A data-driven output regulation method and device for unknown nonlinear systems

Abstract

The application belongs to the technical field of unmanned system control, and particularly relates to a data-driven unknown nonlinear system output regulation method and device. The specific process of the method is as follows: inner membrane system construction: constructing a k-order auxiliary matrix of an evolution matrix according to an external reference signal, calculating an inner membrane matrix pair based on the auxiliary matrix, and forming an inner membrane system; connecting the nonlinear system, the sensor and the inner membrane system in sequence, directly applying a control input to the nonlinear system, taking the difference between the sensor output and a trajectory to be expectedly tracked as the input of the inner membrane system, collecting the state of the nonlinear system and the state of the inner membrane system, and calculating the nonlinear state of the nonlinear system, the derivative of the state and the derivative of the state of the inner membrane system; constructing a filter matrix by using the evolution matrix of the external reference signal; solving a semi-positive definite programming problem by using the collected data and the filter matrix, and obtaining a control gain matrix; and constructing a feedback controller by using the control gain matrix to realize system output control.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned system control, and particularly relates to a data-driven output regulation method and device for an unknown nonlinear system. BACKGROUND

[0002] At present, under the guidance of artificial intelligence, unmanned systems such as unmanned vehicles, robots, unmanned aerial vehicles and unmanned ships have become a large stage for artificial intelligence technology to exert its power. In 2022, the state listed “intelligent unmanned system technology” as one of the priority development areas; the “2023 China Artificial Intelligence Series White Paper” pointed out that intelligent cooperative control is an important application direction of artificial intelligence technology. In many applications of unmanned systems such as unmanned aerial vehicle flight control and mechanical arm operation, tracking a desired trajectory signal or suppressing a specific disturbance is a common requirement, which is collectively referred to as an output regulation problem, and the desired trajectory and the specific disturbance signal are collectively referred to as an external reference signal.

[0003] However, existing methods are based on models, so a mechanism or identification model is needed to establish a mathematical model of the controlled object. However, the scale and complexity of current unmanned systems continue to grow, and it is often difficult to obtain an accurate model of the system, thereby bringing certain challenges to the subsequent design of the output regulation controller. In order to avoid unnecessary errors introduced in the system modeling stage, data-driven methods for learning control rates directly from data have received attention in recent years. Solving the output regulation problem using data-driven methods faces the following challenges. First, considering the coupling noise in the collected data and the nonlinearity in the system model, there are often countless systems that match the collected data. Further, since the output regulation problem generally needs to accurately solve the output regulation equation, under the data-driven setting, this problem becomes a problem of matching a limited equation solution with an infinite system model, so it cannot be solved, which makes the data-driven output regulation problem have no good solution even in the linear system field, not to mention nonlinear systems. In addition, since the external reference signal and the noise have different properties and cannot satisfy the noise boundedness restriction, how to filter this part of the signal in the collected data according to its dynamic evolution matrix is also one of the difficult problems to be solved.

[0004] In summary, there is an urgent need for a method that can be based on noise data and does not need to measure the external reference signal, and directly designs a controller to achieve the output regulation of an unknown nonlinear system without system identification. SUMMARY

[0005] Therefore, the application provides a data-driven unknown nonlinear system output regulation method and device.

[0006] To achieve the above-mentioned application purposes, the technical scheme of the application is as follows:

[0007] In the first aspect, the application provides a data-driven unknown nonlinear system output regulation method, and the specific steps include:

[0008] Step one, inner membrane system construction: constructing a k-order auxiliary matrix of the evolution matrix according to the external reference signal, calculating an inner membrane matrix pair based on the auxiliary matrix, and constituting an inner membrane system;

[0009] Step two, connecting the nonlinear system, the sensor and the inner membrane system in sequence, directly applying a control input to the nonlinear system, taking the difference between the sensor output and the expected tracking trajectory as the input of the inner membrane system, collecting the state of the nonlinear system and the state of the inner membrane system, and calculating the nonlinear state of the nonlinear system, the derivative of the state and the derivative of the state of the inner membrane system;

[0010] Step three, constructing a filter matrix by using the evolution matrix of the external reference signal

[0011] Step four, solving a semi-positive definite programming problem by using the data collected in step two and the filter matrix constructed in step three, and obtaining a control gain matrix

[0012] Step five, constructing a feedback controller by using the control gain matrix calculated in step five;

[0013] Step six, connecting the nonlinear system, the sensor, the inner membrane system and the controller in sequence, and performing online operation to realize output regulation of the closed-loop system.

