithmic-uniform quantizer designed in an embodiment for a control input;

[0072] Figure 3 It is a system state change trajectory diagram in the embodiment;

[0073] Figure 4 The output trajectory of the driven side gear position and the tracking error trajectory in the example simulation;

[0074] Figure 5 The input control torque and quantized input control torque trajectory diagram in the example simulation;

[0075] Figure 6 It is a schematic diagram of the event triggering interval in the example simulation;

[0076] Figure 7 It is a schematic diagram of a global adaptive quantized event-triggered tracking control device for a nonlinear system; DETAILED DESCRIPTION

[0077] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0078] Example 1

[0079] This embodiment provides an adaptive quantized event-triggered control method for a non-triangular nonlinear system, which is used to control a non-triangular nonlinear system with uncertain parameters, such as a permanent magnet brushed DC motor system, a gear transmission system, and a chemical reactor system. Figure 1 As shown, the specific steps include:

[0080] Step 1: According to the system differential equation of the actual physical system, select appropriate state variables, input signals and output signals to establish a mathematical model, so that all states of the system are globally bounded and output a tracking reference signal.

[0081] Step 2: Establish the Lyapunov function of tracking error and virtual error, and recursively construct a robust adaptive tracking controller based on the power integral technique, sign, hyperbolic tangent function technique and improved dynamic gain method.

[0082] The control effect of the network transmission controller designed by the present invention is analyzed and verified from the theoretical aspect and the simulation experiment aspect respectively.

[0083] Step 3: Theoretical analysis

[0084] s3.1. First, prove the boundedness of the closed-loop system.

[0085] Since the closed-loop system signal Continuity, exist The boundedness on exist is bounded above, where Can be a finite constant or Therefore, we only need to prove that The boundedness of the state of the system. For convenience, in the following proof represent .

[0086] According to the designed quantized adaptive controller, it can be deduced that:

[0087] (18)

[0088] in is a time-varying function that satisfies , . Further, we can get:

[0089] (19)

[0090] Substituting (19) into (16), we can get:

[0091] (20)

[0092] in , , and then according to The definition of can be obtained:

[0093] (twenty one)

[0094] (twenty two)

[0095] in , , is a Class function, that is exist is strictly increasing, and . for The inverse function of class function. This means that the state exist is globally bounded. According to the auxiliary dynamic gain and adaptive dynamic gain The definition of and is also globally bounded. Therefore, all states of the system exist Globally bounded, in addition, it can be deduced that:

[0096] (twenty three)

[0097] because , the final tracking error can be converged to a compact set In which .

[0098] s3.2. Secondly, it is proved that the adaptive quantized event-triggered control system under consideration is free from the Zeno phenomenon, that is, the interval between two adjacent trigger moments does not tend to zero.

[0099] definition ,according to , and The continuity can be obtained:

[0100] (twenty four)

[0101] in However, the quantized adaptive controller can be obtained , which means that there is no Zeno behavior in the proposed control scheme.

[0102] It is worth noting that the tracking error Directly controlled by input Smaller tracking errors often require larger control inputs. When the value of remains unchanged, decrease and increase Will cause enlargement and reduce The design parameters involved in the process enhance the flexibility of the control scheme and can more effectively adapt to different application scenarios and system requirements; for a specific system, under the premise of ensuring system stability, and Tune and get satisfactory ; Then, adjust , and To achieve the required control accuracy and control energy consumption, finally adjust , , and To obtain the appropriate quantizer density and event trigger interval.

[0103] Step 4: Simulation verification

[0104] This embodiment takes a gear transmission servo system as an example to verify the actual application effect of the control scheme designed by the present invention. The dynamic model of the gear transmission servo system is expressed as:

[0105] (25)

[0106] in , denote the angular position and angular velocity of the driven side gear respectively, , Respectively represent the angular position and angular velocity of the driving side gear, the unit of the angular position is rad, and the unit of the angular velocity is rad / s; , represent the moment of inertia and friction coefficient of the driven side gear respectively; , represent the moment of inertia and friction coefficient of the driving side gear respectively; is the transmission ratio; is the stiffness coefficient; is the input control torque; is an uncertain disturbance, satisfying , is a positive real number. Select the reference signal .

