Data-driven unknown nonlinear system output adjusting method and device

Abstract

The invention belongs to the technical field of unmanned system control, and particularly relates to a data-driven unknown nonlinear system output adjusting method and device. The method specifically comprises the following steps: constructing an inner membrane system: constructing a k-order auxiliary matrix of an evolution matrix according to an external reference signal, and calculating an inner membrane matrix pair based on the auxiliary matrix to form the inner membrane system; a nonlinear system, a sensor and an inner membrane system are connected in sequence, control input is directly applied to the nonlinear system, the difference between the output of the sensor and a trajectory expected to be tracked is used as the input of the inner membrane system, and the state of the nonlinear system and the state of the inner membrane system are collected. 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 filtering matrix by using the evolution matrix of the external reference signal; solving a positive semidefinite programming problem by using the collected data and the filtering matrix to obtain a construction control gain matrix; and constructing a feedback controller by using the control gain matrix to realize system output control.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned system control, and in particular relates to a data-driven unknown nonlinear system output regulation method and device. Background Art

[0002] At a time when artificial intelligence is leading scientific and technological innovation, unmanned systems represented by unmanned vehicles, robots, drones, and unmanned boats have become a big stage for artificial intelligence technology to display its strength. In 2022, the country listed "intelligent unmanned system technology" as one of the priority development areas; the "2023 China Artificial Intelligence Series White Paper" pointed out that intelligent collaborative control is an important application direction of artificial intelligence technology. In many applications of unmanned systems such as drone flight control and robotic arm operation, tracking a desired trajectory signal or suppressing a specific type of interference is a common requirement. This problem is collectively referred to as an output regulation problem, and the desired trajectory and specific interference signal are often collectively referred to as external reference system signals.

[0003] However, the existing methods are all based on models, so it is necessary to use mechanism or identification model methods 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, which brings certain challenges to the subsequent design of output regulation controllers. In order to avoid unnecessary errors introduced in the system modeling stage, data-driven methods that directly learn control rates from data have attracted people's attention in recent years. Using data-driven methods to solve output regulation problems faces the following challenges. First, considering the coupled noise in the collected data and the nonlinearity contained in the system model, there are often countless systems that match the collected data. Furthermore, since the output regulation problem generally requires the accurate solution of the output regulation equation, under the data-driven setting, this problem becomes a problem of matching the finite equation solution with the infinite system model, so it cannot be solved, which makes the data-driven output regulation problem have no good solution even in the field of linear systems, let alone nonlinear systems. In addition, since the external reference signal is different from the noise in nature and cannot meet the limitation of bounded noise, how to filter this part of the signal in the collected data according to its dynamic evolution matrix is ​​also one of the problems worth solving.

[0004] In summary, there is an urgent need for a method that can directly design a controller to achieve output regulation of an unknown nonlinear system based on noise data without measuring an external reference signal or performing system identification. Summary of the invention

[0005] In view of this, the present invention provides a data-driven unknown nonlinear system output regulation method and device, which can be directly based on noisy input-state data collected offline, without the need to collect external reference signals or prior physical process identification, and can construct a data-driven state feedback output regulation controller.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution of the present invention is:

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

[0008] Step 1, endomembrane system construction: constructing a k-order auxiliary matrix of the evolution matrix according to an external reference signal, and calculating an endomembrane matrix pair based on the auxiliary matrix to form an endomembrane system;

[0009] Step 2: connect the nonlinear system, the sensor and the inner membrane system in sequence, apply control input directly to the nonlinear system, take the difference between the sensor output and the desired tracking trajectory as the input of the inner membrane system, collect the state of the nonlinear system and the state of the inner membrane system, and calculate 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 3: Use the evolution matrix of the external reference signal to construct the filter matrix

[0011] Step 4: Use the data collected in step 2 and the filter matrix constructed in step 3 to solve a semi-positive definite programming problem and obtain the constructed control gain matrix

[0012] Step 5: Use the control gain matrix calculated in step 5 Construct feedback controller;

[0013] Step 6: Connect the nonlinear system, sensor, inner membrane system and controller in sequence and perform online operation to realize output regulation of the closed-loop system.

[0014] Furthermore, the feedback controller of the present invention is:

[0015]

[0016] Among them, u(t) is the control input at time t, 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 state of the nonlinear system of the unknown physical process.

[0017] Furthermore, the endomembrane system of the present invention is:

[0018]

[0019] in, is the derivative of the inner membrane state ζ(t), and e(t) is the tracking deviation.

[0020] Furthermore, the value of k described in the present invention 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 arbitrary integer greater than 1.

