Dynamic event triggered networked nonlinear system fast output feedback control method

Abstract

The invention discloses a fast output feedback control method for a networked nonlinear system triggered by a dynamic event. By designing the dynamic gain, the dynamic gain is bounded, tracking error coupling is avoided, and meanwhile, the influence of a nonlinear term containing an unknown quantity and external disturbance on the system is compensated. In addition, a dynamic event triggering mechanism is provided based on the dynamic gain, and dynamic compensation of a triggering threshold value is achieved. And constructing a composite Lyapunov function by recursively constructing a virtual control quantity, and enabling the Lyapunov function to meet a fast finite time stability criterion in combination with parameter design of dynamic gain and nonlinear term power. Therefore, tracking errors are converged to a tight set, and the states of all closed-loop systems and observers are globally bounded. According to the method, rapid finite-time dynamic event triggering output feedback actual tracking control of a non-strict feedback system can be realized, and the method has urgent engineering application requirements and is of great significance in promoting the development of a networked nonlinear system control theory and an engineering technology.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of automation control technology, and relates to the control of networked nonlinear systems, in particular to a dynamic event-triggered fast output feedback control method for networked nonlinear systems. BACKGROUND

[0002] In order to realize control in a larger area, traditional control systems are gradually transformed into networked systems. Because the signal transmission of the networked system will have an adverse effect on the control convergence speed, control accuracy and other aspects of the control effect, an effective event-triggering mechanism can reduce the bandwidth demand of a large-scale network system while reducing the frequent control of the actuator mechanism, and fast finite-time control under the event-triggering mechanism is the key to guaranteeing the control performance.

[0003] Most networked systems exhibit nonlinear characteristics, and in order to better guarantee the performance of the controller, a more accurate system description is needed, which can describe the networked nonlinear control system as a p-norm general non-strict feedback networked nonlinear system. For this type of nonlinear system, the dynamic gain can compensate for the nonlinear term containing unknown quantities, realize dynamic event-triggered control, and at the same time avoid the problem of cross-coupling between tracking error and dynamic gain, but the boundedness of the dynamic gain is difficult to guarantee and the system state is not measurable, so the traditional controller cannot make the tracking error converge to a small enough interval.

[0004] In order to achieve the expected control performance, the networked system in practical application has a clear requirement for fast finite-time control, however, the construction of Lyapunov function that meets the requirement of fast finite-time stability criterion is a big problem, the problem of fast finite-time output feedback dynamic event-triggered tracking control for p-norm non-strict feedback networked nonlinear systems has not been well solved, especially for this type of networked nonlinear system, there is an urgent engineering application requirement to design a new type of control method that meets the control performance requirement. SUMMARY

[0005] In view of the deficiencies of the prior art, the application provides a dynamic event-triggered fast output feedback control method for networked nonlinear systems, which is designed for a class of p-norm non-strict feedback networked nonlinear systems, avoids the coupling problem between the dynamic gain and the tracking error, eliminates the influence of the nonlinear term of the non-strict feedback on the tracking performance, and combines the parameter design of the power of the nonlinear term to propose a Lyapunov function compensation term and a nonlinear term assumption condition, so that the system meets the fast finite-time stability criterion and realizes the fast finite-time output feedback actual tracking control.

[0006] The dynamic event-triggered fast output feedback control method for networked nonlinear systems specifically comprises the following steps:

[0007] Step 1, Establishing system state model

[0008] A class of p-norm non-strict feedback networked nonlinear system state model is described as:

[0009]

[0010] Where, i = 1, …, n, n represents the number of system states, t represents the time variable, z(t) = (z1(t), …, zn(t))T n (t)) T ∈R n represents the system state, represents the first derivative. y(t) ∈ R, v(t) ∈ R are the system output and the networked control input of the system respectively. p-norm is an odd number, is a continuous nonlinear term containing unknown quantities, and has p n = 1, f n (0, 0) = 0. represents the unknown coefficient of the nonlinear term.

[0011] Step 2, Constructing output feedback controller

[0012] Assume that there exists a continuous bounded function and an external disturbance d, for i = 1, …, n, the above p-norm non-strict feedback nonlinear system satisfies:

[0013]

[0014] Where, Γ1 = 1, are design parameters of the power of nonlinear terms; and the external disturbance d satisfies |d| ≤ C, C is a positive real number.