[0107] The adaptive quantized event-triggered tracking controller is designed as:

[0108] (26)

[0109] in is the coordinate transformation formula, ;Select parameters , , , . Given the initial conditions , , , , and , Figure 2 The designed log-uniform quantizer has the following parameters: , and The simulation results are as follows: Figures 3 to 6 As shown, Figure 3 The trajectory diagram shows the position and angular velocity of the driven side gear and the position and angular velocity of the driving side gear in the gear transmission servo system changing with time. The state of the system is globally bounded. Figure 4 is the output trajectory of the driven side gear position and the tracking error trajectory. Figure 4 It can be seen that the driven side gear position in the gear transmission servo system can track the reference signal very well. Figure 5 is the input control torque and quantized input control torque trajectory diagram, Figure 6 This is a schematic diagram of the event trigger interval. It can be seen that the quantizer and event trigger mechanism work smoothly, reducing network communication pressure and computational burden.

[0110] Example 2

[0111] This embodiment provides an adaptive quantization event-triggered control device for a non-triangular nonlinear system, such as Figure 7 As shown, it includes a system modeling module, a parameter estimation module, a dynamic gain design module, a controller module, an event trigger module and a quantization module.

[0112] The system modeling module is used to select state variables and control inputs of the system according to the differential equations of the non-triangular nonlinear system with uncertain parameters, and to construct accurate dynamic system equations, so as to provide a basis for subsequent analysis and controller design.

[0113] The parameter estimation module is used to construct an adaptive control law according to the state value of the actual system, and gradually approach the unknown dynamic parameters and unknown quantizer parameters in the system by adjusting the parameter estimation strategy in real time, thereby improving the system's adaptability and robustness, and ensuring the stability and performance optimization of the system in complex environments.

[0114] The dynamic gain design module is used to compensate for the quantization error introduced by the quantizer and the unknown nonlinear influence in the system, and ensures that the system can maintain stable tracking performance under different operating conditions by decoupling the relationship between tracking error and dynamic gain.

[0115] The controller module is used to construct a Lyapunov function containing tracking error and virtual error, and recursively design an adaptive controller to achieve precise adjustment of the system output so that it can effectively track the reference signal. The design of the Lyapunov function ensures the stability of the system, while the adaptive mechanism corrects the controller parameters in real time to cope with system dynamic changes and external interference, ensuring that the system output matches the reference signal quickly and accurately.

[0116] The event trigger module is used to construct an adaptive continuous control function according to the dynamic gain, and to design an event trigger threshold. By comparing the event trigger error with the set trigger threshold in real time, it is determined whether to activate the event trigger mechanism. The event trigger module can dynamically adjust the execution frequency of the controller under the premise of ensuring system performance and stability, reduce unnecessary calculation burden, and thus improve the response efficiency and resource utilization of the system.

[0117] The quantization module is used to design the quantizer density according to system requirements and performance indicators to accurately quantize the control input signal calculated by the controller module, ensuring that the control input signal optimizes the use of signal transmission and computing resources while meeting system stability and response speed, avoiding information loss due to over-quantization or control accuracy problems due to under-quantization.

[0118] Example 3

[0119] This embodiment provides an adaptive quantization event-triggered control system for a non-triangular nonlinear system, including a memory for storing a computer program / instruction for network control, and a processor for executing the computer program / instruction in the memory to implement the above-mentioned global adaptive quantization event-triggered tracking control method for the nonlinear system.

[0120] Example 4

[0121] This embodiment provides a computer-readable storage medium on which a computer program / instruction is stored. When the computer program / instruction is executed by a processor, the steps of the above-mentioned adaptive quantization event-triggered control method for non-triangular nonlinear systems are implemented.

