A method for estimating the state of an unknown system based on noisy data

Abstract

The method provides a noise data-based unknown system state estimation method, and real-time of the method is divided into an offline stage and a current stage. In the offline stage, a continuous excitation input sequence is applied to the system, and corresponding states and outputs are recorded. By solving three low-complexity SDP problems, controller parameter design is performed by using the collected input-state-output trajectories. A feedback controller based on state estimation is constructed by using the obtained parameters. In the online operation stage, the system side transmits the output value at the current time to the controller side at each time, the controller system outputs state estimation and control input, and the control input is transmitted back to the system to stabilize the system. As can be seen, the application does not need prior system identification, only needs data sampling for controller design, so as to perform state estimation and stabilization on the unknown system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent manufacturing, and particularly relates to an unknown system state estimation method based on noise data. BACKGROUND

[0002] In order to promote the transformation and upgrading of traditional manufacturing industry to intelligent manufacturing, it is urgent to solve the problems in production line data acquisition, information processing, equipment management and control, operation scheduling, production plan management and decision-making. Considering the reasons that the complex production line information transmission pressure is large, and the confidentiality requirement of information is high, it is a common strategy to send only processed information in the network, and to recover the real information after receiving. This strategy can be modeled as remote state estimation of the system, that is, the state data of the system is recovered by using the collected system input and output data.

[0003] State estimation is widely used in control, monitoring and error diagnosis, and therefore has attracted much attention and has been widely studied by many scholars, such as the commonly used Kalman filtering method and the rolling horizon estimation based on model prediction. However, most of these state estimation methods are based on models, that is, a system model needs to be constructed in advance or system identification is performed by using the collected data. However, as the system size increases, the difficulty and computational complexity of system identification also increase exponentially. On the other hand, traditional state estimation methods are mostly for self-stabilizing systems, that is, only state estimation rules need to be designed without considering the stabilization problem of the system. However, for open-loop unstable systems, additional control rules are still needed for control.

[0004] In order to solve the above problems, data-driven methods have caused a research boom in recent years. This method directly learns the control law of the system from the data, thereby realizing the control of the system. However, most of the existing methods rely on reinforcement learning, which requires a large number of data sets for pre-training, and cannot achieve the expected control effect in the case of small data samples. At the same time, the noise in data acquisition should also be considered, so that the designed controller has a certain robustness to noise.

[0005] Therefore, there is an urgent need for a method that can directly obtain the control law and state estimation of the system based on the data of the noisy system, so that the unknown system can be stably operated, and the more accurate system state estimation value is obtained. SUMMARY

[0006] Therefore, the application provides a noise data-based unknown system state estimation method, which can construct a data-based state observer based on input, state and output data with noise collected offline, and can estimate the state of the system and perform state feedback control on the system by using the estimated state based on the input and output data of the system during online operation, without prior system identification.

[0007] To achieve the above-mentioned application purposes, the technical scheme of the application is as follows:

[0008] A noise data-based unknown system state estimation method, comprising the following steps:

[0009] S1, applying a control input to an unknown system, collecting the state and output values of the unknown system, and constructing an input data matrix U0, a 1-step state matrix X1, a 0-step state matrix X0 and an output data matrix Y0 according to the applied control input, the collected state and output values of the unknown system;

[0010] S2, solving three SDP optimization problems by using the input data matrix U0, the 1-step state matrix X1, the 0-step state matrix X0 and the output data matrix Y0 constructed in S1 to obtain a state-input pseudo-inverse matrix a control gain matrix K * and an observation gain matrix L * ;

[0011] S3, constructing a feedback controller based on state estimation by using the state-input pseudo-inverse matrix the control gain matrix K * and the observation gain matrix L * ;

[0012] S4, in the online operation stage, connecting the unknown system and the controller through a network, wherein the unknown system only sends the output at each time to the controller, the controller side configures the feedback controller based on state estimation designed in S3 to estimate the state of the unknown system at each time, and transmits the control input back to the unknown system through the network channel to stabilize the unknown system;

[0013] The design method of the control input is as follows:

[0014] Let N=(n x +1)n u +n x , and an input sequence composed of N inputs satisfies wherein for any matrix Z, λ (SVD(Z)) represents the minimum singular value of the matrix Z, is defined as

[0015]

