A finite-time trigger control method for switched nonlinear systems

Abstract

The present invention provides a finite time trigger control method for a switching nonlinear system, comprising constructing a state space model of a switching nonlinear system with incompletely measurable states; removing nonlinear function terms of the state space model of the switching nonlinear system to obtain a nominal system, and constructing a continuous time state feedback controller; constructing an observer based on the state measurable of the system output, and using the observer to replace all state values ​​in the continuous time state feedback controller to obtain a continuous output feedback controller; obtaining an event triggering condition, and combining the continuous output feedback controller to make the state space model of the switching nonlinear system become a finite time output feedback control model of the switching nonlinear system based on event triggering, and ensuring that all output signals converge to the same equilibrium point in a finite time. The implementation of the present invention can ensure that the system remains stable and avoid data redundancy and unnecessary waste in the control process.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control technology, and in particular to a finite time trigger control method for a switching nonlinear system. Background Art

[0002] As a typical type of switching system, switched nonlinear systems can accurately describe physical systems with switching and nonlinear characteristics in real life, such as power systems, intelligent transportation systems, and aerospace vehicle attitude control systems.

[0003] In recent years, the stability analysis and controller design of switched nonlinear systems have been very popular research topics in the field of system control. For the stability analysis and stabilization of switched nonlinear systems, the previous asymptotic stability control methods (such as the traditional control methods represented by PID, that is, the system state will converge to the origin when time tends to infinity) cannot determine the dynamic performance of the system within a specific time. If the system has a large overshoot turbulence during operation within a specific time range, it will further cause the equipment to fail to operate normally, and in serious cases, it may cause the entire control system to crash.

[0004] With the development of automation technology and the continuous improvement of system operation requirements, it is increasingly important to pay attention to the dynamic characteristics of the system within a limited time interval in the control process of actual industrial systems. For example, in the process of missile and satellite launch, it is necessary to obtain its trajectory in a specific area and time; for another example, the reaction of a chemical boiler requires the change results of temperature, pressure parameters, etc. in a specific time period. For this reason, the proposal and development of finite-time control methods provide researchers with new ideas and choices, so the study of finite-time control of switching nonlinear systems has certain engineering significance.

[0005] At present, some scholars have proposed to introduce event-triggered control technology into the design of the system controller. Existing research results show that event-triggered control has very obvious control advantages: it can effectively reduce the number of data information transmissions, save communication resources to a large extent, and reduce control costs.

[0006] However, in actual operation, the system is easily disturbed by the external environment, which makes it impossible to measure and obtain system information (such as angular velocity information during the operation of the aircraft), and data redundancy and waste occur during the control process, resulting in limitations in the control results. Summary of the invention

[0007] The technical problem to be solved by the embodiments of the present invention is to provide a finite-time trigger control method for a switching nonlinear system, so that all signals in the system converge to the vicinity of an equilibrium point within a finite time, and effectively reduce the number of data transmissions during the control process, thereby ensuring that the system remains stable and avoiding redundancy and unnecessary waste of data during the control process.

[0008] In order to solve the above technical problems, an embodiment of the present invention provides a finite time trigger control method for a switching nonlinear system, the method comprising the following steps:

[0009] Step S1, constructing a state space model of a switching nonlinear system with incompletely measurable states; wherein the state space model of the switching nonlinear system contains nonlinear function terms;

[0010] Step S2, removing the nonlinear function term in the state space model of the switching nonlinear system to obtain a nominal system under the condition that all state variables are measurable, and further constructing a continuous-time state feedback controller of the nominal system;

[0011] Step S3, based on the fact that the nominal system is limited to outputs that are state-measurable, construct an observer for state order reduction in the state space model of the switching nonlinear system, and use the observer to replace all state values ​​in the continuous-time state feedback controller to obtain a continuous output feedback controller;

[0012] Step S4, obtaining an event trigger condition, and combining with the continuous output feedback controller, performing switching trigger control on the state space model of the switching nonlinear system to form a finite-time output feedback control model of the switching nonlinear system based on event triggering; wherein all signals output by the finite-time output feedback control model of the switching nonlinear system converge to the vicinity of the same equilibrium point within a finite time.

