Mechanical arm control method and system based on switching system under triggering of state event

Abstract

The invention discloses a mechanical arm control method based on a switching system under triggering of a state event, which comprises the following steps of: (1) acquiring modal jump of a mechanical arm system, and modeling the mechanical arm system into a switching nonlinear system model with uncertainty according to different modals; (2) the switching nonlinear system model has unknown parameters and an unknown nonlinear function, approximates the unknown nonlinear function by using a neural network technology, and processes the unknown parameters by using an adaptive parameter updating law; and (3) a state event triggering mechanism is introduced, a state event triggering controller is designed, and the mechanical arm is controlled through the state event triggering controller. The problems of communication congestion and low control efficiency caused by the fact that a sensor needs to monitor the detected state in real time and continuously transmits the detected state to a controller end in traditional control can be effectively solved, and therefore energy loss is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of robot arm trajectory control, and in particular to a robot arm control method and system based on a switching system under state event triggering. Background Art

[0002] The tracking control of robotic arms has long been a research hotspot in robotics, particularly in applications requiring high-precision motion and strict real-time performance, which place higher demands on control performance. Traditional robotic arm control methods, such as adaptive backstepping and PID control, rely on continuous signal input and feedback to ensure precise movement of the robotic arm along the desired trajectory. However, as system control accuracy and response speed requirements increase, the sampling frequency often needs to be very high. This results in a large amount of data acquisition and computation, placing extremely high demands on the processor's computing power. Excessive computational burden not only consumes significant computing resources but can also affect the system's real-time performance and, in extreme cases, even prevent the control task from being completed in a timely manner. Therefore, reducing the computational burden and response latency while ensuring control accuracy and real-time performance has become a major challenge in current robotic arm control research. Summary of the Invention

[0003] Purpose of the invention: To overcome the deficiencies in the prior art, a method and system for controlling a robotic arm based on a switching system triggered by a state event is provided, which solves the problems of communication congestion and low control efficiency caused by the need for sensors to monitor the measured state in real time and continuously transmit it to the controller in traditional control.

[0004] Technical solution: A robotic arm control method based on a switching system triggered by a state event includes the following steps:

[0005] (1) Obtain the modal jump of the robotic arm system and model the robotic arm system into a switching nonlinear system model with uncertainty according to different modes;

[0006] (2) The switching nonlinear system model has unknown parameters and unknown nonlinear functions, and the unknown nonlinear functions are approximated by neural network technology, and the unknown parameters are processed by adaptive parameter update law;

[0007] (3) Introduce the state event trigger mechanism, design the state event trigger controller, and use the state event trigger controller to control the robotic arm.

[0008] Furthermore, the switching nonlinear system model adopts a single-chain manipulator, which includes a rigid link connected to the motor through a gear system. q represents the displacement of the link. is the connecting rod speed, is the connecting rod acceleration; select the state variable x1=MDq, x3=Mτ. Using the Euler-Lagrange equation and Kirchhoff’s voltage law, we can get the state space equation of the single-chain manipulator:

[0009]

[0010] Where τ is the torque generated by the electrical subsystem, u is the motor control torque, y is the output of the system, B is the viscous friction coefficient at the motor and connecting rod joint, M and H are the armature inductance and armature resistance respectively, and K m is the back electromotive force coefficient, N is a positive constant related to the load mass and gravity coefficient, and D represents the mechanical inertia. For different load masses, the mechanical inertia will change accordingly.

[0011] Furthermore, the given working condition is that the robot moves a specified load sequentially, and the goal is to make the robot's motion track a given trajectory;

[0012] Assuming the load mass is unknown, the state space dynamic equation of the manipulator is:

[0013]

[0014] in, is a piecewise constant right continuous switching signal, Indicates that the pth subsystem operates in this interval, t∈[τ s ,τ s+1 ), τ s To switch the time series, represents the set of positive integers;

[0015] Assume σ∈{1,2}, because mechanical inertia and back electromotive force are affected by the unknown load mass, D1, D2, N1, N2, K m All of them are unknown constant parameters; because D1, D2, N1, N2, K m The existence of these unknown parameters makes the state space equation Considered as an unknown constant parameter θ σ , x2 is regarded as a bounded smooth function The unknown nonlinear function includes an unknown nonlinear function f σ,2 (x1,x2) and unknown nonlinear function f σ,3 (x1,x2,x3), As an unknown nonlinear function f σ,2 (x1, x2), in order to demonstrate the powerful technical potential of this invention, As an unknown nonlinear function f σ,3 (x1,x2,x3).