[0016] The control input is brought into the unknown system to run, and the state and output values corresponding to the unknown system are collected An input data matrix is constructed by using the applied control input, the collected state and output values 1-step state data matrix 0-step state data matrix Output data matrix Input-state data matrix

[0017] In the step S2, the three SDPs are respectively a control gain matrix, a state-input pseudo-inverse matrix and an observation gain matrix, and the method for solving the control gain matrix optimization problem is:

[0018]

[0019] wherein (γ, Q, P, V, M1) are to-be-solved variables, the scalar γ is a cost gain, the matrix Q is an N×n x matrix, the matrix P is an n x ×n x positive definite symmetric real matrix, the matrix V is an n u ×n u matrix, the matrix M1 is N×N, the matrix I is a unit matrix with appropriate dimensions, α1>0 is a process noise adjustment parameter, the matrices W x ,W u are system control performance adjustment parameter matrices, tr(T) represents the trace of the matrix T for any matrix T, and the obtained optimal value is denoted as , and the control gain matrix K * = U0Q * (P * ) -1 is constructed.

[0020] The method for solving the state-input pseudo-inverse matrix optimization problem is:

[0021]

[0022] wherein (ρ, M2, D1, D2) are to-be-solved variables, the scalar ρ is a cost gain, the matrix M2 is an n x ×n x matrix, the matrix D1 is an N×n x matrix, the matrix D2 is an N×n u matrix, and the obtained optimal value is denoted as The state-input pseudo-inverse matrix is constructed.

[0023] The method for solving the observation gain matrix optimization problem is as follows:

[0024]

[0025] Where (∈,Π,Σ,Υ) are the variables to be solved, scalar ∈ represents the cost gain, and matrix Π is an n-dimensional matrix. x ×n y The matrix Σ is n x ×n x The matrix, where matrix Y is n y ×n y The matrix N, where α2 > 0 represents the transmission noise adjustment parameter. x N y This is the system estimation accuracy adjustment parameter matrix, and the obtained optimal value is denoted as (∈ * ,Π * ,Σ * ,Υ * Construct the observation gain matrix L. * =(Σ * ) -1 Π * ;

[0026] In step S3, the matrix K obtained in S2 is used. * ,L * , The feedback controller based on state estimation is constructed as follows:

[0027]

[0028]

[0029] in y(t) and u(t) are the estimated state of the system, the system output, and the system control input, respectively.

[0030] Beneficial effects

[0031] This invention provides a method for estimating the state of an unknown system based on noise data. It designs a state-estimation-based controller using offline collected system input-state-output trajectories. During online operation, a relatively accurate system state estimate and a control input capable of stabilizing the unknown system can be obtained solely from the system's output data. Therefore, this invention does not require prior system identification; only data sampling is needed for state estimation and closed-loop control of an unknown system.

[0032] In the method, the state estimation controller design of the unknown system only needs to solve three low complexity SDPs offline, and no optimization problem needs to be solved in online operation, so the calculation amount required for obtaining the state estimation and the control input is small.

[0033] In the method, the unknown system receives bounded unknown noise, and the proposed method can guarantee the robustness of the system to the noise.

[0034] The method provides an unknown system state estimation method based on noise data, and the real-time of the method is divided into an offline stage and an online stage. In the offline stage, a continuous excitation input sequence is applied to the system, and the corresponding state and output values are recorded. By solving three low complexity SDP problems, the controller parameters are designed by using the collected input-state-output trajectories. The feedback controller based on state estimation is constructed by using the obtained parameters. In the online operation stage, the output of the system side is transmitted to the controller side at each moment, the state estimation and the control input are output by the controller system, and the control input is transmitted back to the system to stabilize the system. Therefore, the method does not need to pre-identify the system, only needs to sample the data for controller design, so as to estimate and stabilize the unknown system. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 It is a structural diagram of the system;

[0036] Figure 2 It is a flowchart of the method of the application;

[0037] Figure 3 It is a state estimation and control effect diagram of the nuclear reactor embodiment of the application. DETAILED DESCRIPTION

[0038] The application will be described in detail below with reference to the drawings and embodiments.

[0039] As shown in the prior art, Figure 1 In the closed-loop control system designed for the unknown system, the system and the controller are included. The method of the application is designed for the controller of the unknown system, can estimate the state of the system, and can stabilize the system subjected to unknown noise.