[0013] Wherein, in step S1, the state space model of the switching nonlinear system is:

[0014]

[0015] Where x=[x1,…,x n ] T ∈R n is a state variable, and x2,…,x n is an unmeasurable state quantity; u∈R is the control input of the system; y∈R is the system output; piecewise right continuous function is the switching signal, N represents the number of subsystems; p n =1 is the power of the system;

[0016] For any There is a constant c k ≥0, And r1=1,r i+1 p i =r i +τ, where the numerator of the parameter τ is an even number and the denominator is an odd number, r i , The numerator and denominator of the system are both odd numbers, so that the nonlinear function term f k (·) satisfies f k (0)=0 and assume:

[0017] Furthermore, a switching sequence t' is defined p <t' p+1 , {t′ p ,p∈z +}, and assume that for any t∈[t′ p ,t′ p+1 ), the system state will not change suddenly at the switching moment.

[0018] Wherein, the step S2 specifically includes:

[0019] Step S21: in the state space model of the switching nonlinear system, the nonlinear function term is removed to obtain a nominal system under the condition that all state variables are measurable; wherein the nominal system is expressed as:

[0020]

[0021]

[0022] y=ξ1

[0023] For the above nominal system, define the coordinate transformation:

[0024]

[0025]

[0026] Among them, the gain β i-1 >0, i=2,3,…,n;

[0027] Step S22: construct a continuous-time state feedback controller of the nominal system by means of backstepping method:

[0028] Constructing Lyapunov functions Taking the derivative of V1, we get:

[0029]

[0030] Among them, the virtual controller Gain in

[0031] Similarly, in the i-th step, the Lyapunov function V can be constructed i (ξ1,…,ξ i )=V i-1 +W i (ξ1,…,ξ i ),in,

[0032] V i (ξ1,…,ξ i ) is derived with respect to time, and through a series of inequalities, we can obtain:

[0033]

[0034] In addition, by r i and p i The relationship between 0<r i p i-1 <1, and through the scaling of some inequalities we can get:

[0035]

[0036] Among them, b i (τ)>0 is a constant with respect to τ;

[0037] Designed virtual controller Substituting into the above inequality, we can see:

[0038]

[0039] Furthermore, in the nth step, the Lyapunov function is constructed And design the continuous state feedback controller of the nominal system as follows:

[0040]

[0041] Among them, the control gain β n ≥1+b n (τ), constant b n (τ)>0;

[0042] V n (ξ) is derived and the controller is substituted into the equation:

[0043]

[0044] Wherein, the step S3 specifically includes:

[0045] Based on the continuous-time state feedback controller described in step S2, considering that only y=x1 is measurable in the nominal system, that is, only ξ1 is measurable in the nominal system, the observer is constructed as follows:

[0046]

[0047]

[0048] In the formula, is the state ξ l The estimated value of The observation error generated by the observer is

[0049] The unobservable state values ​​in the state feedback controller are all replaced by the estimated state quantity Replace it and get the following continuous output feedback controller:

[0050]

[0051] The continuous output feedback controller selects an appropriate control gain through the Lyapunov function to ensure that the system achieves finite time stability. The specific process is as follows:

[0052] Construct the Lyapunov function as

[0053] To U i Taking the derivative and combining a series of inequalities to scale them up, we get:

[0054]

[0055] Using the inequality between parameters and Further we get:

[0056]

[0057] in, c l,1 >0 and c l,2 >0 is a constant with respect to parameter τ, is about the observation gain a l , l=2,…,n non-negative function;

[0058] Introduce a transformation, namely Where M>1 is a constant gain, q1=0, The state after the coordinate change ξ i ,i=2,…,n is unmeasurable;

[0059] According to the above coordinate transformation, the system will be transformed into the following form:

[0060]

[0061]

[0062] y=z1,

[0063] Among them, the nonlinear function The following conditions must be met:

[0064]

[0065] According to r i , p i and q i Relationship:

[0066]

[0067] because So we have:

[0068] Further scaling gives:

[0069] Wherein, the step S4 specifically includes:

[0070] Step S41, by defining the event trigger error as The event trigger condition is Among them, {t j ,j=1,2,…},t j <t j+1 is the trigger sequence; ||ξ(t)||=|ξ1(t)|+|ξ2(t)|+···+|ξ n (t)|,r∈(0,1) is the event trigger parameter;