[0014] Further, the feedback controller of the application is:

[0015]

[0016] Wherein, u(t) is the control input at t moment, x(t) is the state of the unknown physical process, ζ(t) is the state of the inner membrane system, and Q(x(t)) is a nonlinear function of the nonlinear system state of the unknown physical process.

[0017] Further, the inner membrane system of the application is:

[0018] ​

[0019] wherein, is the derivative of the internal state ζ(t), and e(t) is the tracking error.

[0020] Further, the value of k in the present application is: when the nonlinear part of the unknown physical process nonlinear system is only a polynomial function of the state, k is the highest order of the function, otherwise, k is an integer greater than 1 selected arbitrarily.

[0021] Further, the auxiliary matrix is calculated as:

[0022]

[0023] wherein, v [l] (t) represents the l-order monomial expansion vector of the external reference signal v(t);

[0024]

[0025] wherein, β is a constant matrix, the characteristic polynomial of which is the same as the minimum polynomial of the auxiliary matrix , blockdiag(β, …, β) represents a block diagonal matrix constructed with β as the diagonal submatrix, n y -tuple represents that the block diagonal matrix has n y submatrices, and σ is a constant column vector.

[0026] Further, for any time period 0 to T1, the present application generates a sequence of inputs randomly in real time to the unknown physical process nonlinear system, obtains the state of the unknown physical process and the internal state in this period of time, and the T = (n x +n ζ +1)n u +n x +n ζ -1 time points correspond to the input sequence that satisfies n x +n ζ +1 order sustained excitation; wherein, n x represents the state dimension of the nonlinear system, n ζ represents the state dimension of the internal membrane system, and n u represents the dimension of the control input.

[0027] Further, according to the data collected in step two, the present application constructs an augmented state data matrix Ξ - and an augmented state derivative data matrix Ξ + .

[0028]

[0029] Among them, U - is the input data matrix, X - is the system linear state data matrix, Q - is the system nonlinear state data matrix, X + is the system state derivative data matrix, Z - is the endomembrane system state data matrix, Z + Endomembrane system state derivative data matrix.

[0030] Furthermore, the present invention assumes that the evolution matrix S is composed of r different real characteristic roots and s different complex characteristic root pairs, where λ1,…,λ r Denote real characteristic roots, using k1,…,k r Denote the multiplicity of these characteristic roots by λ r+i =β i +jφ i represents the i-th complex characteristic root, β i is the real part, j is the imaginary number sign, φ i is the imaginary part, Represents λ r+i The conjugate complex characteristic root of r+1 ,…,k r+s represents the complex characteristic root pair The multiplicity of , construct the filter matrix as follows:

[0031]

[0032] Where, for the time t from i 1 to T i have

[0033]

[0034] Where, for a positive integer k, k! represents the factorial of k.

[0035] Furthermore, the semi-positive programming problem in step 4 of the present invention is:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] in, is the variable to be solved, The maximum upper bound of the noise introduced by the system in the data collection phase is T, the length of the offline data, and the solution obtained is denoted as The control gain matrix is constructed R Q is a constant matrix preset.

[0042] In another aspect of the present application, an embodiment of the data-driven output regulation device for an unknown nonlinear system comprises:

[0043] A sensor is configured to acquire an output state of the unknown nonlinear system.

[0044] An inner membrane system is configured to subtract a trajectory expected to be tracked from the output of the sensor as an input of the inner membrane system, and send a current inner membrane state to a controller.

[0045] The controller is configured to generate a control input according to the output state of the nonlinear system, the state of the inner membrane system, and a nonlinear function of the state of the nonlinear system.

[0046] Advantages:

[0047] First, the data-driven output regulation method for an unknown nonlinear system provided by the present application designs a state feedback output regulation controller through system input-state trajectories collected offline with noise. As can be seen, the present application does not need to identify a physical process in advance, and only needs to sample data, so that the output regulation of the unknown system can be realized.

[0048] Second, the data-driven output regulation method for an unknown nonlinear system provided by the present application does not need to collect disturbances and external reference signals in offline and online operation phases, and the external reference signal can be arbitrarily large in the offline data collection process, so that the output regulation of the unknown system can be realized only through the state data of the system.

[0049] Third, the output regulation controller for the unknown system in the present application only needs to solve a low-complexity semi-definite programming problem offline, and does not need to solve an optimization problem online, so that the calculation amount of the output regulation control obtained by the present application is small. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0051] Figure 1A data-driven unknown nonlinear system output regulation method provided by the application is shown in a schematic diagram of offline data collection principle.