[0021] Furthermore, the auxiliary matrix of the present invention Calculated as:

[0022]

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

[0024]

[0025] Among them, β is a constant square matrix, whose characteristic polynomial is the same as the auxiliary matrix The minimum polynomial is the same as that of , blockdiag(β, ..., β) represents the block diagonal matrix constructed with β as the submatrix on the diagonal, n y -tuple indicates that the block diagonal matrix has n y submatrices, σ is a constant column vector.

[0026] Furthermore, the present invention randomly samples T time points for any period of time from 0 to T1, generates a sequence randomly in real time and inputs it into the nonlinear system process of the unknown physical process to run, and obtains the state of the unknown physical process and the inner membrane state during this period of time, wherein T=(n x +n ζ +1)n u +n x +n ζ -1, the input sequence corresponding to the time point Satisfy n x +n ζ +1-order continuous excitation; where n x represents the state dimension of the nonlinear system, n ζ represents the state dimension of the endomembrane system, n u Represents the dimension of the control input.

[0027] Furthermore, the present invention constructs an augmented state data matrix Ξ according to the data collected in step 2 - and the 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 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 definite programming problem in step 4 of the present invention is:

[0036]

[0037]

[0038]

[0039]

[0040]

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

[0042] In another aspect of the present application, an embodiment of the present application provides a data-driven unknown nonlinear system output adjustment device, comprising:

[0043] Sensors, used to obtain the output state of unknown nonlinear systems;

[0044] The inner membrane system takes the difference between the sensor output and the desired tracking trajectory as the input of the inner membrane system and sends the current inner membrane state to the controller;

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

[0046] Beneficial effects:

[0047] First, the present invention provides a data-driven unknown nonlinear system output regulation method, which designs a state feedback output regulation controller through the noisy system input-state trajectory collected offline. It can be seen that the present invention does not require prior identification of the physical process, but only requires data sampling to achieve output regulation of the unknown system.

[0048] Second, the present invention provides a data-driven output regulation method for an unknown nonlinear system, which does not require the collection of interference and external reference signals in both offline and online operation stages, and the external reference signal can be arbitrarily large during offline data collection. The output regulation of the unknown system can be achieved only through the system status data.

[0049] Third, the output regulation controller of the unknown system in the present invention only needs to solve a low-complexity semi-positive definite programming problem offline, and there is no need to solve the optimization problem online. It can be seen that the calculation amount of the output regulation control obtained by the present invention is relatively small. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0051] Figure 1This is a schematic diagram of the offline data collection principle architecture of a data-driven unknown nonlinear system output regulation method provided by the present invention.

[0052] Figure 2 A principle architecture diagram of a data-driven unknown nonlinear system output regulation method provided by the present invention.

[0053] Figure 3 This is a diagram of the output adjustment effect of the single-connection robotic arm model provided by the present invention. DETAILED DESCRIPTION

[0054] The embodiments of the present invention 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 may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

[0056] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0057] like Figure 1 As shown, the unknown physical process nonlinear system, sensor, inner membrane system and controller together constitute a closed-loop system, in which the unknown physical process nonlinear system is subject to external disturbances, and the output of the sensor is expected to follow the external reference signal.

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

[0059] like Figure 1As shown, during the offline operation phase, the unknown physical process nonlinear system is not connected to the controller. The inner membrane system of the external reference signal is constructed according to the evolution matrix of the external reference signal, and the inner membrane system is connected to the physical process nonlinear system. An input sequence for a period of time is applied to the unknown physical process nonlinear system, the state of the unknown physical process and the state of the inner membrane system during this period are collected, and the first-order derivatives of these two states are estimated. Using the collected input, the state of the unknown physical process and the inner membrane system, and the calculated first-order derivative data of the state, the relevant parameters of the controller are obtained by solving a semi-positive definite programming problem. These parameters are used to construct a state feedback controller.

[0060] like Figure 2 As shown, during the online operation stage, the controller is connected to the unknown physical process nonlinear system. The controller collects the state data sent by the unknown physical process nonlinear system and the inner membrane state sent by the inner membrane system at every moment, generates control input to control the unknown physical process, thereby achieving output regulation.

[0061] In the embodiment of the present invention, 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] in, They are the derivative of the state of the unknown physical process at time t, the state value, the control input, the external reference signal, the sensor output, the desired tracking signal, and the tracking deviation. And the state x(t) dimension is n x , the dimension of the control input u(t) is n u , the dimension of the external reference signal v(t) is n v , the dimension of the sensor output y(t), the expected tracking signal r(t) and the tracking error e(t) is n y , state dictionary vector The dimension is n z , where the nonlinear state dictionary vector Q(x(t)) contains all nonlinear functions of the state x(t) and has a dimension of n q ; Matrix A is n x ×n zAn unknown real matrix of dimension B is n x ×n u An unknown real matrix of dimension E is n x ×n v An unknown real matrix of dimension C is n y ×n z An unknown real matrix of dimension F is n y ×n v An unknown real matrix of dimension S is n v ×n v A known real matrix of dimension .