[0071] Step S42: When the above event triggering conditions are met, the system controller will j ,t j+1 ) maintains a fixed value and continues to run, that is, And the controller Substitute into The last term in , we can get:

[0072]

[0073] From the above inequality, we can see that since 0<r n +τ<1, after a series of scaling, we can get:

[0074]

[0075] Because 1 / r l <1,l=1,2,…,n, so the following inequality holds:

[0076]

[0077] Among them, α is a positive constant, d l >0 is about r l and r l-1 The constant of

[0078] use Scaling and some inequalities, we can get:

[0079]

[0080]

[0081] Among them, the constant σ>0, It's about l and τ are constants;

[0082] Combining the above inequalities with the designed event trigger mechanism, we can get:

[0083]

[0084] Substituting the above inequality into By simple calculation, the finite-time output feedback control model of the switching nonlinear system can be obtained as follows:

[0085]

[0086] Among them, α i >0,i=1,2 are 3 constants.

[0087] Implementing the embodiments of the present invention has the following beneficial effects:

[0088] The present invention can solve the problem of finite-time control of a switching nonlinear system with unmeasurable states, and the operation of the controller depends on specific events and is updated only when the event conditions are met, thereby effectively reducing the number of data transmissions, so that all signals in the system converge to the vicinity of the equilibrium point within a finite time, and effectively reducing the number of data transmissions during the control process, thereby ensuring that the system remains stable and avoiding redundancy and unnecessary waste of data during the control process. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, without paying creative labor, other drawings obtained based on these drawings still belong to the scope of the present invention.

[0090] Figure 1 A flow chart of a finite time trigger control method for a switching nonlinear system provided by an embodiment of the present invention;

[0091] Figure 2 A switching rule diagram in an application scenario of the finite time trigger control method for a switching nonlinear system provided by an embodiment of the present invention;

[0092] Figure 3 for Figure 2 The state trajectory diagram;

[0093] Figure 4 for Figure 2 Controller output value diagram;

[0094] Figure 5 for Figure 2 The event trigger interval diagram;

[0095] Figure 6 A position error curve diagram of a permanent magnet synchronous motor in another application scenario of the finite time trigger control method for a switching nonlinear system provided by an embodiment of the present invention;

[0096] Figure 7 for Figure 6 Output value diagram of position controller of permanent magnet synchronous motor;

[0097] Figure 8 for Figure 6 Event trigger interval diagram of permanent magnet synchronous motor. DETAILED DESCRIPTION

[0098] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings.

[0099] like Figure 1 As shown in the figure, a finite time trigger control method for a switching nonlinear system is proposed in an embodiment of the present invention, and the method comprises the following steps:

[0100] Step S1, constructing a state space model of a switching nonlinear system with incompletely measurable states; wherein the state space model of the switching nonlinear system contains nonlinear function terms;

[0101] Step S2, removing the nonlinear function term in the state space model of the switching nonlinear system to obtain a nominal system under the condition that all state variables are measurable, and further constructing a continuous-time state feedback controller of the nominal system;

[0102] Step S3, based on the fact that the nominal system is limited to outputs that are state-measurable, construct an observer for state order reduction in the state space model of the switching nonlinear system, and use the observer to replace all state values ​​in the continuous-time state feedback controller to obtain a continuous output feedback controller;

[0103] Step S4, obtaining an event trigger condition, and combining with the continuous output feedback controller, performing switching trigger control on the state space model of the switching nonlinear system to form a finite-time output feedback control model of the switching nonlinear system based on event triggering; wherein all signals output by the finite-time output feedback control model of the switching nonlinear system converge to the vicinity of the same equilibrium point within a finite time.

[0104] The specific process is that in step S1, the state space model of the switching nonlinear system is:

[0105]

[0106] Where x=[x1,…,x n ] T ∈R n is a state variable, and x2,…,x n is an unmeasurable state quantity; u∈R is the control input of the system; y∈R is the system output; piecewise right continuous function is the switching signal, N represents the number of subsystems; p n =1 is the power of the system;

[0107] For any There is a constant c k ≥0, And r1=1,r i+1 p i =r i +τ, where the numerator of the parameter τ is an even number and the denominator is an odd number, r i , The numerator and denominator of the system are both odd numbers, so that the nonlinear function term f k (·) satisfies f k (0)=0 and assume:

[0108] Furthermore, a switching sequence t' is defined p <t' p+1 , {t′p ,p∈z +}, and assume that for any t∈[t′ p ,t′ p+1 ), the system state will not change suddenly at the switching moment.