[0015] Firstly, for the p-norm non-strict feedback networked nonlinear system, the following coordinate transformation is proposed:

[0016]

[0017] Where, y r (t) is the output reference signal of the system, and there exists a normal number M, such that q1 = 0, L(t) represents the dynamic gain. Based on this coordinate transformation, the p-norm non-strict feedback networked nonlinear system is rewritten as:

[0018]

[0019] y(t) = x1(t)

[0020] According to the existing control theory and practice, the nominal system has universal applicability and feasibility in constructing various networked nonlinear system controllers. For the nominal system with fixed gain parameters l i and p i , it is only necessary to compensate for the different nonlinear terms of the networked system by adjusting the scaled dynamic gain L(t), i.e.

[0021]

[0022] where x = (x1(t), …, x n (t)) T ∈ R n represents the state of the nominal system, u(t) ∈ R represents the control input of the nominal system, and y(t) ∈ R represents the output of the nominal system.

[0023] For the above nominal system, a set of virtual controllers a1(t), …, a n (t) and corresponding virtual errors η1(t), …, η n (t) are defined as follows:

[0024]

[0025] λ = max 1≤i≤n {Γ i}

[0026] For i = 1, …, n, there exists a Lyapunov function V(x(t)) as follows:

[0027]

[0028] where s is the independent variable of integration, and μ is a constant to be determined.

[0029] For i = 1, …, n-1, there exists a constant l i > 0, such that the continuous state feedback controller a n+1 (t) is:

[0030]

[0031] and when l n ≥ 0, it has:

[0032]

[0033] To reduce computational complexity and the complexity of p-norm non-strict feedback network nonlinear systems, a dimension-reduced observer ξ with dimension n-1 is constructed as follows. i (t), for the continuous state feedback controller α n+1 The unmeasurable states (x2(t),...,x) in (t) n Estimate (t)

[0034]

[0035] In the formula, Represents the estimated state of the nominal system, ρ1,…,ρ n-1 This represents the positive gain of the reduced-dimensional observer to be determined. The estimated state obtained using the reduced-dimensional observer is used to replace the continuous-state feedback controller α. n+1 Given the unobservable system state in (t), construct the following output feedback controller u. * (t):

[0036]

[0037] Step 3: Construct the Lyapunov function U i (x(t))

[0038]

[0039] in, For U i Differentiate (x(t)):

[0040]

[0041] Where, x n+1 (t)=u(t).

[0042] Define the estimation error of the dimension reduction observer

[0043] When i = 2, ..., n, there exists Make:

[0044]

[0045] When i = 2, ..., n-1, there exists a constant φ. i >0 and continuous functions m i (ρ i-1 ), n i (ρ i-1 ), so that:

[0046]

[0047] exist and continuous function mn (ρ n-1 ), such that:

[0048]

[0049] Therefore, the derivative of Lyapunov function satisfies:

[0050]

[0051] Step 4, dynamic event-triggered strategy and dynamic event-triggered output feedback controller u(t) based on dynamic gain design:

[0052]

[0053] where 0 < β1 < 1, 0 < β2 < 1, is a positive constant, t k is the kth event-triggering time, is the measurement error under the dynamic event-triggering mechanism, is the dynamic event-triggering threshold. When the measurement error is greater than the dynamic event-triggering threshold, the controller works, u(t) = w(t k+1 ). When the measurement error is less than or equal to the dynamic event-triggering threshold, the controller does not work, u(t) = w(t k ), and the control input is realized by a zero-order holder, so as to reduce the communication resources and control update frequency of the controller and avoid frequent control of the actuator.

[0054] There exist and two continuous functions a1(t), a2(t) satisfying a1(t) ∈ [-1, 1], a2(t) ∈ [-1, 1], such that:

[0055]

[0056] The parameters β1, β2 and dynamic gain of the controller u(t) are designed according to the actuator power limit and tracking accuracy requirement in the actual system.

[0057] The present application has the following beneficial effects:

[0058] 1. By designing the dynamic gain, the dynamic gain is bounded, the tracking error coupling is avoided, the non-strict feedback nonlinear term is compensated, and a reduced dimension observer is constructed, so as to ensure that the tracking error can converge to a compact set in a finite time.