[0068] Based on the above description, a data-driven unknown nonlinear system output regulation method is implemented, which includes six stages: offline endomembrane system construction (S1 and S2), data collection (S3), filter matrix construction (S4), control gain matrix solution (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, preselect any integer k greater than 1 to construct the k-order auxiliary matrix of the evolution matrix S k-order auxiliary matrix construction The construction is as follows:

[0070]

[0071] in, Representation vector Take the derivative with respect to time t, v [l] (t) represents the external reference signal The l-order monomial expansion vector of The definition is as follows:

[0072]

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

[0074]

[0075] Among them, β is the dimension n β ×n β A constant square matrix whose characteristic polynomial is the same as the matrix have the same minimal polynomial, blockdiag(β,…,β) represents a block diagonal matrix constructed with β as the submatrix on the diagonal, and n y -tuple indicates that this block diagonal matrix has n y submatrices. σ is an arbitrarily selected constant column vector of dimension n β ×1, as long as it is ensured that (β,σ) is controllable.

[0076] S2. Using the inner membrane matrix pair (G1,G2) constructed in step S1, construct the inner membrane state ζ(t) of dimension n ζ ×1, where n ζ = n y n β , and the inner membrane system generating the inner membrane state is as follows

[0077]

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

[0079] S3. During the data collection phase, the controller is not connected to the unknown physical process nonlinear system, and the inner membrane system is connected to the sensor. A randomly generated control input is directly applied to the unknown physical process in real time. At the same time, the output of the sensor is subtracted from the desired tracking trajectory as the input of the inner membrane system, and the state of the physical process and the state of the inner membrane system are collected.

[0080] Specifically, for any period of time from 0 to T1 where 0 < T1, an input is randomly generated in real time to run the unknown physical process, and the state of the unknown physical process and the inner membrane state during this period are obtained. T time points are randomly sampled in the time period from 0 to T1 satisfying 0 < t1 < t2 < … < t T ≤ T1, where T = (n x + n ζ + 1)n u + n x + n ζ - 1. If the input sequence corresponding to these T time points is persistently exciting of order n x + n ζ + 1, then record these time points and this sequence of inputs. Record the state of the unknown physical process at the corresponding moments inner membrane state According to the state calculate the nonlinear state dictionary vector at each moment 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 that are 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 states of the physical process, the collected states of the endomembrane system, the calculated derivatives of the physical process states, and the calculated derivatives of the endomembrane system states. - =[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 )], the 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 S 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 ith 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 is the imaginary part, and 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 normal number 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 expected physical process operation region, 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 is 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 ξA positive definite real symmetric matrix of dimension is T×(n ξ +n q )-dimensional matrix, matrix =T×n q Dimensional matrix, scalar α is a positive real number, scalar μ is a positive real number, for positive real numbers n and m, I n represents the identity matrix of dimension n×n, 0 n×m represents an all-zero matrix of dimension n×m, is the maximum upper bound of the noise introduced by the system during the data collection phase, T is the length of the offline data in S3, and the matrix Ξ - and + is the data matrix defined in S3. The solution is recorded as Construct the control gain matrix

[0095] S6. Use the control gain matrix obtained in S5 Constructing a controller based on state feedback

[0096] S7, during the online operation phase, the unknown physical process sends the current state x(t) to the controller at every moment, and the inner membrane system sends the current inner membrane state ζ(t) to the controller. The state feedback-based controller designed in the controller configuration S6 sends the generated control input u(t) back to the unknown physical system to realize the output regulation of the closed-loop system.

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

[0098] Sensors, used to obtain the output state of unknown nonlinear systems;

[0099] The inner membrane system takes the difference between the sensor output and the desired tracking trajectory as the input of the inner membrane system and sends the current inner membrane state to the controller;

[0100] The controller is used to generate a control input according to the output state of the nonlinear system, the state of the endomembrane system and a nonlinear function of the state of the nonlinear system.