[0109] In step S2, based on the condition that all system state variables are measurable, a continuous-time state feedback controller is constructed according to the backstepping method so that the closed-loop system can reach stability within a finite time, as follows:

[0110] Step S21: in the state space model of the switching nonlinear system, the nonlinear function term is removed to obtain a nominal system under the condition that all state variables are measurable; wherein the nominal system is expressed as:

[0111]

[0112]

[0113] y=ξ1

[0114] For the above nominal system, define the coordinate transformation:

[0115]

[0116]

[0117] Among them, the gain β i-1 >0, i=2,3,…,n;

[0118] Step S22: construct a continuous-time state feedback controller for the nominal system using the backstepping method:

[0119] Constructing Lyapunov functions Taking the derivative of V1, we get:

[0120]

[0121] Among them, the virtual controller Gain in

[0122] Similarly, in the i-th step, the Lyapunov function V can be constructed i (ξ1,…,ξ i )=V i-1 +W i (ξ1,…,ξ i ),in,

[0123] V i (ξ1,…,ξ i) is derived with respect to time, and through a series of inequalities, we can obtain:

[0124]

[0125] In addition, by r i and p i The relationship between 0<r i p i-1 <1, and through the scaling of some inequalities we can get:

[0126]

[0127] Among them, b i (τ)>0 is a constant with respect to τ;

[0128] Designed virtual controller Substituting into the above inequality, we can see:

[0129]

[0130] Furthermore, in the nth step, the Lyapunov function is constructed And design the continuous state feedback controller of the nominal system as follows:

[0131]

[0132] Among them, the control gain β n ≥1+b n (τ), constant b n (τ)>0;

[0133] V n (ξ) is derived and the controller is substituted into the equation:

[0134]

[0135] In step S3, under the continuous-time state feedback controller designed in step S2, considering the situation that only the output signal of the system can be measured, a reduced-order state observer suitable for the switching nonlinear system in step S1 is constructed, and then all state values ​​in the continuous-time state feedback controller in step S2 are replaced by the observed values ​​obtained by the observer to obtain a continuous output feedback controller. At this time, the specific process is as follows:

[0136] Step S31: Based on the continuous-time state feedback controller in step S2, considering that only y=x1 is measurable in the nominal system, that is, only ξ1 is measurable in the nominal system, the observer is constructed as follows:

[0137]

[0138]

[0139] In the formula, is the state ξ l The estimated value of The observation error generated by the observer is

[0140] The unobservable state values ​​in the state feedback controller are all replaced by the estimated state quantity Replace it and get the following continuous output feedback controller:

[0141]

[0142] Next, a Lyapunov function containing the estimated state is constructed, and the designed output feedback controller is analyzed to select appropriate control gains so that the system can achieve finite-time stability, specifically:

[0143] Construct the Lyapunov function as

[0144] To U i Taking the derivative and combining a series of inequalities to scale them up, we get:

[0145]

[0146] Using the inequality between parameters and Further we get:

[0147]

[0148] in, c l,1 >0 and c l,2 >0 is a constant with respect to parameter τ, is about the observation gain a l , l=2,…,n non-negative function;

[0149] At this time, for the switching nonlinear system considered in the present invention, a transformation is introduced, namely Where M>1 is a constant gain, q1=0, i=1,2,…,n+1, the state after the coordinates change ξ i ,i=2,…,n is unmeasurable;

[0150] According to the above coordinate transformation, the system will be transformed into the following form:

[0151]

[0152]

[0153] y=z1,

[0154] Among them, the nonlinear function The following conditions must be met:

[0155]

[0156] According to r i , p i and q i Relationship:

[0157]

[0158] because So we have:

[0159] Further scaling gives:

[0160] In step S4, the event trigger mechanism is introduced into the design of the controller to determine whether the event trigger condition is met, reduce the number of data transmissions in the control system, and finally use the public Lyapunov function method to analyze the finite time stability of the entire closed-loop system. At this time, the specific process is as follows:

[0161] First, we further discuss the event-triggered control scheme and the observer gain a l-1 ,l=2,3,…,n and the specific design of gain M:

[0162] First, combining the coordinate transformation and the designed output feedback controller, the output feedback controller of the system of the present invention is designed:

[0163]

[0164] Consider the system at t = t j At the triggering moment, only the output y=ξ1 can be measured, so the above output feedback controller needs to rely on the value at the triggering moment, that is:

[0165]

[0166] At this time, the observer will also be transformed into

[0167] Secondly, by defining the event trigger error as The event trigger condition is Among them, {t j ,j=1,2,…},t j <t j+1is the trigger sequence; ||ξ(t)||=|ξ1(t)|+|ξ2(t)|+···+|ξ n (t)|,r∈(0,1) is the event trigger parameter;

[0168] Then, when the above event triggering conditions are met, the system controller will be in the triggering interval t∈[t j ,t j+1 ) maintains a fixed value and continues to run, that is, And the controller Substitute into The last term in , we can get:

[0169]

[0170] From the above inequality, we can see that since 0<r n +τ<1, after a series of scaling, we can get:

[0171]

[0172] Because 1 / r l <1,l=1,2,…,n, so the following inequality holds:

[0173]

[0174] Among them, α is a positive constant, d l >0 is about r l and r l-1 The constant of

[0175] use Scaling and some inequalities, we can get:

[0176]

[0177]

[0178] Among them, the constant σ>0, It's about l and τ are constants;

[0179] Combining the above inequalities with the designed event trigger mechanism, we can get:

[0180]

[0181] Substituting the above inequality into By simple calculation, the finite-time output feedback control model of the switching nonlinear system can be obtained as follows:

[0182]

[0183] Among them, α i >0,i=1,2 are 3 constants.

[0184] It should be noted that based on the results discussed above, the selection rules of the gain parameters are further analyzed: First, construct a common Lyapunov function right Taking the derivative we get:

[0185]

[0186] Therefore, the appropriate observer gain a can be selected l and gain M, so that

[0187]

[0188] Finally, the method of common Lyapunov function is used to analyze the finite-time stability of the entire closed-loop system.

[0189] pass and It can be seen that:

[0190] From this we can see that the Lyapunov function is bounded and all signals of the entire closed-loop system converge within a finite time.

[0191] It should be noted that the control scheme designed by the present invention will not cause the Zeno phenomenon in the system by taking partial derivative of the trigger error. The specific process is as follows:

[0192] When t∈[t j ,t j+1 ), the event trigger error The derivative with respect to time is:

[0193]

[0194] In addition, due to 1 / r n -1-τ>1, so we can get:

[0195]

[0196] according to The definition of and scaling using a series of inequalities yields: Among them, γ>0 is a constant.

[0197] From this we can infer

[0198] In summary, the trigger interval has a positive lower bound d, namely That is, the present invention will not have the possibility of the Zeno phenomenon.

[0199] like Figures 2 to 5 As shown, an application scenario of a finite time trigger control method for a switching nonlinear system in an embodiment of the present invention is further described as follows:

[0200] There is a switched nonlinear system consisting of two subsystems:

[0201] Subsystem 1: and subsystem 2:

[0202] In the formula, τ = -4 / 15, r1 = 1, q1 = 0, Using the design steps of S41-S51, we select the control parameters of appropriate size, i.e., observation gain a1=6, M=1.2, controller gain β1=2, β2=5, and the initial state of the system is set to [x1(0), x2(0)] T =[1.6,-0.5] T and

[0203] pass Figure 2 It can be seen that the output feedback controller constructed by the present invention can ensure that the system state converges to the equilibrium point within a limited time. Figure 3 It can be seen that the proposed control scheme is effective. Figure 4 Indicates that the control input signal is based on event triggering, Figure 5 The number of controller updates in the actual operation of this trigger control scheme is given, which is only 21 times, indicating that the proposed control scheme saves the system's data transmission resources to a great extent.

[0204] like Figures 6 to 8 As shown, another application scenario of a finite time trigger control method for a switching nonlinear system in an embodiment of the present invention is further described as follows:

[0205] The mathematical model of permanent magnet synchronous motor is constructed as follows:

[0206] In the formula, u d and u q is the stator winding dq axis voltage; i d and i q is the stator winding dq axis current; L d and L q is the stator winding dq axis inductance; R s is the stator resistance; is the magnetic potential generated by the permanent magnet of the rotor; np is the number of motor pole pairs; J is the moment of inertia; B is the viscous friction coefficient; T l is the load torque; ω is the mechanical angular velocity of the rotor; θ is the rotation angle of the motor.