[0040] The method of the application is divided into two stages of offline data collection and online operation. In the offline operation stage, the system does not transmit data with the controller, a continuous excitation input sequence is applied to the system, and the state and output sequence of the system are collected. By solving three SDP problems, the related parameters of the controller are obtained by using the collected input, state and output data. The controller based on state estimation is constructed by using the parameters;

[0041] In the online running stage, the controller side collects the output sent by the system side at each moment, obtains the state estimation quantity at the current moment through the state estimation-based controller, and sends the generated control input to the system side to control the system by using the state feedback control law.

[0042] The dynamic equation of the unknown system to be stabilized is:

[0043] x(t+1)=Ax(t)+Bu(t)+w(t)

[0044] y(t)=Cx(t)+V(t)

[0045] where x(t), u(t), y(t), w(t), v(t) are the state value, input value, output value, process noise and transmission noise of the unknown system at time t respectively, the state dimension of the system is n x , the dimension of the input is n u , and the dimension of the output is n y . The process and transmission noise of the system are random bounded, that is, for any time t, it has where is a bounded unknown constant. The matrix A is an n x ×n x dimensional real matrix, the matrix B is an n x ×n u dimensional real matrix, and the matrix C is an n y ×n x dimensional real matrix. These matrices are unknown, the matrix pair (A, B) is controllable, and (C, A) is observable.

[0046] As shown in Figure 2 , based on the above description, the present application provides a state estimation method for an unknown system based on noise data, and the specific steps are as follows:

[0047] S1, apply a control input to the unknown system, and collect the state and output values of the unknown system. Let N=(n x +1)n u +n x , an input sequence composed of N inputs satisfies where for any matrix Z, λ (Z) represents the smallest singular value of the matrix Z, defined as

[0048]

[0049] Bring the input into the system for running, and collect the state and output Constructing an input data matrix using the applied control inputs, collected states and output values 1-step state data matrix 0-step state data matrix Output data matrix Y0= Input-state data matrix

[0050] S2, solve three SDP using the data matrix constructed in S1, which are control gain matrix, state-input pseudo-inverse matrix and observation gain matrix, the method for solving control gain matrix optimization problem is:

[0051]

[0052] where (γ, Q, P, V, M1) are variables to be solved, scalar γ is cost gain, matrix Q is N x n x matrix, matrix P is n x x n x dimension positive definite symmetric real matrix, matrix V is n u x n u matrix, matrix M1 is N x N, matrix I is a unit matrix with appropriate dimension, α1>0 is process noise adjustment parameter, matrix W x ,W u is system control performance adjustment parameter matrix. For any matrix T, tr(T) represents the trace of matrix T. The optimal value obtained is denoted as Construct control gain matrix K * = U0Q * (P * ) -1 .

[0053] The method for solving state-input pseudo-inverse matrix optimization problem is:

[0054]

[0055] where (ρ, M2, D1, D2) are variables to be solved, scalar ρ is cost gain, matrix M2 is n x x n x matrix, matrix D1 is N x n x matrix, matrix D2 is N x n u matrix. The optimal value obtained is denoted as Construct state-input pseudo-inverse matrix

[0056] The method for solving observation gain matrix optimization problem is:

[0057]

[0058] Where (∈,Π,Σ,Υ) are the variables to be solved, scalar ∈ represents the cost gain, and matrix Π is an n-dimensional matrix. x ×n y The matrix Σ is n x ×n x The matrix, where matrix Y is n y ×n y The matrix N, where α2 > 0 represents the transmission noise adjustment parameter. x N y This is the system estimation accuracy adjustment parameter matrix. The optimal value obtained is denoted as (∈ * ,Π * ,Σ * ,Υ * Construct the observation gain matrix L. * =(Σ * ) -1 Π * .

[0059] S3. Using the matrix K obtained in S2 * ,L * , Constructing a feedback controller based on state estimation

[0060]

[0061]

[0062] in y(t) and u(t) are the estimated state of the system, the system output, and the system control input, respectively.

[0063] S4, the online operation phase, connects the unknown system and the controller via a network. The system only sends the output y(t) at each time step to the controller. The controller side is configured with the state estimation-based feedback controller designed in S3 to estimate the state of the system at each time step. Furthermore, the control input u(t) is transmitted back to the system through the network channel to stabilize the unknown system.