[0122] Example 5

[0123] This embodiment provides a computer program product, including a computer program / instruction, which implements the steps of the above-mentioned adaptive quantization event-triggered control method for non-triangular nonlinear systems when the computer program / instruction is executed by a processor.

[0124] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0125] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0126] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0127] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0128] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

Claims

1. An adaptive quantized event-triggered control method for non-triangular nonlinear systems, characterized in that: The specific steps include: Step 1: Establish an n-dimensional state space model for a non-triangular nonlinear system with quantized input q(u(t)), where u(t) is the control input; Step 2: Assume that the nonlinear quantity f of the non-triangular nonlinear system i (θ,x(t)) satisfies: Among them, x(t) is the system state at time t, x j (t) represents the j-dimensional system state at time t; θ is an unknown positive real number; L(t) and N(t) are the dynamic gains at time t, κ j ,υ j is the power index, i=1,...,n, j=1,2,...,∞, And r1=1, κ1=1, υ1=-ω, ω is a positive integer; when i=1, When i=2,...,n, Assume that the system reference signal y d (t) and its derivative is bounded and continuous, satisfying in is a known positive constant, max{} means taking the maximum value; Step 3: Define the virtual control law α i and virtual error ζ i as follows: where β1,...,β n is the design parameter, sgn(·) represents the sign function; η1(t), η i (t) represents the construction coordinate transformation formula Establish the Lyapunov function of tracking error and virtual error, and recursively construct the adaptive controller. The specific steps are as follows: s3.

1. Select the first candidate Lyapunov function And define the first virtual control law According to the definition of virtual control law and virtual error and the rewritten state space model, we can get: Among them, λ 1,1 and λ 1,2 is a positive real number; is the control coefficient of the system, satisfying in are all positive real numbers and || means to find the absolute value; s3.

2. For k<n, assume that there exists a positive candidate Lyapunov function V k-1 (t) and a series of virtual controllers α1(t),...,α k-1 (t), virtual error ζ1(t),...,ζ k-1 (t), design parameters μ1>1,...,μ k-2 >1,λ k-1,1 >0,λ k-1,2 >0 makes the following equation true: Select the kth candidate Lyapunov function V k (t) = μ k-1 V k-1 (t)+E k (t), μ k-1 ≥1, based on the power-integration technique and inequality scaling: S3.3, according to the recursive design steps in S3.2, combined with the quantization error |q(u(t))-u(t)|≤△ q ,definition For the nth candidate Lyapunov function V n (t) Existence: Select the auxiliary dynamic gain N(t) as follows: Substituting the auxiliary dynamic gain into Inequality of and scaling: in are unknown parameters, m1, m2 and m3 are all positive real numbers; s3.

4. Selecting a Lyapunov-like function in Represent unknown parameters The estimated value and estimation error of ; γ>0, is the gain coefficient of the adaptive law; define the adaptive law And the adaptive dynamic gain L(t) are: Among them, π>0, which represents the correction parameter; according to the definition of the adaptive law and adaptive dynamic gain, we get: s3.5, the event trigger mechanism is designed as follows: △ e (t)=w(t)-v(t), Among them, ε>0 and g>0 are the design parameters of the event trigger mechanism, and they satisfy Step 4: Design an event trigger mechanism. When there is a time t h satisfy When the event is triggered, let v(t h )=w(t h ); and before the next event triggering moment, the controller does not transmit the control signal to the actuator; where t0 = 0, inf{} represents the infimum of the set, w(t) is the continuous control function, Indicates the event trigger threshold, △ e (t) is the event trigger error; Design parameters for event triggering mechanisms; Design of quantized adaptive controller based on event-triggered mechanism.