[0207] The control objective of this embodiment is: in the above-mentioned permanent magnet synchronous motor position servo system, considering the problem that only the position error can be measured but the error variation law cannot be measured, a finite time output feedback controller based on event triggering is designed to enable the motor position output to track the given position signal.

[0208] Define position error: e θ =θ * -θ, where θ * is a given constant position signal. According to the provided motor mathematical model, the state space equation of the position error system can be obtained as:

[0209]

[0210] In addition, define x1 = e θ , in, Using the controller construction process in Section 4.3, the following observer and controller are designed:

[0211]

[0212]

[0213]

[0214]

[0215] Select control parameters: τ = -2 / 5, r1 = 1, q1 = 0, q2 = 1, q3 = 2, The observation gain is a1=22, M=0.8, the controller gain is β1=1.5, β2=15, and the initial state is set to [x1(0), x2(0)] T =[0.1,-0.3] T and

[0216] The parameters of the permanent magnet synchronous motor are: rated power P = 0.75kW, orthogonal axis inductance L d =L q =0.01H, rated speed n N =2500r / min, pole pair number n p =4, moment of inertia J = 7.24 × 10 -4 kg·m 2, stator resistance R s =1.9Ω, B = 0.02μNms / rad, rotor permanent flux Rated torque T N =2.67N·m.

[0217] pass Figure 6 It can be seen that the designed controller can make the position error of the synchronous motor converge to 0 within a finite time. Figure 7 Output of the synchronous motor position controller of changes. Figure 8 is the result of the triggering time and event triggering interval in the event-triggered control scheme. Each event triggering interval is greater than 0, and it is only triggered 52 times, indicating that the proposed event triggering scheme effectively saves the communication resources of the system and avoids the occurrence of the Zeno phenomenon.

[0218] Implementing the embodiments of the present invention has the following beneficial effects:

[0219] The present invention can solve the problem of finite-time control of a switching nonlinear system with unmeasurable states, and the operation of the controller depends on specific events and is updated only when the event conditions are met, thereby effectively reducing the number of data transmissions, so that all signals in the system converge to the vicinity of the equilibrium point within a finite time, and effectively reducing the number of data transmissions during the control process, thereby ensuring that the system remains stable and avoiding redundancy and unnecessary waste of data during the control process.

[0220] A person skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium, such as ROM / RAM, disk, CD-ROM, etc.

[0221] The above disclosure is only a preferred embodiment of the present invention, which certainly cannot be used to limit the scope of the present invention. Therefore, equivalent changes made according to the claims of the present invention are still within the scope of the present invention.

Claims

1. A finite time trigger control method for a switching nonlinear system, characterized in that: The method comprises the following steps: Step S1, constructing a state space model of a switching nonlinear system with incompletely measurable states; wherein the state space model of the switching nonlinear system contains nonlinear function terms; Step S2, removing the nonlinear function term in the state space model of the switching nonlinear system to obtain a nominal system under the condition that all state variables are measurable, and further constructing a continuous-time state feedback controller of the nominal system; Step S3, based on the fact that the nominal system is limited to outputs that are state-measurable, construct an observer for state order reduction in the state space model of the switching nonlinear system, and use the observer to replace all state values ​​in the continuous-time state feedback controller to obtain a continuous output feedback controller; Step S4, obtaining an event trigger condition, and combining the continuous output feedback controller to perform switching trigger control on the state space model of the switching nonlinear system, so as to form a switching nonlinear system finite time output feedback control model based on event triggering; wherein all signals output by the switching nonlinear system finite time output feedback control model converge to the same equilibrium point within a finite time; The step S4 specifically includes: Step S41, by defining the event trigger error as The event trigger condition is Among them, {t j ,j=1,2,…},t j <t j+1 is the trigger sequence; ||ξ(t)||=ξ1(t)|+ξ2(t)|+…+ξ n (t)|,r∈(0,1) is the event trigger parameter; Step S42: When the above event triggering conditions are met, the system controller will j ,t j+1 ) maintains a fixed value and continues to run, that is, And the controller Substitute into The last term in , we can get: From the above inequality, we can see that due to 0 <r n +τ<1, after a series of scaling, we can get: Because 1 / r l <1,l=1,2,…,n, so the following inequality holds: Among them, α is a positive constant, d l >0 is about r l and r l-1 The constant of use Scaling and some inequalities, we can get: Among them, the constant σ>0, It's about r l and the constants of τ; Combining the above inequalities with the designed event trigger mechanism, we can get: Substituting the above inequality into By simple calculation, the finite-time output feedback control model of the switching nonlinear system can be obtained as follows: Among them, α i >0,i=1,2 are 3 constants.