[0016] Furthermore, the use of neural network technology to approximate unknown nonlinear functions includes, in a suitable compact set Ω χ Among them:

[0017]

[0018] where χ k is the input vector of the neural network, W p,k is the ideal weight matrix, is the transpose of the ideal weight matrix, φ k (χ k )=[φ k1 (χ k ),…,φ kl (χ k )] T is the basis function vector, ω p,k (χ k ) is the approximation error.

[0019] Assume that in the compact set Ω χ In the equation, the approximation error satisfies Then there exists:

[0020]

[0021] in is an unknown positive constant,

[0022] Furthermore, the basis function selects the Gaussian kernel function Among them C h is the center of the receptive field, b h is the width of the Gaussian kernel function.

[0023] Furthermore, the adaptive parameter update law is used to process unknown parameters: for the unknown parameter η k ,θ σ , the present invention uses the following adaptive parameter update law to estimate:

[0024]

[0025] where ε k , δ k , g, β, γ k are all positive design parameters, which are parameters set autonomously according to requirements; Proj{·} represents the parameter projection operator, and θ0 is a positive constant; To introduce tracking error after event triggering, z k is the tracking error;

[0026] Furthermore, the triggering mechanism of the introduction status event is as follows:

[0027]

[0028] in are all positive design parameters, x k (t) represents the kth system state quantity, represents the trigger value of the kth system state quantity, α kf (t) represents the output of the kth first-order filter, Represents the trigger value of the output of the kth first-order filter, inf represents the infimum, represents the lth triggering moment of the kth state, represents the l+1th triggering moment of the kth state, represents the lth triggering moment of the kth first-order filter output, Represents the l+1th triggering moment of the kth first-order filter output. Once the triggering condition is met, the above state event trigger mechanism will The state quantity x at this moment k (t) will be used for feedback transmission and at time intervals remains unchanged in The output of the first-order filter at this moment will be used for feedback transmission and at time intervals remains unchanged;

[0029] For systems with state trigger settings, only the trigger state Can be used in system design, so as to design state event trigger controller, including virtual control law, control input u σ , adaptive parameter update law, and the virtual control law is:

[0030]

[0031] Control input u σ for:

[0032]

[0033] The adaptive parameter update law is:

[0034]

[0035] Among them, c k , γ k , ε k , δ k , k=1,2,3 and g,β are all positive design parameters, To introduce tracking error after the event is triggered, is the kth virtual control law αk Introducing the virtual control law after event triggering, To introduce the output of the first-order filter after the event trigger, the first-order filter is expressed as α k-1 is the virtual control law before event triggering is introduced, μ k is the time constant, represents the reference trajectory y d The third-order derivative of Indicates the relationship between η k The estimated value of Represents theta σ , tanh represents the hyperbolic tangent function, Proj{·} represents the parameter projection operator, and θ0 is a positive constant.

[0036] Furthermore, the method also includes performing stability analysis on the closed-loop system, and the process is as follows:

[0037] Given the reference trajectory of the robot arm is y d (t) = sin(1.5t), define the error variable

[0038] z1=x1-y d

[0039]

[0040] Among them, α 2f , α 3f is the output of the first-order filter, and the first-order filter is expressed as α kf (0) = α k-1 (0), k=2,3,μ k is the time constant, α k-1 is the virtual control law, It is y d First-order derivative, It is y d Second-order derivative; select the Lyapunov function of the manipulator system

[0041]

[0042] in, is the unknown parameter η r Estimates, is the unknown parameter θ σ Estimates of ζ r+1 is the error of the first-order low-pass filter, γ r >0 is a design parameter;

[0043] V σ Taking the derivative with respect to time t, we get

[0044]

[0045] Substitute the control law and adaptive law into In the example, combined with the properties of the hyperbolic tangent function in κ=0.2785, and applying Young's inequality we get

[0046]

[0047] Where T max , k=1,2,3, are all positive numbers; △z k , ρ kd , τ k , k=1,2,3 depends on the trigger threshold and And the design parameter μ k and c k A positive constant; and also satisfies the following inequalities:

[0048]

[0049] because right By combining similar items, we can obtain:

[0050]

[0051] in

[0052]

[0053]

[0054] Special attention should be paid to the switching point τ s V 1,3 and V 2,3 According to the properties of parameter projection, we can get and Then there is and

[0055] Difference of V1 and V2 gives:

[0056]

[0057] Since the Lyapunov function derivatives of each subsystem have the same form, we assume that the piecewise continuous differentiable function ν(t): = V σ,n (t), For any t∈[τs ,τ s+1 )

[0058]

[0059] Represents τ s The left boundary value of λ is the attenuation term, △ is the positive term boundary, and Λ is the maximum jump error value of the Lyapunov function caused by switching; applying mathematical induction and the properties of the dwell time, we can get

[0060]

[0061] From the above formula, we can get This means that ν(t) has an upper bound independent of t, given by We can get z1, z2, z3, is bounded, and the properties of parameter projection show that θ σ , Is bounded, the reference signal y d (t) is bounded, which guarantees that x1 is bounded. In a similar way, we can get x1, x2, x3 and f σ,2 ,f σ,3 is bounded, so it follows that the control input u is also bounded. Therefore, all signals in the closed-loop system are bounded;

[0062] Depend on Desirable limit

[0063]

[0064] because For all All hold true, so z1 will converge to an adjustable tight set.

[0065] Furthermore, Zeno behavior is avoided in event-triggered control, that is, there is a strictly positive lower bound on the time interval between two adjacent triggering moments.

[0066] A switching system-based robotic arm control system triggered by state events includes a single-chain robotic arm including a rigid link connected to a motor via a gear train. Given a working condition where the robotic arm sequentially moves a specified load, the goal is to make the robotic arm's motion track a given trajectory.

[0067] The step of making the robot arm track a given trajectory includes:

[0068] The modal jump of the robotic arm system is obtained, and the robotic arm system is modeled into a switching nonlinear system model with uncertainty for different modes; the switching nonlinear system model has unknown parameters and unknown nonlinear functions, and the unknown nonlinear functions are approximated by neural network technology, and the unknown parameters are processed by adaptive parameter update law; a state event trigger mechanism is introduced, and a state event trigger controller is designed, which is used to control the robotic arm.

[0069] Beneficial effects: By reducing unnecessary real-time transmission, the present invention can effectively solve the problems of communication congestion and low control efficiency caused by the need for sensors to monitor the measured state in real time and continuously transmit it to the controller in traditional control, thereby reducing energy loss. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 A schematic diagram of tracking the output trajectory of the robotic arm of the present invention;

[0071] Figure 2 is a parameter estimation diagram of the present invention;

[0072] Figure 3 This is the state triggering moment diagram of the present invention. DETAILED DESCRIPTION

[0073] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0074] Example 1:

[0075] The control method of a robotic arm based on a switching system under state event triggering includes the following steps:

[0076] (1) Obtain the modal jump of the robotic arm system and model the robotic arm system into a switching nonlinear system model with uncertainty according to different modes;

[0077] (2) The switching nonlinear system model has unknown parameters and unknown nonlinear functions, and the unknown nonlinear functions are approximated by neural network technology, and the unknown parameters are processed by adaptive parameter update law;

[0078] (3) Introduce the state event trigger mechanism, design the state event trigger controller, and use the state event trigger controller to control the robotic arm.

[0079] Furthermore, the switching nonlinear system model adopts a single-chain manipulator, which includes a rigid link connected to the motor through a gear system. q represents the displacement of the link. is the connecting rod speed, is the connecting rod acceleration; select the state variable x1=MDq, x3=Mτ. Using the Euler-Lagrange equation and Kirchhoff’s voltage law, we can get the state space equation of the single-chain manipulator:

[0080]

[0081] Where τ is the torque generated by the electrical subsystem, u is the motor control torque, y is the output of the system, B is the viscous friction coefficient at the motor and connecting rod joint, M and H are the armature inductance and armature resistance respectively, and K m is the back electromotive force coefficient, N is a positive constant related to the load mass and gravity coefficient, and D represents the mechanical inertia. For different load masses, the mechanical inertia will change accordingly.