[0052] Figure 2 A data-driven unknown nonlinear system output regulation method provided by the application is shown in a schematic diagram of principle.

[0053] Figure 3 An output regulation effect diagram of a single-connection mechanical arm model provided by the application. DETAILED DESCRIPTION

[0054] The embodiments of the application are described in detail below with reference to the accompanying drawings.

[0055] It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict; and all other embodiments obtained by those skilled in the art based on the embodiments in the present disclosure without creative labor are within the protection scope of the present disclosure.

[0056] It should be noted that various aspects of the embodiments described below are within the scope of the appended claims. It should be apparent that the aspects described herein can be embodied in a wide variety of forms and that any specific structure and / or function described herein is merely illustrative. Based on the teachings herein one skilled in the art should appreciate that an aspect described herein can be implemented independently of any other aspects and that two or more aspects can be implemented in conjunction with each other. For example, a device can implement one, some or all of the aspects described herein, and / or a method can incorporate one, some or all of the aspects described herein. In addition, two or more aspects described herein can be implemented by way of one or more computer programs or software. However, one skilled in the art should appreciate that any program or software mentioned herein can be designed using one or more programming languages, and a program or software can implement one, some, or all of the aspects described herein.

[0057] As shown in Figure 1 An unknown physical process nonlinear system, a sensor, an inner loop system and a controller jointly constitute a closed loop system, wherein the unknown physical process nonlinear system is disturbed by an external disturbance, and an output of the sensor is expected to follow an external reference signal.

[0058] The data-driven unknown nonlinear system output regulation method provided by the embodiment of the application is designed for the inner loop system and the controller in the closed loop system, and can achieve the following in a given expected physical process operating region: (1) the state of the unknown physical process nonlinear system is bounded under the action of a non-zero external reference signal; (2) if the unknown physical process nonlinear system only contains a polynomial function of the state, the tracking deviation between the sensor output and the external signal is zero, and if the unknown physical process nonlinear system contains a nonlinear term other than a polynomial, the tracking deviation is a high-order infinitesimal of the external reference signal.

[0059] As shown in Figure 1As shown, in the offline running stage, the unknown physical process nonlinear system is not connected with the controller. An internal membrane system of the external reference signal is constructed according to an evolution matrix of the external reference signal, and the internal membrane system is connected with the physical process nonlinear system. An input sequence is applied to the unknown physical process nonlinear system for a period of time, the states of the unknown physical process and the internal membrane system in the period of time are collected, and the first-order derivatives of the states are estimated. By using the collected input, the states of the unknown physical process and the internal membrane system, and the calculated first-order derivative data of the states, the relevant parameters of the controller are obtained by solving a semi-positive programming problem. The state feedback controller is constructed by using the parameters.

[0060] As shown in the figure, Figure 2 in the online running stage, the controller is connected with the unknown physical process nonlinear system, the state data sent by the unknown physical process nonlinear system and the internal membrane state sent by the internal membrane system are collected at each time on the controller side, the control input is generated to control the unknown physical process, so that the output regulation is realized.

[0061] In the embodiment of the application, the dynamic equation of the unknown physical process nonlinear system is:

[0062]

[0063]

[0064] y(t)=CZ(x(t))

[0065] r(t)=Fv(t)

[0066] e(t)=y(t)-r(t)=CZ(x(t))-Fv(t)

[0067] wherein, respectively, the derivative of the state of the unknown physical process at t, the state value, the control input, the external reference signal, the sensor output, the signal to be tracked, and the tracking deviation. The derivative of the state of the unknown physical process and the state x(t) are n x dimensional u , the dimension of the control input u(t) is n v , the dimension of the external reference signal v(t) is n y , the dimension of the sensor output y(t), the signal to be tracked r(t) and the tracking deviation e(t) is n z , the dimension of the state dictionary vector is n q , wherein the nonlinear state dictionary vector Q(x(t)) contains all nonlinear functions of the state x(t), and the dimension is n x ; the matrix A is n zunknown real matrix of dimension n x ×n u unknown real matrix of dimension n x ×n v unknown real matrix of dimension n y ×n z unknown real matrix of dimension n y ×n v unknown real matrix of dimension n v ×n v known real matrix of dimension n

[0068] The data-driven unknown nonlinear system output regulation method is implemented based on the above description, including six stages of offline inner membrane system construction (S1 and S2), data collection (S3), filter matrix construction (S4), control gain matrix solving (S5), feedback controller construction (S6) and online operation (S7); the specific process is as follows:

[0069] S1, the inner membrane system construction stage, if the nonlinear part of the unknown physical process is only a polynomial function of the state and the highest order is k, then the k-order auxiliary matrix of the evolution matrix S is constructed according to the external reference signal Otherwise, an arbitrary integer k greater than 1 is selected in advance, and the k-order auxiliary matrix of the evolution matrix S is constructed The k-order auxiliary matrix is constructed as follows:

[0070]

[0071] wherein, denotes the vector The derivative of time t is v [l] (t) denotes the l-order monomial expansion vector of the external reference signal , which is abbreviated as is defined as follows:

[0072]

[0073] According to the k-order auxiliary matrix The n y order inner membrane matrix pair (G1, G2) is designed as follows:

[0074]

[0075] wherein, β is a constant matrix of dimension n β ×n β , and the characteristic polynomial of the matrix is ​The minimum polynomial of the block diagonal matrix is the same as that of β, and blockdiag(β, · · ·, β) represents the block diagonal matrix constructed by β as the diagonal sub-matrix, n y The tuple indicates that the block diagonal matrix has n y sub-matrices. σ is an arbitrary constant column vector with dimension n β × 1, as long as (β, σ) is controllable.

[0076] S2, construct the internal membrane state ζ(t) with dimension n ζ × 1 using the internal membrane matrix (G1, G2) constructed in step S1, where n ζ = n y n β The internal membrane system generating the internal membrane state is as follows

[0077]

[0078] where, is the derivative of the internal membrane state ζ(t), and e(t) is the tracking error.

[0079] S3, in the data collection phase, the controller is not connected to the unknown physical process nonlinear system, the internal membrane system is connected to the sensor, and the random generated control input is directly applied to the unknown physical process in real time, while the sensor output is subtracted from the expected trajectory to be tracked as the input of the internal membrane system, and the state of the physical process and the state of the internal membrane system are collected.

[0080] Specifically, for any time period 0 to T1, where 0 < T1, the real-time random input is generated to the unknown physical process, and the state of the unknown physical process and the internal membrane state in this period are obtained. In any sampling T time points in the time period 0 to T1, 0 < t1< t2< ··· < t T ≤ T1, where T = (n x + n ζ + 1) n u + n x + n ζ - 1, if the T input sequences corresponding to these time points are n x + n ζ + 1 order sustained excitation, then record these time points and the sequence input. Record the state of the unknown physical process and the internal membrane state According to the state , calculate the nonlinear state dictionary vector at each time point When recording the state of the unknown physical process and the state of the endomembrane system at time τ, the state values ​​at two moments very close to each other are also recorded at the same time, that is, x(τ-Δt), x(τ+Δt), ζ(τ-Δt) and ζ(τ+Δt), where the closer Δt is to zero, the better.

[0081] For each moment τ, the derivative of the unknown physical process state is estimated as The derivative of the state of the endomembrane system is The input data matrix U is constructed using the applied control inputs, the collected physical process states, the collected endomembrane system states, the calculated physical process state derivatives, and the calculated endomembrane system state derivatives. - =[u (t1)u (t2)…u(t T )], physical process linear state data matrix X _ =[x (t1)x (t2)…x (t T )], physical process nonlinear state data matrix Q - =[Q(x(t1))Q(x(t2))…Q(x(t T ))], physical process state derivative data matrix Endomembrane system state data matrix Z _ =[ζ(t1)ζ (t2)…ζ (t T )], endomembrane system state derivative data matrix And define is the augmented state data matrix, is the augmented state derivative data matrix, define n ξ =n x +n ζ .

[0082] S4, construct a matrix with dimension n according to the external signal evolution matrix S v ×T filter matrix

[0083] The specific steps are as follows: First, assume that the evolution matrix S consists of r different real characteristic roots and s different complex characteristic root pairs, where λ1,…,λ r Denote real characteristic roots, using k1,…,k r Denote the multiplicity of these characteristic roots by λ r+i =β i +jφ i Denote the i-th complex characteristic root, using represents the conjugate complex characteristic root of the i-th complex characteristic root, where β i is the real part, j is the imaginary number sign, φ i For the imaginary part, use k r+1 ,…,kr+s represents the complex characteristic root pair Under these definitions, the filter matrix is ​​constructed as follows

[0084]

[0085] Where, for the time t from i 1 to T i have

[0086]

[0087] Among them, for a positive integer k, k! = k×(k-1)×…×1 represents the factorial of k, for a constant t, sin(t) represents the sine function of t, cos(t) represents the cosine function of t, e t Represents the exponential function of t.