2. The finite time trigger control method for a switching nonlinear system according to claim 1, characterized in that: In step S1, the state space model of the switching nonlinear system is: Where x=[x1,…,x n ] T ∈R n is a state variable, and x2,…,x n is an unmeasurable state quantity; u∈R is the control input of the system; y∈R is the system output; piecewise right continuous function is the switching signal, N represents the number of subsystems; p n =1 is the power of the system; For any There is a constant c k ≥0, And r1=1,r i+1 p i =r i +τ, where the numerator of the parameter τ is an even number and the denominator is an odd number, The numerator and denominator of the system are both odd numbers, so that the nonlinear function term f k (·) satisfies f k (0)=0 and assume: Furthermore, a switching sequence t' is defined p <t' p+1 , {t′ p ,p∈z + }, and assume that for any t∈[t′ p ,t′ p+1 ), the system state will not change suddenly at the switching moment.

3. The finite time trigger control method for a switching nonlinear system according to claim 2, characterized in that: The step S2 specifically includes: Step S21: in the state space model of the switching nonlinear system, the nonlinear function term is removed to obtain a nominal system under the condition that all state variables are measurable; wherein the nominal system is expressed as: y=ξ1 For the above nominal system, define the coordinate transformation: Among them, the gain β i-1 > 0, i = 2, 3, ..., n; Step S22: construct a continuous-time state feedback controller of the nominal system by means of backstepping method: Constructing Lyapunov functions Taking the derivative of V1, we get: Among them, the virtual controller Gain in Similarly, in the i-th step, the Lyapunov function V can be constructed i (ξ1,…,ξ i )=V i-1 +W i (ξ1,…,ξ i ),in, V i (ξ1,…,ξ i ) is derived with respect to time, and through a series of inequalities, we can obtain: In addition, by r i and p i The relationship between <r i p i-1 <1, and through scaling of some inequalities we can get: Among them, b i (τ)>0 is a constant with respect to τ; Designed virtual controller Substituting into the above inequality, we can see: Furthermore, in the nth step, the Lyapunov function is constructed And design the continuous state feedback controller of the nominal system as follows: Among them, the control gain β n ≥1+b n (τ), constant b n (τ)>0; V n (ξ) is derived and the controller is substituted into the equation:

4. The finite time trigger control method for a switching nonlinear system according to claim 3, characterized in that: The step S3 specifically includes: Based on the continuous-time state feedback controller described in step S2, considering that only y=x1 is measurable in the nominal system, that is, only ξ1 is measurable in the nominal system, the observer is constructed as follows: In the formula, is the state ξ l The estimated value of The observation error generated by the observer is The unobservable state values ​​in the state feedback controller are all replaced by the estimated state quantity Replace it and get the following continuous output feedback controller: The continuous output feedback controller selects an appropriate control gain through the Lyapunov function to ensure that the system achieves finite time stability. The specific process is as follows: Construct the Lyapunov function as i=2,3,…,n; To U i Taking the derivative and combining a series of inequalities to scale them up, we get: Using the inequality between parameters and Further we get: in, c l,1 >0 and c l,2 >0 is a constant with respect to the parameter τ, is about the observation gain a l ,l=2,…,n non-negative function; Introduce a transformation, namely Where M>1 is a constant gain, q1=0, i=1,2,…,n+1, the state after the coordinates change ξ i ,i=2,…,n is unmeasurable; According to the above coordinate transformation, the system will be transformed into the following form: y=z1, Among them, the nonlinear function The following conditions must be met: According to r i , p i and q i Relationship: because So we have: Further scaling gives:

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