[0082] Furthermore, the given working condition is that the robot moves a specified load sequentially, and the goal is to make the robot's motion track a given trajectory;

[0083] Assuming the load mass is unknown, the state space dynamic equation of the manipulator is:

[0084]

[0085] in, is a piecewise constant right continuous switching signal, Indicates that the pth subsystem operates in this interval, t∈[τ s ,τ s+1 ), τ s To switch the time series, represents the set of positive integers;

[0086] Assume σ∈{1,2}, because mechanical inertia and back electromotive force are affected by the unknown load mass, D1, D2, N1, N2, K m All of them are unknown constant parameters; because D1, D2, N1, N2, K m The existence of these unknown parameters makes the state space equation Considered as an unknown constant parameter θ σ , x2 is regarded as a bounded smooth function The unknown nonlinear function includes an unknown nonlinear function f σ,2 (x1,x2) and unknown nonlinear function f σ,3 (x1,x2,x3), As an unknown nonlinear function f σ,2 (x1, x2), in order to demonstrate the powerful technical potential of this invention, As an unknown nonlinear function f σ,3 (x1,x2,x3).

[0087] Furthermore, the use of neural network technology to approximate unknown nonlinear functions includes, in a suitable compact set Ωχ Among them:

[0088]

[0089] where χ k is the input vector of the neural network, W p,k is the ideal weight matrix, is the transpose of the ideal weight matrix, φ k (χ k )=[φ k1 (χ k ),…,φ kl (χ k )] T is the basis function vector, ω p,k (χ k ) is the approximation error.

[0090] Assume that in the compact set Ω χ In the equation, the approximation error satisfies Then there exists:

[0091]

[0092] in is an unknown positive constant,

[0093] Furthermore, the basis function selects the Gaussian kernel function Among them C h is the center of the receptive field, b h is the width of the Gaussian kernel function.

[0094] Furthermore, the adaptive parameter update law is used to process unknown parameters: for the unknown parameter η k ,θ σ , the present invention uses the following adaptive parameter update law to estimate:

[0095]

[0096] where ε k , δ k , g, β, γ k are all positive design parameters, Proj{·} represents the parameter projection operator, and θ0 is a positive constant; To introduce tracking error after event triggering, z k is the tracking error;

[0097] Furthermore, the triggering mechanism of the introduction status event is as follows:

[0098]

[0099] in are all positive design parameters, x k (t) represents the kth system state quantity, represents the trigger value of the kth system state quantity, α kf (t) represents the output of the kth first-order filter, Represents the trigger value of the output of the kth first-order filter, inf represents the infimum, represents the lth triggering moment of the kth state, represents the l+1th triggering moment of the kth state, represents the lth triggering moment of the kth first-order filter output, Represents the l+1th triggering moment of the kth first-order filter output. Once the triggering condition is met, the above state event trigger mechanism will The state quantity x at this moment k (t) will be used for feedback transmission and at time intervals remains unchanged in The output of the first-order filter at this moment will be used for feedback transmission and at time intervals remains unchanged;

[0100] For systems with state trigger settings, only the trigger state Can be used in system design, so as to design state event trigger controller, including virtual control law, control input u σ , adaptive parameter update law, and the virtual control law is:

[0101]

[0102] Control input u σ for:

[0103]

[0104] The adaptive parameter update law is:

[0105]

[0106] Among them, c k , γ k , ε k , δ k , k=1,2,3 and g,β are all positive design parameters, To introduce tracking error after the event is triggered, is the kth virtual control law α k Introducing the virtual control law after event triggering, To introduce the output of the first-order filter after the event trigger, the first-order filter is expressed as α k-1 is the virtual control law before event triggering is introduced, μ k is the time constant, represents the reference trajectory y d The third-order derivative of Indicates the relationship between η k The estimated value of Represents theta σ , tanh represents the hyperbolic tangent function, Proj{·} represents the parameter projection operator, and θ0 is a positive constant.