[0059] ​2. A dynamic event-triggered mechanism is proposed by combining dynamic gain and event-triggering. Thanks to the real-time adjustment of dynamic gain, dynamic compensation of nonlinear terms can be achieved, reducing the need for offline parameter tuning when the nonlinear term has a large fluctuation. Moreover, the system state is not limited, ensuring the stability of the system in the Lyapunov sense, reducing network bandwidth occupation and avoiding Zeno phenomenon.

[0060] 3. Based on Lyapunov stability theory, a composite Lyapunov function is constructed by recursively constructing a virtual control variable. Combined with the design of dynamic gain and the parameter design of the power of nonlinear terms, a Lyapunov function compensation term is proposed to solve the construction difficulty of fast finite-time Lyapunov function, meet the fast finite-time stability criterion, and propose a fast finite-time controller to solve the problem of system tracking speed depending on the initial state, and realize the fast finite-time actual tracking control of networked nonlinear system.

[0061] 4. The method can be used for various actual networked control systems described by p-norm non-strict feedback nonlinear systems, and can realize fast finite-time dynamic event-triggered output feedback actual tracking control of non-strict feedback nonlinear networked control systems. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 A control schematic diagram of the networked control system of the bridge crane in the embodiment;

[0063] Figure 2 A dynamic event-triggered fast output feedback control block diagram of the networked control system of the bridge crane in the embodiment;

[0064] Figure 3 A load swing angle of the networked control system of the bridge crane in the embodiment;

[0065] Figure 4 A trolley position output trajectory and reference signal trajectory diagram of the networked control system of the bridge crane in the embodiment;

[0066] Figure 5 A controller input control torque trajectory diagram of the networked control system of the bridge crane in the embodiment;

[0067] Figure 6 An event-triggered interval schematic diagram of the networked control system of the bridge crane in the embodiment. DETAILED DESCRIPTION

[0068] The application will be further explained in connection with the accompanying drawings; it is to be clearly understood that the examples and their technical features are merely used to illustrate the technical solutions of the application, and do not limit the same. The technical features involved in each example can be freely combined and applied without conflict.

[0069] The embodiment takes the networked control system of the bridge crane shown in Figure 1 Fig. 1 as an example to illustrate the application of the dynamic event-triggered networked nonlinear system fast output feedback control method proposed in the application in actual scenarios.

[0070] The dynamic model of the networked control system of the bridge crane is:

[0071]

[0072] wherein v(t) is the trolley driving force, M=2, m=0.5, l=0.5, and d=1 are respectively the trolley mass, the load mass, the rope length, and the concentrated disturbance applied on the networked control system of the bridge crane, the units of M, m, and d are kilograms, and the unit of l is meter. g is the gravitational acceleration, is the second derivative of the trolley horizontal displacement x(t), and θ(t) is the load swing angle, is the load swing angular velocity, is the load swing angular acceleration.

[0073] The control task is to drive the trolley to move along the reference trajectory y r (t) while simultaneously attenuating and eliminating the payload swing, i.e. -gtanθ(t)→0. In this embodiment, the reference step signal y r (t) is set to 1 meter.

[0074] In order to convert the dynamic model into a state equation, the following coordinate transformation is proposed based on the above control task:

[0075]

[0076] z3(t)=-θ(t)

[0077]

[0078] According to the coordinate transformation, the dynamic system model of the bridge crane is constructed:

[0079]

[0080] Considering the range of the load swing angle in actual working conditions The control coefficient can be obtained is approximately 1, so the overhead traveling crane system meets the form of p-norm non-strict feedback networked nonlinear system. According to the coordinate transformation, the dynamic gain is introduced, and the dynamic system model of the overhead traveling crane is rewritten as follows:

[0081]

[0082]

[0083] The dynamic system model of the overhead traveling crane after the coordinate transformation meets the p-norm non-strict feedback nonlinear system. According to the dynamic event-triggered nonlinear networked system fast output feedback control method described in the method, a reduced dimension observer and a dynamic event-triggered networked nonlinear system fast output feedback controller are designed, as shown in Figure 2

[0084]

[0085] According to the parameter design of the power in the nonlinear assumption, the parameter design of the observer and the controller is as follows:

[0086] p1=p2=p3=p4=1

[0087]

[0088]

[0089] q1=0、q2=1、q3=2、q4=3、q5=4

[0090] l1=0.82、l2=3.4、l3=1.7、l4=0.45

[0091] ρ1=28、ρ2=20、ρ3=12

[0092] In order to realize a larger scope of application, β1=0.1, β2=0.05 are designed in the dynamic gain and the dynamic event-triggered threshold, By adjusting the parameters, better control performance and ideal trigger times can be realized within the power limit of the actuator.