[0088] S5. Set a given positive constant As the maximum upper bound of the noise introduced by the system during the data collection phase, this noise includes the derivative estimation error and the noise that may be introduced during the data collection phase, and the dimension is given in advance as n x ×n r The constant matrix R Q , using this matrix to describe the upper bound of the evolution of the derivative of the nonlinear state in the desired physical process operation area, satisfying in Represents the partial derivative of the function Q(x(t)) with respect to x(t), the matrix Representation matrix The transpose of the matrix Represents the matrix B Q For any matrix X, X T The matrix representing the matrix X, the same below. Using the data matrix in step S3 and the filter matrix in S4 Construct the following semidefinite programming problem

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] in, is the variable to be solved, the matrix n ξ ×n ξpositive definite real symmetric matrix of dimension, matrix is a matrix of dimension T x (n ξ +n q ), matrix is a matrix of dimension T x n q , scalar a is a positive real number, scalar μ is a positive real number, I n denotes an identity matrix of dimension n x n, 0 n×m denotes an all-zero matrix of dimension n x m, is the maximum upper bound of the noise introduced by the data collection phase system, T is the length of the offline data in S3, matrices Ξ - and Ξ + are data matrices defined in S3. The solution obtained is denoted as constructs the control gain matrix

[0095] S6, uses the control gain matrix obtained by solving in S5 to construct a state feedback-based controller

[0096] S7, in the online running phase, the unknown physical process sends the current state x(t) to the controller at each time, and the internal membrane system sends the current internal membrane state ζ(t) to the controller, and the controller configures the state feedback-based controller designed in S6 to send the generated control input u(t) back to the unknown physical system, so as to realize output regulation of the closed-loop system.

[0097] In another aspect of the present application, a data-driven unknown nonlinear system output regulation device comprises:

[0098] a sensor for acquiring the output state of the unknown nonlinear system;

[0099] an internal membrane system, which takes the difference between the sensor output and the trajectory expected to be tracked as the input of the internal membrane system, and sends the current internal membrane state to the controller;

[0100] a controller for generating a control input according to the output state of the nonlinear system, the state of the internal membrane system, and the nonlinear function of the nonlinear system state.

[0101] As shown in FIG. 3, it is an effect diagram of an embodiment of the data-driven output regulation controller of the present application running on a connected mechanical arm system for 300 seconds. The corresponding unknown physical state is: Figure 3

[0102]

[0103]

[0104] ​

[0105]

[0106] y(t) = x1(t)

[0107]

[0108]

[0109] r(t) = v1(t)

[0110] where K c = 0.4, F2 = 0.1, J2 = 0.2, N c = 2, F1 = 0.1, J1 = 0.15, m = 0.4, g = 9.8, f = 0.1, ω1 = π / 5. It can be seen that the nonlinear function of the state is Q(x(t)) = cosx1(t), n x = 4, n q = 1, n y = 1, n v = 2, and the evolution matrix of the external reference signal is Select k = 4, and design the inner film matrices G1 and G2 according to step S1 as

[0111]

[0112] In the data collection stage, the system is run in open loop from 0 to 3 seconds, set T = 25, and let t1 = 0.1, t2 = 0.2,..., t T = 2.5. Since the S matrix has only one pair of complex eigenvalue pairs (ω1, -ω1), construct the filter matrix according to step S4 Since Q(x(t)) = cosx1(t) has a value range of -1 to 1 for any t, let R Q = blockdiag(1, 0 12 , 12 ) where 0 12×12 is a 12x12 all-zero matrix. By solving the semi-definite programming problem in S5, Figure 3 The solid line is the signal to be expected to track, the dashed line is the system output, and the dotted line is the tracking error trajectory. It can be seen that the system achieves output regulation. This shows the effectiveness of the invented data-driven output regulation method for unknown nonlinear systems.

[0113] The above merely illustrates the specific embodiments of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of the changes or replacements within the technical range disclosed by the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A data-driven output regulation method for unknown nonlinear systems, characterized in that, The specific steps include: Step one, inner membrane system construction: constructing a k-order auxiliary matrix of the evolution matrix according to an external reference signal, calculating an inner membrane matrix pair based on the auxiliary matrix, and constituting an inner membrane system; Step two, connecting the nonlinear system, the sensor and the inner membrane system in sequence, directly applying a control input to the nonlinear system, subtracting the sensor output from a trajectory to be tracked as the input of the inner membrane system, collecting the state of the nonlinear system and the state of the inner membrane system, and calculating the nonlinear state of the nonlinear system, the derivative of the state and the derivative of the state of the inner membrane system; Step three, constructing a filter matrix using an evolving matrix of external reference signals Step four, using the data collected in step two and the filter matrix constructed in step three, solve a semi-definite programming problem to obtain a constructed control gain matrix Step five, using the control gain matrix calculated in step five constructing a feedback controller; Step six, connecting the nonlinear system, the sensor, the inner membrane system and the controller in sequence, and performing online operation to realize output adjustment of the closed-loop system.