[0107] Furthermore, the method also includes performing stability analysis on the closed-loop system, and the process is as follows:

[0108] Given the reference trajectory of the robot arm is y d (t) = sin(1.5t), define the error variable

[0109] z1=x1-y d

[0110]

[0111] Among them, α 2f , α 3f is the output of the first-order filter, and the first-order filter is expressed as α kf (0) = α k-1 (0), k=2,3,μ k is the time constant, α k-1 is the virtual control law, and the Lyapunov function of the manipulator system is selected:

[0112]

[0113] in, is the unknown parameter η r Estimates, is the unknown parameter θ σ Estimates of ζ r+1 is the error of the first-order low-pass filter, γ r >0 is a design parameter;

[0114] V σ Taking the derivative with respect to time t, we get

[0115]

[0116] Substitute the control law and adaptive law into In the example, combined with the properties of the hyperbolic tangent function in κ=0.2785, and applying Young's inequality we get

[0117]

[0118] Where T max , k=1,2,3, are all positive numbers; △z k , ρ kd , τ k , k=1,2,3 depends on the trigger threshold and And the design parameter μ k and c k A positive constant; and also satisfies the following inequalities:

[0119]

[0120] because right By combining similar items, we can obtain:

[0121]

[0122] in

[0123]

[0124]

[0125] Special attention should be paid to the switching point τ s V 1,3 and V 2,3 According to the properties of parameter projection, we can get and Then there is and

[0126] Difference of V1 and V2 gives:

[0127]

[0128] Since the Lyapunov function derivatives of each subsystem have the same form, we assume that the piecewise continuous differentiable function ν(t): = V σ,n (t), For any t∈[τ s ,τ s+1 )

[0129]

[0130] Represents τ s The left boundary value of λ is the attenuation term, △ is the positive term boundary, and Λ is the maximum jump error value of the Lyapunov function caused by switching; applying mathematical induction and the properties of the dwell time, we can get

[0131]

[0132] From the above formula, we can get This means that ν(t) has an upper bound independent of t, given by We can get z1, z2, z3, is bounded, and the properties of parameter projection show that θ σ , Is bounded, the reference signal y d (t) is bounded, which guarantees that x1 is bounded. In a similar way, we can get x1, x2, x3 and f σ,2 ,f σ,3 is bounded, it follows that the control input u is also bounded. Therefore, all signals in the closed-loop system are bounded.

[0133] Depend on Desirable limit

[0134]

[0135] because For all All hold true, so z1 will converge to an adjustable tight set.

[0136] Furthermore, Zeno behavior is avoided in event-triggered control, that is, there is a strictly positive lower bound on the time interval between two adjacent triggering moments.

[0137] The process is as follows:

[0138] First, we define the sampling error

[0139]

[0140] Right|e k (t)|Find the derivative with respect to time t and we get

[0141]

[0142] From the above stability analysis of the closed-loop system, it can be seen that all signals in the closed-loop system are bounded, which means that the right side of the above equation is bounded, that is, there is a constant T * >0, so that Combined with event triggering mechanism

[0143]

[0144] Available

[0145]

[0146] Special attention should be paid to the situation at the switching moment. When the system is at the switching point τ s When switching occurs, we know that the state of the system before and after the switching point does not jump, which means that the error e k (t) is continuous at the switching point, that is, the error e k The derivative of (t) before and after the switching point is also bounded.

[0147] According to the above discussion, when no switching occurs between two adjacent trigger intervals, the error e k The derivative of (t) is always bounded, which means that there is always a minimum lower limit for the trigger interval. When there are finite switching behaviors between two adjacent trigger intervals, e k (t) is also bounded in the finite time interval excluding the switching point, and the error e k (t) is continuous at the switching point. Therefore, it can be concluded that the event-triggered strategy is Zeno-free.

[0148] In order to verify the feasibility of the proposed method, the present invention provides the simulation results of the control method on the MATLAB platform: the parameters are given as follows: the width b of the Gaussian function h =3.5, the centers of the RBF neural network are evenly distributed in the interval [-1,1]×[-1.5,1.5], c1=3, c2=8.04, c3=22.4, γ1=4.5,γ2=5.5,γ3=5,ε1=0.01,ε2=0.005,ε3=0.01,g=0.1,β=0.5。The initial conditions are as follows: x1(0)=0.5,x2(0)=-0.5,x3(0)=0.8, τ d =2s.

[0149] Example 2:

[0150] A switching system-based robotic arm control system triggered by state events includes a single-chain robotic arm including a rigid link connected to a motor via a gear train. Given a working condition where the robotic arm sequentially moves a specified load, the goal is to make the robotic arm's motion track a given trajectory.

