A noise data unknown system output adjustment method and device

Abstract

The application provides a noise data unknown system output adjusting method and device, and belongs to the technical field of unmanned system control. The specific steps comprise the following steps: constructing an evolution matrix according to an external reference signal, calculating an inner membrane matrix pair, and constructing an inner membrane state; adding process noise on the inner membrane system and the unknown physical process linear system, connecting the linear system, the sensor and the inner membrane system, directly applying a control input to the linear system, taking the difference between the sensor output and the expected tracking trajectory as the input of the inner membrane system, collecting the output data, and constructing a state matrix; constructing a filtering matrix by using the evolution matrix of the external reference signal; calculating a control gain matrix; constructing a controller based on state feedback by using the control gain matrix; connecting the linear system, the sensor, the inner membrane system and the controller in sequence, and performing online operation to realize the output adjustment of the closed loop system.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of unmanned system control, and particularly relates to a noise data unknown system output regulation method and device. 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 strength. In many applications of unmanned systems such as unmanned aerial vehicle flight control and mechanical arm operation, tracking a trajectory signal or suppressing a specific type of disturbance is a common requirement, which is collectively referred to as an output regulation problem.

[0003] However, the existing methods are all model-based, and therefore require a mechanism or identification model 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. On the other hand, data-driven methods have attracted attention in recent years, but considering the coupling noise in the collected data, there are countless systems that match the collected data, which makes the data-driven output regulation problem still have no good solution. Specifically, the design of the output regulation controller requires solving the output regulation equation, and the equation that satisfies countless systems has no solution, which makes it impossible to construct the output regulation controller. Since 2021, Junjie Jiao et al. have solved the output regulation problem by using noise-free data and assuming that the external reference signal is measurable. However, in actual use, noise cannot be avoided and the initial value of the external reference signal is often unknown. In 2024, Yifei Li et al. solved the approximate output regulation by approximately solving the matrix equation, but it cannot achieve zero deviation tracking. It can be seen that for the output regulation problem, how to use noisy data to achieve zero deviation tracking when the external reference signal is not measurable has not been solved.

[0004] In summary, there is an urgent need for a method that can directly design a controller based on noisy data to achieve zero deviation tracking of unknown systems. SUMMARY

[0005] Therefore, the present application provides a noise data unknown system output regulation method and device, which can directly use offline collected input-state data with noise, without collecting disturbance and external tracking signal, and without prior physical process identification, to construct a data-based state feedback output regulation controller, to achieve the suppression of a class of disturbances and the zero deviation tracking of a class of trajectory signals for linear time-invariant systems.

[0006] In order to achieve the above-mentioned purposes, the technical scheme of the present application is as follows:

[0007] A noise data unknown system output adjustment method, the specific steps include:

[0008] Step one, according to the evolution matrix S of the external reference signal, calculate the inner membrane matrix pair (G1, G2), and construct the inner membrane state z(t) based on the inner membrane matrix pair (G1, G2);

[0009] Step two, add process noise to the inner membrane system and the unknown physical process linear system, connect the linear system, the sensor and the inner membrane system, directly apply the control input to the linear system, subtract the sensor output from the expected tracking trajectory as the input of the inner membrane system, collect the output data, and construct the state matrix;

[0010] Step three, use the evolution matrix of the external reference signal to construct the filter matrix

[0011] Step four, based on the data collected in step two and the filter matrix constructed in step three Calculate the control gain matrix K ξ ;

[0012] Step five, use the control gain matrix K ξ calculated in step four to construct a state feedback-based controller;

[0013] Step six, connect the linear system, the sensor, the inner membrane system and the controller in sequence, and perform online operation to realize the output adjustment of the closed-loop system.

[0014] Further, the step one of the present application designs the inner membrane system z(t+1)=G1z(t)+G2e(t) according to the evolution matrix S of the external reference signal, wherein z(t) is the inner membrane state, is the derivative of the inner membrane state, e(t) is the tracking error, and (G1, G2) is the inner membrane matrix pair;

[0015]

[0016] Wherein, β is a constant matrix with dimension n β ×n β , the characteristic polynomial of which is the same as the minimum polynomial of the matrix S, blockdiag(β, …, β) represents a block diagonal matrix with β as the diagonal line, n y -tuple indicates that the block diagonal matrix has n y submatrices. σ is an arbitrarily selected constant column vector with dimension n β ×1.

[0017] Further, the present application adds process noise d1(t) and d2(t) to the inner membrane system and the unknown physical process linear system, then the system for collecting data composed of the linear system, the sensor and the inner membrane system is:

[0018]

[0019] v(t+1)=Sv(t)

[0020] wherein, is the state of the unknown physical system with added noise, u(t) is the control input of the unknown physical system, v(t) is the external reference signal, e(t) is the tracking error, is the state of the inner membrane system with added noise, A, B, E, C, F are unknown real matrices, and S is a known real matrix.