2. The data-driven output regulation method for unknown nonlinear systems as claimed in claim 1, wherein, The feedback controller is: Wherein, u(t) is the control input at t time, x(t) is the state of the unknown physical process, ζ(t) is the state of the inner membrane system, and Q(x(t)) is the nonlinear function of the nonlinear state of the unknown physical process.

3. The data-driven unknown nonlinear system output adjustment method according to claim 2, characterized in that: The inner membrane system is: wherein is the derivative of the intima state ζ(t) and e(t) is the tracking error.

4. The data-driven output regulation method for unknown nonlinear systems of claim 1, wherein, The value of k is: when the nonlinear part of the nonlinear system of the unknown physical process is only a polynomial function of the state, k is the highest order of the function, otherwise, k is an integer greater than 1 selected at will.

5. The data-driven output regulation method for unknown nonlinear systems as claimed in claim 4, wherein, The auxiliary matrix The calculation is: where v [l] (t) denotes the monomial expansion vector of order l of the external reference signal v(t); where β is a constant matrix whose characteristic polynomial is the same as the minimal polynomial of the auxiliary matrix blockdiag(β,..., β) denotes a block diagonal matrix constructed with β as the diagonal sub-matrix, n y -tuple indicates that the block diagonal matrix has n y sub-matrices, and σ is a constant column vector.

6. The data-driven output regulation method for unknown nonlinear systems as claimed in claim 1, wherein, The direct application of control input to the nonlinear system is: for any time 0 to T1, any sampling T time points, real-time random sequence input to the unknown physical process nonlinear system process operation, obtain the state and inner membrane state of the unknown physical process in this period, and the T = (n x +1)n ζ +1)n u +1)n x +1)n ζ -1 time point corresponding input sequence Satisfy n x +1 order sustained excitation; wherein, n ζ +1 order sustained excitation; wherein, n x Indicates the state dimension of the nonlinear system, n ζ Indicates the state dimension of the inner membrane system, and n u Indicates the dimension of the control input.

7. The data-driven output regulation method for unknown nonlinear systems as claimed in claim 6, wherein, Based on the data collected in Step Two, construct the augmented state data matrix Ξ - and the augmented state derivative data matrix Ξ + ; where U - is the input data matrix, X - is the system linear state data matrix, Q - is the system nonlinear state data matrix, X + is the system state derivative data matrix, Z - is the inner membrane system state data matrix, Z + is the inner membrane system state derivative data matrix.

8. The data-driven output regulation method for unknown nonlinear systems of claim 1, wherein setting The evolution matrix S is composed of r different real eigenvalues ​​and s different complex eigenvalue pairs, where λ1,…,λ r Denote real characteristic roots, using k1,…,k r Denote the multiplicity of these characteristic roots by λ r+i =β i +jφ i represents the i-th complex characteristic root, β i is the real part, j is the imaginary number sign, φ i is the imaginary part, Represents λ r+i The conjugate complex characteristic root of r+1 ,…,k r+s represents the complex characteristic root pair The multiplicity of , construct the filter matrix as follows: where, for a time t, i from 1 to T i There are Wherein, for a positive integer k, k! represents the factorial of k.

9. The data-driven output regulation method for unknown nonlinear systems of claim 7, wherein, The semi-positive programming problem in step four is: wherein, is the variable to be solved, is the maximum upper bound of the noise introduced by the system in the data collection phase, T is the length of the offline data, and the solution is denoted as constructing the control gain matrix R Q is a pre-set constant matrix.

10. A data-driven unknown nonlinear system output adjustment device based on any one of claims 1-9, comprising: a sensor for obtaining the output state of the unknown nonlinear system; an inner membrane system, which subtracts the sensor output from a trajectory to be tracked as the input of the inner membrane system, and sends the current inner membrane state to the controller; a controller for generating a control input according to the output state of the nonlinear system, the state of the inner membrane system and the nonlinear function of the nonlinear system state.

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