2. The adaptive quantization event-triggered control method for non-triangular nonlinear systems according to claim 1, characterized in that: The non-triangular nonlinear system is one of a permanent magnet brushed DC motor system, a gear transmission system or a chemical reactor system.

3. The adaptive quantization event-triggered control method for non-triangular nonlinear systems according to claim 1, characterized in that: The following n-dimensional state space model is established for non-triangular nonlinear systems with quantized inputs: in, is the system state at time t, represents a set of n-dimensional vectors, x i (t) represents the state of the i-th dimension system at time t, Represents x i The first derivative of (t); is the system output at time t, represents the set of real numbers; is the power of the system, represents the set of real numbers whose ratio of two positive odd numbers is greater than or equal to 1; d i (t) is the external disturbance, satisfying in is a positive real number.

4. The adaptive quantization event-triggered control method for non-triangular nonlinear systems according to claim 3, characterized in that: The quantized signal q(u(t)) is in the form of a log-uniform quantizer: Among them, u j =ρ (1-j) u1, j = 1, 2, ..., ∞, u1>0; 0<ρ<1, used to determine the logarithmic quantizer q l Quantization density of (u); logarithmic quantizer q l The dead zone size u of (u) min =u1 / (1+δ), where δ=(1-ρ) / (1+ρ); is a specified positive constant, indicating the switching threshold between the logarithmic quantizer and the uniform quantizer, j th is a positive integer; Int[a] represents the largest integer less than or equal to a; It is a design parameter used to determine the quantization density of the uniform quantizer.

5. The adaptive quantization event-triggered control method for non-triangular nonlinear systems according to claim 3, characterized in that: Introduce a set of constructive coordinate transformation formulas The n-dimensional state space model of the system is rewritten as: Where, η(t)=(η1(t),η2(t),...,η n (t)) T , κ=Diag(κ1,κ2,…,κ n ), υ=Diag(υ1,υ2,…,υ n ); Diag() represents a diagonal matrix.

6. An adaptive quantization event-triggered control device for a non-triangular nonlinear system, characterized in that: The device is used to implement the global adaptive quantization event-triggered tracking control method of the nonlinear system as claimed in any one of claims 1 to 5, comprising a system modeling module, a parameter estimation module, a dynamic gain design module, a controller module, an event triggering module and a quantization module; The system modeling module is used to select state variables and control inputs of the system and construct dynamic system equations according to differential equations of non-triangular nonlinear systems with uncertain parameters; The parameter estimation module is used to construct an adaptive control law according to the state value of the actual system, and adjust the parameter estimation in real time to gradually approach the unknown dynamic parameters and unknown quantizer parameters in the system; The dynamic gain design module is used to compensate for the quantization error introduced by the quantizer and the unknown nonlinear influence in the system, and decouple the relationship between the tracking error and the dynamic gain; The controller module is used to construct a Lyapunov function including a tracking error and a virtual error, and recursively design an adaptive controller so that the system output can track a reference signal; The event trigger module is used to construct an adaptive continuous control function according to the dynamic gain, design an event trigger threshold, and determine whether to activate the event trigger mechanism by comparing the event trigger error with the set trigger threshold in real time; The quantization module is used to design the quantizer density according to system requirements and performance indicators.

7. Adaptive quantized event-triggered control system for non-triangular nonlinear systems, characterized by: It comprises a memory for storing a computer program / instruction for network control, and a processor for executing the computer program / instruction in the memory to implement the global adaptive quantization event-triggered tracking control method for a nonlinear system as claimed in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: A computer program / instruction is stored thereon, and when the computer program / instruction is executed by a processor, the steps of the adaptive quantization event-triggered control method for a non-triangular nonlinear system as claimed in any one of claims 1 to 5 can be implemented.

9. A computer program product, characterized in that: It comprises a computer program / instruction, which, when executed by a processor, can implement the steps of the adaptive quantization event-triggered control method for a non-triangular nonlinear system as claimed in any one of claims 1 to 5.

Images