[0093] Finally, combined with the initial state of the actual system, the initial conditions of the system are selected as [z1(0), z2(0), z3(0), z4(0)]=[0.1, 1, 0, -4], [ξ1(0), ξ2(0), ξ(0)]=[0, 0, 0], L(0)=1, and the simulation experiment is carried out, Figure 3 ​For the simulation results of the load swing angle θ(t) changing with time, the load swing angle θ(t) starts from the initial angle of 0°, and tends to be flat after swinging in the positive and negative directions for 3 seconds, which shows that under the control of the method, the load swing can be attenuated and eliminated. Figure 4 For the output trajectory and reference signal trajectory diagram, it can be seen from the comparison that there is a slight overshoot from the initial position of 0.1 meters at 2 seconds, which shows that the system has good dynamic characteristics, and tends to be stable and close to the reference trajectory after 3 seconds, which shows that the system has good tracking accuracy. Figure 5 For the controller input v(t) control torque trajectory diagram, within 0-1 seconds, due to the large error, the controller performs strong adjustment to quickly push the system state to the desired value, within 1-3 seconds, there are still frequent event triggers for fine adjustment of the system state and elimination of the load swing θ(t), and after 3 seconds, the controller is mostly in the inactive state, which proves that the dynamic event-triggered control strategy not only ensures the rapid stability of the system, but also effectively reduces the control update frequency. Figure 6 For the dynamic event-triggered interval diagram, combined with v(t), the working mechanism and dynamic adjustment capability of the dynamic event-triggered control system are fully demonstrated, and it can be seen that under the control of the method, unnecessary actuator actions in the control of the bridge crane system are avoided, and the control performance and resource utilization efficiency are good.

[0094] The following is theoretically proved that under the conditions of nonlinear assumption and dynamic event-triggered mechanism, the method can realize the fast finite-time tracking and stable control of the p-norm non-strict feedback networked nonlinear system, and avoid Zeno behavior in dynamic event-triggered control.

[0095] Step 1, nominal system Lyapunov function construction

[0096] Define the Lyapunov function T(x) of the nominal system of the system V(x)+U(x), and take the derivative of it:

[0097]

[0098] Substitute into it to get:

[0099]

[0100] where Therefore, we have:

[0101]

[0102] In order to estimate the redundant term in , the increasing power integral technique is used for scaling: there exists a constant a3>0 such that:

[0103]

[0104] There is a constant So that:

[0105]

[0106] Therefore:

[0107]

[0108] The derivative of Lyapunov function T(x) is substituted In the middle:

[0109]

[0110] The observer gain is selected Then:

[0111]

[0112] Step 2, nominal closed-loop system control performance analysis

[0113] To simplify the description, define the system coordinates X(t) = [X1(t),..., X 2n-1 (t)] := [x1(t), x2(t), …, x n (t), ξ1(t), …, ξ n (t)] T According to the above nominal system state observer and output feedback controller, the closed-loop system can be derived as:

[0114]

[0115] According to the homogeneous system theory, it can be determined that the Lyapunov function T(X(t)) is a 2μ-τ order homogeneous function. There is a normal number b 、 b1, it can be obtained:

[0116]

[0117] Therefore, the dynamic event-triggered output feedback controller u(t) designed in this application can realize the fast output feedback actual tracking control of the nominal system.