[0151] The step of making the robot arm track a given trajectory includes:

[0152] The modal jump of the robotic arm system is obtained, and the robotic arm system is modeled into a switching nonlinear system model with uncertainty for different modes; the switching nonlinear system model has unknown parameters and unknown nonlinear functions, and the unknown nonlinear functions are approximated by neural network technology, and the unknown parameters are processed by adaptive parameter update law; a state event trigger mechanism is introduced, and a state event trigger controller is designed, which is used to control the robotic arm.

[0153] Traditional control systems rely too heavily on real-time sensor data transmission, forcing the controller to process a large amount of redundant information. This not only increases computational complexity but can also affect system response time. This invention, however, uses event triggering to ensure that the controller is updated only when necessary, thereby optimizing the use of controller resources and improving overall control efficiency.

Claims

1. A robotic arm control method based on a switching system triggered by a state event, characterized in that: The following steps are involved: (1) Obtain the modal jump of the robotic arm system and model the robotic arm system into a switching nonlinear system model with uncertainty according to different modes; (2) The switching nonlinear system model has unknown parameters and unknown nonlinear functions, and the unknown nonlinear functions are approximated by neural network technology, and the unknown parameters are processed by adaptive parameter update law; (3) Introduce the state event trigger mechanism, design the state event trigger controller, and use the state event trigger controller to control the robotic arm.

2. The method for controlling a robotic arm based on a switching system under state event triggering according to claim 1, characterized in that: The switching nonlinear system model adopts a single-chain manipulator, which includes a rigid link connected to a motor through a gear system. q represents the displacement of the link. is the connecting rod speed, is the connecting rod acceleration; Select the state variable x1=MDq, x3=Mτ. Using the Euler-Lagrange equation and Kirchhoff’s voltage law, we can get the state space equation of the single-chain manipulator: Where τ is the torque generated by the electrical subsystem, u is the motor control torque, y is the output of the system, B is the viscous friction coefficient at the motor and connecting rod joint, M and H are the armature inductance and armature resistance respectively, and K m is the back electromotive force coefficient, N is a positive constant related to the load mass and gravity coefficient, and D represents the mechanical inertia. For different load masses, the mechanical inertia will change accordingly.

3. The method for controlling a robotic arm based on a switching system under state event triggering according to claim 1, characterized in that: The given working condition is that the robot arm moves a specified load in sequence, and the goal is to make the robot arm's movement track a given trajectory; Assuming the load mass is unknown, the state space dynamic equation of the manipulator is: in, is a piecewise constant right continuous switching signal, Indicates that the pth subsystem operates in this interval, t∈[τ s ,τ s+1 ), τ s To switch the time series, represents the set of positive integers; The state space equation Considered as an unknown constant parameter θ σ , x2 is regarded as a bounded smooth function The unknown nonlinear function includes an unknown nonlinear function f σ,2 (x1,x2) and unknown nonlinear function f σ,3 (x1,x2,x3), As an unknown nonlinear function f σ,2 (x1,x2), As an unknown nonlinear function f σ,3 (x1,x2,x3).

4. The method for controlling a robotic arm based on a switching system under state event triggering according to claim 1, characterized in that: The method of using neural network technology to approximate unknown nonlinear functions includes: χ Among them: where χ k is the input vector of the neural network, W p,k is the ideal weight matrix, is the transpose of the ideal weight matrix, is the basis function vector, ω p,k (χ k ) is the approximation error; Assume that in the compact set Ω χ In the equation, the approximation error satisfies Then there exists: in is an unknown positive constant, 5. The method for controlling a robotic arm based on a switching system under triggering of a state event according to claim 4, characterized in that: The basis function selects Gaussian kernel function Among them C h is the center of the receptive field, b h is the width of the Gaussian kernel function.

6. The method for controlling a robotic arm based on a switching system under triggering of a state event according to claim 1, characterized in that: The method of using the adaptive parameter update law to process unknown parameters is specifically to process the unknown parameters η. k ,θ σ , estimated using the following adaptive parameter update law: where ε k , δ k , g, β, γ k All are positive design parameters. Design parameters are parameters that are set independently according to requirements. and Represents η k and θ σ The estimated value of the first-order derivative, Proj{·} represents the parameter projection operator, and θ0 is a positive constant; To introduce tracking error after event triggering, z k is the tracking error.