[0021] Further, the present application directly applies the control input to the linear system, which is: at any sampling T time points, a sequence of input is generated in real time and applied to the linear system for process operation, wherein T=(n x +n z +1)n u +n x +n z -1, the input sequence corresponding to the T time points is a sustained excitation satisfying n x +n z +1; wherein n x represents the state dimension of the linear system, n z represents the state dimension of the inner membrane system, and n u represents the dimension of the control input.

[0022] Further, the present application comprises the following steps for constructing the state matrix:

[0023] The input data matrix U - =[u(0)u(1)…u(T-1)];

[0024] The state data matrix of the unknown physical system with added noise

[0025] The state evolution data matrix of the unknown physical system with added noise

[0026] The state data matrix of the inner membrane system with added noise

[0027] The state evolution data matrix of the inner membrane system with added noise

[0028] Further, the present application constructs the augmented state data matrix Ξ -and augmented state evolution data matrix Ξ + ;

[0029]

[0030] And further calculate the matrices Ψ, γ, and ∑;

[0031]

[0032] Furthermore, the present invention utilizes the evolution matrix of an external reference signal to construct a filtering matrix.

[0033] Let the evolution matrix S consist of r distinct real eigenvalues ​​and s distinct pairs of complex eigenvalues, where λ1,…,λ2 are used to represent the evolution matrix S. r Representing real characteristic roots, denoted by ρ1,…,ρ r The multiplicity of these eigenvalues ​​is represented by λ. r+i =β i +jφ i Let the i-th complex eigenvalue be represented by... Let λ represent the i-th complex eigenvalue. r+i The conjugate complex eigenvalues, where β i φ is the real part, j is the imaginary number marker, and φ is the imaginary number. i For the imaginary part, use k r+1 ,…,k r+s Represents a pair of complex characteristic roots The multiplicity of , let and Constructing the filter matrix as follows

[0034]

[0035] Among them, for k from 0 to T,

[0036]

[0037] Where k! represents the factorial of k.

[0038] Furthermore, this invention is based on the data collected in step two and the filter matrix constructed in step three. Solve the following system of matrix inequalities:

[0039]

[0040] Where (P,Y) are the variables to be solved, and the solution is denoted as (P... * ,Y * Construct the control gain matrix K ξ =U_Y * (P * )-1 .

[0041] Further, the application uses the control gain matrix K calculated in step four ξ constructing a state feedback based controller;

[0042]

[0043] wherein u(t) is the control input at time t, x(t) is the state of the unknown physical process, and z(t) is the state of the internal membrane system.

[0044] In a second aspect, another embodiment of the present application provides a noise data unknown system output adjustment device, comprising:

[0045] a sensor for acquiring the output state of the unknown linear system;

[0046] an internal membrane system, which takes the difference between the sensor output and the trajectory to be expectedly tracked as the input of the internal membrane system, and sends the current internal membrane state to the controller;

[0047] a controller for generating a control input according to the output state of the linear system and the state of the internal membrane system.

[0048] Advantages:

[0049] First, the noise data unknown system output adjustment method provided by the present application designs a state feedback output adjustment controller through the offline collected system input-state trajectory with noise. As can be seen, the present application does not need to pre-identify the physical process, and only needs to sample data to realize the output adjustment of the unknown system.

[0050] Second, the noise data unknown system output adjustment method provided by the present application does not need to collect interference and external reference signals in offline and online running stages, and only through the state data of the system, the output adjustment of the unknown system can be realized.

[0051] Third, in the present application, the output adjustment controller of the unknown system only needs to solve a low complexity linear matrix inequality offline, and does not need to solve optimization problems online. As can be seen, the present application has small calculation amount for obtaining the output adjustment control. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used 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.

[0053] Figure 1 A noise data unknown system output adjustment method principle architecture diagram provided by the present application.

[0054] Figure 2 An offline data collection principle architecture diagram of a noise data unknown system output adjustment method provided by the present application.

[0055] Figure 3 An output adjustment effect diagram of a robot motion model provided by the present application. DETAILED DESCRIPTION

[0056] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0057] 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 scope of protection of the present disclosure.

[0058] It should be noted that the 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 combined in various ways. For example, an apparatus can be implemented and / or a method practiced using any number of the aspects described herein. In addition, an apparatus can be implemented and / or a method practiced using other structure and / or functionality in addition to or other than one or more of the aspects described herein.