[0118] Step 3, p-norm non-strict feedback networked nonlinear system closed-loop system stability analysis

[0119] According to the definition of X, the closed-loop system composed of the state observer of the p-norm non-strict feedback nonlinear system and the output feedback controller can be derived as:

[0120]

[0121] where,

[0122] Taking the derivative of Lyapunov function T(X(t)) along the closed-loop system, we have

[0123]

[0124] Combining the nominal system closed-loop system, we finally get the Lyapunov function of the p-norm non-strict feedback nonlinear system closed-loop system

[0125] Based on the assumption of nonlinear terms, there exists We have

[0126]

[0127] Since Let Then we have

[0128]

[0129] According to the homogeneous lemma, we have is a homogeneous function of 2μ-τ-r i There exists a constant d i such that

[0130]

[0131] where By the definition of and the homogeneous lemma, we can prove that there exists a normal number b2such that

[0132]

[0133] Substituting Lyapunov function we finally have

[0134]

[0135] By scaling through the young inequality, there exists and a constant b3<0 such that

[0136]

[0137] In order to achieve fast finite-time stability, we propose a Lyapunov function compensation term Substituting Lyapunov function we finally have

[0138]

[0139] where is an unknown constant.

[0140] Step 4, Proof of global fast finite-time stability for p-norm non-strict feedback nonlinear systems

[0141] To prove the boundedness of L(t), first assume that L(t) does not escape at t = t0, satisfying 0 < t0 < t f , and t f < t r , t r is the reaching time. Since there exists for finite time t0 ∈ [0, t f ), we have

[0142]

[0143] where is a positive constant. Assume defined by we have This means that L(t) is a constant, which contradicts the assumption, so it can be proved that L(t) is bounded in finite time t0 ∈ [0, t f ). According to the definition of Lyapunov function T(X(t)) above, can be rewritten as:

[0144]

[0145] Let Select we can get ψ1 > 0, ψ2 > 0, proving that the system satisfies the fast finite-time stability criterion, making the system have a faster convergence speed. Compared with finite-time stability, fast finite-time stability eliminates the dependence of the convergence time on the initial system state, and by the fast finite-time lemma, there exists 0 < δ < 1 satisfying:

[0146]

[0147] This shows that within finite time t0 ∈ [0, t f ), for any initial condition, all states (x(t), ξ(t)) of the closed-loop system are bounded, and due to the continuity of the solution, t fmay be infinite, which makes all the signals (x(t), ξ(t), L(t)) of the closed-loop system bounded in [0, +∞). Because the coordinate transformation is reversible, the system state z(t) is globally bounded. In addition, combined with the definition of Lyapunov function V(x(t)), the following can be obtained:

[0148]

[0149] Further, it can be concluded that the tracking error ε(t) = y(t) - y r (t) can converge to the compact set Ω(t):

[0150]

[0151] In a fast finite time t r , the stabilization time t

[0152]

[0153] Therefore, the method can make the tracking error converge to the compact set Ω(t) in a fast finite time t r .

[0154] Step 5, Proof of p-norm non-strict feedback networked nonlinear system without Zeno phenomenon

[0155] Definition According to the definition of dynamic event triggering, the following can be obtained:

[0156]

[0157] According to the definitions of w and , the following can be obtained:

[0158]

[0159] Since β2 and L(t) are both greater than 0, then is greater than 0, and it is not difficult to find that the conclusions of the above two formulas are contradictory. Therefore, it can be proved that the fast finite time dynamic event triggered controller designed by the method has a strict minimum value between any two adjacent trigger time t k and t k+1 , and the system does not have Zeno phenomenon.

[0160] The specific embodiments described above are merely illustrative, rather than limiting, and those skilled in the art can make many forms under the inspiration of the present application without departing from the purpose of the present application and the scope protected by the claims, which are all within the protection of the present application.

[0161] Those skilled in the art will appreciate that embodiments of the present application can be devised for a method, a system, or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, without limitation, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code thereon for use by or in connection with an instruction execution system.