7. The method for controlling a robotic arm based on a switching system under triggering of a state event according to claim 1, characterized in that: The triggering mechanism of the introduction status event is as follows: in are all positive design parameters, x k (t) represents the kth system state quantity, represents the trigger value of the kth system state quantity, α kf (t) represents the output of the kth first-order filter, Represents the trigger value of the output of the kth first-order filter, inf represents the infimum, represents the lth triggering moment of the kth state, represents the l+1th triggering moment of the kth state, represents the lth triggering moment of the kth first-order filter output, Represents the l+1th triggering moment of the kth first-order filter output. Once the triggering condition is met, the above state event trigger mechanism will The state quantity x at this moment k (t) will be used for feedback transmission and at time intervals remains unchanged in The output of the first-order filter at this moment will be used for feedback transmission and at time intervals remains unchanged; For systems with state trigger settings, only the trigger state Can be used in system design, so as to design state event trigger controller, including virtual control law, control input u σ , adaptive parameter update law, and the virtual control law is: Control input u σ for: The adaptive parameter update law is: Among them, c k , γ k , ε k , δ k , k=1,2,3 and g,β are all positive design parameters, k=1, 2, 3 is the tracking error after the event trigger is introduced, is the kth virtual control law α k Introducing the virtual control law after event triggering, To introduce the output of the first-order filter after the event trigger, the first-order filter is expressed as α k-1 is the virtual control law before event triggering is introduced, μ k is the time constant, represents the reference trajectory y d The third-order derivative of Indicates the relationship between η k The estimated value of Represents theta σ , tanh represents the hyperbolic tangent function, Proj{·} represents the parameter projection operator, and θ0 is a positive constant.

8. The method for controlling a robotic arm based on a switching system under triggering of a state event according to claim 1, characterized in that: This method also includes stability analysis of the closed-loop system, the process is as follows: Given the reference trajectory of the robot arm is y d (t) = sin(1.5t), define the error variable z1=x1-y d Among them, α 2f , α 3f is the output of the first-order filter, and the first-order filter is expressed as α kf (0) = α k-1 (0), k=2,3,μ k is the time constant, α k-1 is the virtual control law, It is y d First-order derivative, It is y d Second-order derivative; choose the Lyapunov function for the manipulator system: in, is the unknown parameter η r Estimates, is the unknown parameter θ σ Estimates of ζ r+1 is the error of the first-order low-pass filter, γ r >0 is a design parameter; V σ Taking the derivative with respect to time t, we get Substitute the virtual control law and adaptive parameter update law into According to the properties of parameter projection, we can get and Then we have: and The derivative of the Lyapunov function of each subsystem has the same form, so let the piecewise continuous differentiable function ν(t) = V σ,n (t), For any t∈[τ s ,τ s+1 ) have: Represents τ s The left boundary value of , λ is the attenuation term, △ is the positive term boundary, and Λ is the maximum jump error value of the Lyapunov function caused by switching; applying mathematical induction and the properties of the dwell time, we get: From the above formula, we can get This means that ν(t) has an upper bound independent of t, given by We can get z1, z2, z3, is bounded, and the properties of parameter projection show that θ σ , Is bounded, the reference signal y d (t) is bounded to ensure that x1 is bounded and the control input u is also bounded, so all signals in the closed-loop system are bounded; Depend on Desirable limit because For all All hold true, so z1 will converge to an adjustable tight set.

9. The method for controlling a robotic arm based on a switching system under triggering of a state event according to claim 1, characterized in that: Zeno behavior is avoided in event-triggered control, that is, there is a strictly positive lower bound on the time interval between two adjacent triggering moments.

10. A robotic arm control system based on a switching system triggered by a state event, characterized in that: A single-chain manipulator includes a rigid link connected to a motor via a gear train, wherein the manipulator sequentially moves a specified load, and the goal is to make the manipulator's motion track a given trajectory. The step of making the robot arm track a given trajectory includes: The modal jump of the robotic arm system is obtained, and the robotic arm system is modeled into a switching nonlinear system model with uncertainty for different modes; the switching nonlinear system model has unknown parameters and unknown nonlinear functions, and the unknown nonlinear functions are approximated by neural network technology, and the unknown parameters are processed by adaptive parameter update law; a state event trigger mechanism is introduced, and a state event trigger controller is designed, which is used to control the robotic arm.

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