[0059] As shown in Figure 1 The unknown physical process, the sensor, the internal model system and the controller together constitute a closed loop system, where the unknown physical process is subject to external disturbance, and the output of the sensor is expected to follow the external reference signal. The method of the present application is designed for the internal model system and the controller in the closed loop system, which can achieve exponential convergence of the unknown physical process when the external disturbance and the external reference signal are 0, and can achieve zero bias tracking of the sensor output to the external reference signal when the external disturbance and the external reference signal are not 0. These two properties are collectively referred to as output regulation of the closed loop system.

[0060] The method of the present application is divided into three stages: internal model system design, offline data collection and online operation. As shown in Figure 2As shown, (1) the inner membrane system design: according to the evolution matrix of the external reference signal, the inner membrane system of the external reference signal is constructed, and the inner membrane system is connected with the physical process. (2) Offline data collection: the unknown physical process is not connected with the controller. The input sequence of the continuous excitation is applied to the unknown physical process for a period of time, and the state of the unknown physical process and the state of the inner membrane system are collected. By using the collected input, state data of the unknown physical process and the inner membrane system, the related parameters of the controller are obtained by solving a matrix inequality problem. The state feedback controller is constructed by using the parameters. Figure 1 As shown, the controller is connected with the unknown physical process, the state data sent by the unknown physical process and the inner membrane state sent by the inner 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 physical process to be output regulated is:

[0062] x (t + 1) = Ax (t) + Bu (t) + E w w (t)

[0063] y (t) = Cx (t) + F w w (t)

[0064] r (t + 1) = S r r (t)

[0065] w (t + 1) = S w w (t)

[0066] e (t) = y (t) - r (t)

[0067] Wherein, x (t), u (t), w (t), r (t), y (t), e (t) are respectively the state value of the unknown physical process at t time, the control input, the external disturbance, the expected tracking trajectory signal, the sensor output, and the tracking deviation. The state x (t) of the unknown physical process at t time is n x , the dimension of the control input u (t) is n u ; the dimension of the external disturbance w (t) is n w , the dimension of the expected tracking trajectory signal is n r , the dimension of the sensor output y (t) and the tracking deviation e (t) is n y ; the matrix A is an unknown real matrix of n x ×n x dimension, the matrix B is an unknown real matrix of n x ×n u dimension, and the matrix E w is n x ×n wunknown real matrix of dimension n y ×n x unknown real matrix of dimension n w ×n y unknown real matrix of dimension n w ×n w known real matrix of dimension n w ×n w known real matrix of dimension n r ×n r known real matrix of dimension n r known real matrix of dimension n w and S r All the real parts of the eigenvalues of S v are zero or positive; define n w = n r , and represent the external disturbance and the trajectory signal to be tracked as an external reference signal, let

[0068]

[0069] The closed loop system is represented as

[0070] x(t+1) = Ax(t) + Bu(t) + Ev(t)

[0071] e(t) = Cx(t) + Fv(t)

[0072] v(t+1) = Sv(t)

[0073] The goal of the output regulation of the closed loop system is to design the control input u(t) such that the physical process is exponentially stable when there is no external reference signal (i.e., v(t) is identically zero), and the tracking error e(t) tends to zero as time t tends to infinity for any system initial value x(0), v(0) when there is an external reference signal (i.e., v(t) is not zero).

[0074] The embodiment of the present application is an output regulation method for a system with unknown noise data, and the specific process is as follows:

[0075] S1, according to the evolution matrix S of the external reference signal, design the n y order inner membrane matrix pair (G1, G2) as follows

[0076]

[0077] where β is a constant matrix of dimension n β ×n β , the characteristic polynomial of which is the same as the minimal polynomial of the matrix S, blockdiag(β, …, β) represents a block diagonal matrix constructed by the sub-matrices on the diagonal line of β, and ny -tuple indicates that the block diagonal matrix has n y β sub-matrices. σ is an arbitrary chosen constant column vector of dimension n

[0078] S2, construct the internal model state z(t) of dimension n z z = n y β , the internal model system generating the internal model state is as follows

[0079] z(t+1) = G1z(t) + G2e(t) where, is the derivative of the internal model state z(t).

[0080] S3, in the data collection phase, the controller is not connected to the unknown physical process, the internal model system is connected to the sensor, and the unknown physical process has extra process noises d1(t) and d2(t) with the internal model system. In other words, the noise system for collecting data is

[0081]

[0082] v(t+1) = Sv(t)

[0083] where, is the state of the offline noise unknown physical system, of dimension n x ; is the offline noise internal model system, of dimension n z ; d1(t) is the state process noise, of dimension d2(t) is the internal model state process noise, of dimension and for any time t, we have where, is a bounded unknown non-negative constant, and ||d1(t)|| and ||d2(t)|| represent the two-norms of the noises d1(t) and d2(t), respectively.