[0101] like Figure 3 As shown in FIG. 1 , it is a diagram showing the effect of running the data driven output regulation controller of the present invention for 300 seconds on a connected robot arm system. The corresponding unknown physical state is:

[0102]

[0103]

[0104]

[0105]

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

[0107]

[0108]

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

[0110] Among them, 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 Select k = 4, and design the inner membrane matrices G1 and G2 according to step S1 as follows:

[0111]

[0112] During the data collection phase, the system was run in open loop from 0 to 3 seconds, and T = 25. And let t1=0.1,t2=0.2,…,t T =2.5. Since the S matrix has only one pair of complex characteristic roots (ω1, -ω1), the filter matrix is ​​constructed according to step S4. Since the value range of Q(x(t)) = cosx1(t) for any t is between -1 and 1, let R Q =blockdiag(1,0 12 , 12 ) where 0 12×12 is a 12×12 all-zero matrix. By solving the semi-positive definite programming problem in S5, Figure 3 The solid line in the middle is the desired tracking signal, 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, which shows the effectiveness of the invented data-driven unknown nonlinear system output regulation method.

[0113] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A data-driven unknown nonlinear system output regulation method, characterized in that: The specific steps include: Step 1, endomembrane system construction: constructing a k-order auxiliary matrix of the evolution matrix according to an external reference signal, and calculating an endomembrane matrix pair based on the auxiliary matrix to form an endomembrane system; Step 2: connect the nonlinear system, the sensor and the inner membrane system in sequence, apply control input directly to the nonlinear system, take the difference between the sensor output and the desired tracking trajectory as the input of the inner membrane system, collect the state of the nonlinear system and the state of the inner membrane system, and calculate the nonlinear state of the nonlinear system, the derivative of the state and the derivative of the state of the inner membrane system; Step 3: Use the evolution matrix of the external reference signal to construct the filter matrix Step 4: Use the data collected in step 2 and the filter matrix constructed in step 3 to solve a semi-positive definite programming problem and obtain the constructed control gain matrix Step 5: Use the control gain matrix calculated in step 5 Construct feedback controller; Step 6: Connect the nonlinear system, sensor, inner membrane system and controller in sequence and perform online operation to realize output regulation of the closed-loop system.

2. The data-driven unknown nonlinear system output adjustment method according to claim 1, characterized in that: The feedback controller is: Among them, u(t) is the control input at time t, 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 state of the nonlinear system of the unknown physical process.

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

4. The data-driven unknown nonlinear system output adjustment method according to claim 1, characterized in that: 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 arbitrarily selected integer greater than 1.

5. The data-driven unknown nonlinear system output adjustment method according to claim 4, characterized in that: The auxiliary matrix Calculated as: Among them, v [l] (t) represents the l-th order monomial expansion vector of the external reference signal v(t); Among them, β is a constant square matrix, whose characteristic polynomial is the same as the auxiliary matrix The minimum polynomial is the same as that of , blockdiag(β,…,β) represents the block diagonal matrix constructed with β as the submatrix on the diagonal, n y -tuple indicates that the block diagonal matrix has n y submatrices, σ is a constant column vector.

6. The data-driven unknown nonlinear system output adjustment method according to claim 1, characterized in that: The direct application of control input to the nonlinear system is: for any period of time from 0 to T1, randomly sample T time points, generate a random sequence in real time and input it into the unknown physical process nonlinear system process to run, and obtain the state of the unknown physical process and the inner membrane state during this period, wherein T = (n x +n ζ +1)n u +n x +n ζ -1 input sequence corresponding to a time point Satisfy n x +n ζ +1-order continuous excitation; where n x represents the state dimension of the nonlinear system, n ζ represents the state dimension of the endomembrane system, n u Represents the dimension of the control input.

7. The data-driven unknown nonlinear system output adjustment method according to claim 6, characterized in that: Based on the data collected in step 2, construct the augmented state data matrix Ξ - and the augmented state derivative data matrix Ξ + ; 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.

8. The data-driven unknown nonlinear system output regulation method according to claim 1, characterized in 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 as follows: Where, for the time t from i 1 to T i have Where, for a positive integer k, k! represents the factorial of k.

9. The data-driven unknown nonlinear system output adjustment method according to claim 7, characterized in that: The semi-positive programming problem in step 4 is: in, is the variable to be solved, is the maximum upper bound of the noise introduced by the system during the data collection phase, T is the length of offline data, and the solution is recorded as Construct the control gain matrix R Q is a preset constant matrix.

10. A data-driven unknown nonlinear system output adjustment device based on any one of claims 1 to 9, comprising: Sensors, used to obtain the output state of unknown nonlinear systems; The inner membrane system takes the difference between the sensor output and the desired tracking trajectory as the input of the inner membrane system and sends the current inner membrane state to the controller; The controller is used to generate a control input according to the output state of the nonlinear system, the state of the endomembrane system and a nonlinear function of the state of the nonlinear system.

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