Claims

1. A fast output feedback control method for a networked nonlinear system triggered by dynamic events, characterized in that: Specifically, the following steps are included: Step 1: Establish a state model for a class of p-norm non-strict feedback networked nonlinear systems; Step 2: Assume there exists a continuous bounded function. And external perturbation d, which causes the continuous nonlinear term f of the nth-order p-norm nonstrict feedback networked nonlinear system to... i (z(t),v(t)) satisfies: Where Γ1=1、 All are design parameters of the power order of nonlinear terms; and the external disturbance d satisfies |d|≤C, where C is a positive real number; t represents the time variable, and z(t) and v(t) represent the system state and control input of the p-norm non-strict feedback networked nonlinear system, respectively; p i Describing the p-norm, It is an odd number and p n =1; By employing a coordinate transformation method, the p-norm non-strict feedback networked nonlinear system is simplified into a nominal system that ignores nonlinear terms. For this nominal system, a set of virtual controllers α1(t),…,α are defined. n (t) and the corresponding virtual errors η1(t),…,η n (t), using a dimension-reduced observer ξ i (t) for the unmeasurable state (x2(t),…,x n Estimate (t) and construct the output feedback controller u. * (t); Step 3: Design of the dynamic event triggering strategy and dynamic event triggering output feedback controller u(t): Where 0 < β1 < 1, 0 < β2 < 1, t is a positive constant. k For the time when the k-th event is triggered, Measurement error under a dynamic event-triggered mechanism This is the dynamic event trigger threshold; when the measurement error exceeds the dynamic event trigger threshold, the controller activates, u(t) = w(t). k+1 Otherwise, u(t) = w(t) k ); exist And two continuous functions a1(t) and a2(t) satisfying a1(t)∈[-1,1] and a2(t)∈[-1,1]. Make: The parameters β1, β2 and dynamic gain of the controller u(t) parameter The design is based on the actuator power limitations and tracking accuracy requirements of the actual system.

2. The fast output feedback control method for a networked nonlinear system triggered by dynamic events as described in claim 1, characterized in that: The state model of the p-norm nonstrict feedback networked nonlinear system is as follows: Where z(t)=(z1(t),…,z n (t)) T ∈R n Indicates the system status. denoted by ; y(t) and v(t) represent the system output and the networked control input of the system, respectively; It is a continuous nonlinear term containing unknowns, and has p n =1,f n (0,0)=0.

3. The fast output feedback control method for a networked nonlinear system triggered by dynamic events as described in claim 1, characterized in that: For p-norm nonstrict feedback networked nonlinear systems, the following coordinate transformation is proposed: Where x=(x1(t),…,x n (t)) T ∈R n Let y(t) represent the nominal system state and y(t) represent the nominal system output. r (t) is the system's output reference signal, and there exists a positive constant M such that q1 = 0, L(t) represents the dynamic gain; The nominal system is defined as follows: in, Indicates the control input of the nominal system; The virtual controller α1(t),…,α n (t) and virtual error η1(t),…,η n (t) is: λ=max 1≤i≤n {C i } For i = 1, ..., n-1, there exists a constant l i >0, making the continuous state feedback controller α n+1 (t): And when l n When ≥0, we have: The first derivative of the Lyapunov function V(x(t)): Where s is the independent variable of the integral, and μ is a constant to be determined.

4. The fast output feedback control method for a networked nonlinear system triggered by dynamic events as described in claim 3, characterized in that: The dimensionality reduction observer ξ i (t) is: in, Represents the estimated state of the nominal system, ρ1,…,ρ n-1 The positive gain of the reduced-dimensional observer to be determined is represented; the estimated state obtained using the reduced-dimensional observer is used to replace the continuous state feedback controller α. n+1 Given the unobservable system state in (t), construct the following output feedback controller u. * (t):

5. A control method for a networked control system of a bridge crane, characterized in that: Using the method described in any one of claims 1 to 4, a dynamic event-triggered output feedback controller for a bridge crane networked control system is constructed to drive the trolley in the system along a reference trajectory x. d (t) Move forward.

6. The control method for a networked control system of a bridge crane as described in claim 5, characterized in that: Establish a dynamic model for the networked control system of a bridge crane: Where v(t) is the driving force of the trolley, d represents the concentrated interference applied to the networked control system of the bridge crane, M, m, and l are the trolley mass, load mass, and rope length, respectively, and g is the acceleration due to gravity. Let x(t) be the second derivative of the horizontal displacement of the trolley, and θ(t) be the load swing angle. The angular velocity of the load swing. The angular acceleration of the load; The design control task is to drive the car along the reference trajectory x. d (t) Moving forward, while attenuating and eliminating effective load oscillation, the following coordinate transformation is proposed: z3(t)=-θ(t) Based on coordinate transformation, a dynamic model of the networked control system of the bridge crane is constructed: Introducing dynamic gain, the dynamic system model of the bridge crane is rewritten as follows: Design a dimension-reduced observer and a dynamic event-triggered output feedback controller to drive the car forward.

7. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method of any one of claims 1 to 4.

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