[0084] Directly apply randomly generated control inputs to the noise unknown physical process in real time, and the sensor output is subtracted from the desired trajectory to be tracked as the input of the noise internal model system, and the state of the noise physical process and the state of the noise internal model system are collected. Specifically, let T = (n x + n z + 1)n u + n x + n z - 1, the input sequence composed of these T inputs is a sequence satisfying n​​​x +1 z +1 Endo state Using the applied control input, the collected noise physical process state and the collected noise endo system state, construct:

[0085] Input data matrix U - = [u(0) u(1)... u(T-1)];

[0086] Noise physical process state data matrix

[0087] Noise physical process state evolution data matrix

[0088] Noise endo system state data matrix

[0089] Noise endo system state evolution data matrix

[0090] And define as the augmented state data matrix, as the augmented state evolution data matrix.

[0091] S4. To handle noise in the collected data process, construct the following matrix using the data matrices constructed in step S3

[0092]

[0093] where I denotes an identity matrix of appropriate dimension, here dimension n ξ × n ξ , as an upper bound on the noise introduced by the system in the collected data phase, T is the length of the offline data in S3, matrix U - , Ξ - and Ξ + are the data matrices defined in S3, is the transpose of matrix , is the transpose of matrix Ξ + .

[0094] S5. To handle the position external reference signal v(t), construct a filter matrix of dimension n v × T from the external signal evolution matrix S

[0095] The specific steps are as follows: First, assume that the evolution matrix S consists of r distinct real eigenvalues ​​and s distinct pairs of complex eigenvalues, where λ1,…,λ2 are used. r Representing real characteristic roots, denoted by ρ1,…,ρ r The multiplicity of these eigenvalues ​​is represented by λ. r+i =β i +jφ i Let the i-th complex eigenvalue be represented by... Let β represent the conjugate complex eigenvalue of the i-th complex eigenvalue, where β i φ is the real part, j is the imaginary number marker, and φ is the imaginary number. i For the imaginary part, use k r+1 ,…,k r+s Represents a pair of complex characteristic roots The multiplicity of , let and Under these definitions, construct the filter matrix. as follows

[0096]

[0097] Among them, for k from 0 to T,

[0098]

[0099] Where, for a positive integer k, k! = k × (k-1) × … × 1 represents the factorial of k, and for a constant k, sin(k) represents the sine function of k, and cos(k) represents the cosine function of k.

[0100] S6. Using the data matrix constructed in S4 and the filter matrix constructed in S5, solve the following system of matrix inequalities.

[0101]

[0102] Where (P,Y) are the variables to be solved, and matrix P is n ξ ×n ξ A positive definite real symmetric matrix of dimension T, where matrix Y is T×n. ξ A matrix of dimension. The solution obtained is denoted as (P). * ,Y * Construct the control gain matrix K. ξ =U_Y * (P * ) -1 .

[0103] S7. Using the control gain matrix K obtained in S5 ξ Constructing a controller based on state feedback

[0104] S8. During the online operation phase, the unknown physical process sends its current state x(t) to the controller at every moment, while the endometrial system sends its current endometrial state z(t) to the controller. The controller, configured in S6, uses a state feedback-based controller to send the generated control input u(t) back to the unknown physical system, thereby achieving output regulation of the closed-loop system.

[0105] Secondly, another embodiment of this application provides an output adjustment device for a system with unknown noise data, comprising:

[0106] Sensors are used to acquire the output state of unknown linear systems;

[0107] The endometrial system takes the difference between the sensor output and the trajectory to be tracked as its input and sends the current endometrial state to the controller.

[0108] The controller is used to generate control inputs based on the output state of the linear system and the state of the endomembrane system.

[0109] like Figure 3 The diagram shows the effect of using the data-driven output control controller of this invention to run 50 steps on a robot system according to an embodiment. The corresponding system matrix is:

[0110] C = [IO,,

[0111] F = [-1 0 -1 0],

[0112] Where ω1 = π / 5 and ω2 = 1. Based on the intima principle mentioned in step S2, the intima matrices G1 and G2 are designed as follows:

[0113]

[0114] Set parameter T = 20, Since the S matrix has two pairs of eigenvalues ​​that are repeated (ω1, -ω1) and (ω2, -ω2), the filter matrix is ​​constructed according to step S5.