[0064] It should be noted that the parameters in SDP are related to the maximum values ​​of the process noise and transmission noise of the unknown system during the selection process. The higher the noise, the larger the values ​​of α1 and α2 should be to ensure the solvability of SDP. However, if these two values ​​are chosen too large, the system's settling time will increase, and the accuracy of the system's state estimation will decrease.

[0065] like Figure 3 The image shows the effect of running an embodiment on a nuclear reactor system for 100 unit times. The corresponding system matrix is:

[0066]

[0067]

[0068] Set parameter N=15, process noise and random noise are maximum value in -0.03 to 0.03 between random sequence, control performance matrix is set as W x =I, W u =0.1I, estimation accuracy matrix is set as N x =0.03, N y =0.03, select α1=0.1, α2=0.5.Simulation results in the horizontal coordinate represents the step length of time, simulation results show that the effectiveness of the application based on noise data unknown system state estimation method.

[0069] To sum up, the above is only the preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for estimating the state of an unknown system based on noise data, characterized in that... The steps include: S1. Apply control input to the unknown system, collect the state and output values ​​of the unknown system, and construct an input data matrix, a 1-step state matrix, a 0-step state matrix, and an output data matrix based on the applied control input and the collected state and output values ​​of the unknown system. S2. Using the input data matrix, 1-step state matrix, 0-step state matrix and output data matrix constructed in step S1, solve the SDP optimization problem to obtain the state-input pseudo-inverse matrix, control gain matrix and observation gain matrix. S3. Construct a feedback controller based on state estimation using the state-input pseudo-inverse matrix, control gain matrix, and observation gain matrix obtained in step S2. S4, Online Operation Phase: The unknown system and the controller are connected via a network. The unknown system sends its output at each moment to the controller. The state estimation-based feedback controller designed in step S3 is used to estimate the state of the unknown system at each moment. In step S1, the design method for the control input is as follows: make ,Depend on The input sequence consisting of 1 input satisfy For any matrix Z, Represents the minimum singular value of matrix Z. Defined as In step S1, the method for collecting the state and output values ​​of the unknown system is as follows: The control input... Run the system in an unknown system and collect the state of the corresponding unknown system. and output value .

2. The method for estimating the state of an unknown system based on noise data according to claim 1, characterized in that: In step S1, the input data matrix constructed is: ; The state matrix for step 1 is: ; The zero-step state matrix is: ; The output data matrix is: .

3. The method for estimating the state of an unknown system based on noise data according to claim 2, characterized in that: In step S2, solving the SDP optimization problem means solving it as a control gain matrix optimization problem, a state-input pseudo-inverse matrix optimization problem, and an observation gain matrix optimization problem.

4. The method for estimating the state of an unknown system based on noise data according to claim 3, characterized in that: The method for solving the control gain matrix optimization problem is as follows: in For the variable to be solved, scalar The cost gain is given by matrix Q. The matrix P is A positive definite symmetric real matrix of dimension V, where matrix V is The matrix, the matrix yes The matrix For an identity matrix of appropriate dimensions, For process noise adjustment parameters, matrix It is the system control performance adjustment parameter matrix. For any matrix... , Representation matrix The trace is used to determine the optimal value obtained. Construct the control gain matrix .

5. The method for estimating the state of an unknown system based on noise data according to claim 4, characterized in that: The method for solving the state-input pseudo-inverse matrix optimization problem is as follows: in For the variable to be solved, scalar For cost gain, matrix for The matrix, the matrix for The matrix, the matrix for The matrix is ​​used to denot the optimal value obtained. Constructing the state-input pseudo-inverse matrix .

6. The method for estimating the state of an unknown system based on noise data according to claim 5, characterized in that: The method for solving the observation gain matrix optimization problem is as follows: in For the variable to be solved, scalar For cost gain, matrix for The matrix, the matrix for The matrix, the matrix for The matrix, To transmit noise adjustment parameters, the matrix This is the system estimation accuracy adjustment parameter matrix, and the optimal value obtained is denoted as... Construct the observation gain matrix .

7. The method for estimating the state of an unknown system based on noise data according to claim 6, characterized in that: In step S3, the matrix is ​​used , , The feedback controller based on state estimation is constructed as follows: in , , These are the estimated state of the system, the system output, and the system control input, respectively.

8. The method for estimating the state of an unknown system based on noise data according to claim 3, characterized in that: In step S4, the control input is transmitted back to the unknown system through the network channel to calm the unknown system.

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