[0115]

[0116] In the figure, the solid line represents the trajectory signal to be tracked, the dashed line represents the system output, and the dotted line represents the tracking error. It can be seen that the system can track the external reference signal without deviation, thus achieving output regulation. This demonstrates the effectiveness of the invented method for regulating the output of an unknown system with noise data.

[0117] 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 method of adjusting the output of a system with unknown noise data, characterized by, The specific steps include: Step one, constructing evolution matrix S according to external reference signals, calculating inner membrane matrix pair (G1, G2), and constructing inner membrane state z(t) based on the inner membrane matrix pair (G1, G2); Step two, adding process noise on the inner membrane system and the unknown physical process linear system, connecting the linear system, the sensor and the inner membrane system, directly applying the control input to the linear system, making the difference between the sensor output and the expected tracking trajectory as the input of the inner membrane system, collecting the output data, and constructing the state matrix; Step three, constructing a filter matrix using an evolving matrix of external reference signals Step four, based on the data collected in step two and the filter matrix constructed in step three Computing the control gain matrix K ξ ; Step five, using the control gain matrix K calculated in step four ξ constructing a state feedback based controller; Step six, connecting the linear 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; The step one designs the inner membrane system z(t+1)=G1z(t)+G2e(t) according to the evolution matrix S of the external reference signal, wherein z(t) is the inner membrane state, e(t) is the tracking error, and (G1, G2) is the inner membrane matrix pair; where β is an n β × n β constant matrix whose characteristic polynomial is the same as the minimal polynomial of the matrix S, blockdiag(β,..., β) denotes a block diagonal matrix constructed with β as the diagonal sub-matrices, n y -tuple indicates that the block diagonal matrix has n y sub-matrices; σ is an n β × 1 constant column vector chosen arbitrarily. Adding process noise d1(t) and d2(t) on the inner membrane system and the unknown physical process linear system, then the system for collecting data composed of the linear system, the sensor and the inner membrane system is: v(t+1)=Sv(t) wherein, is the state of the unknown physical system with additive noise, u(t) is the control input of the unknown physical system, v(t) is an external reference signal, e(t) is a tracking error, is the state of the unknown physical system with additive noise, A, B, E, C, F are unknown real matrices, S is a known real matrix; The direct application of control input to the linear system is: at any sampling T time points, real-time random sequence input to the linear system process operation, T = (n x +n z +1)n u +n x +n z -1, T time points corresponding to the input sequence Satisfy n x +n z +1 order sustained incentive; Wherein, n x Indicates the state dimension of the linear system, n z Indicates the state dimension of the inner membrane system, n u Indicate the dimension of the control input; The step of constructing the state matrix includes: Input data matrix U - = [u(0) u(1)... u(T-1)]; Adding noise to a state data matrix of an unknown physical system Adding noise to a state evolution data matrix of an unknown physical system Adding noise to an internal membrane system state data matrix Adding noise to an inner membrane system state evolution data matrix Based on the constructed state matrix, an augmented state data matrix Ξ is constructed - and an augmented state evolution data matrix Ξ + ; And further calculating the matrices Ψ, Υ and ∑ as: Evolution matrix construction filter matrix using external reference signal Let the evolution matrix S consist of r distinct real eigenvalues ​​and s distinct pairs of complex eigenvalues, where λ1,…,λ2 are used to represent the evolution matrix S. r Representing real characteristic roots, denoted by ρ1,…,ρ r The multiplicity of these eigenvalues ​​is represented by λ. r+i =β i +jφ i Let the i-th complex eigenvalue be represented by... Let λ represent the i-th complex eigenvalue. r+i The conjugate complex eigenvalues, where β i φ is the real part, j is the imaginary number marker, and φ is the imaginary number. i For the imaginary part, use k r+1 ,…,k r+s Represents a pair of complex characteristic roots The multiplicity of , let and Constructing the filter matrix as follows Wherein, for k from 0 to T Wherein, k! represents the factorial of k; Based on the data collected in step two and the filter matrix constructed in step three Solving the following system of matrix inequality equations: Where (P,Y) are the variables to be solved, and the solution is denoted as (P... * ,Y * Construct the control gain matrix K ξ =U_Y * (P * ) -1 ; The control gain matrix K calculated in step four is used ξ constructing a state feedback based controller; Wherein, u(t) is the control input at t time, x(t) is the state of the unknown physical process, and z(t) is the state of the inner membrane system.

2. An apparatus for implementing the method of claim 1, wherein It includes: A sensor for acquiring the output state of the unknown linear system; An inner membrane system for making the difference between the sensor output and the expected tracking trajectory as the input of the inner membrane system, and sending the current inner membrane state to the controller; A controller for generating a control input according to the output state of the linear system and the state of the inner membrane system.

Images