Adaptive parameter estimation method and system based on input and output data of linear time-varying system

Abstract

The present invention discloses an adaptive parameter estimation method and system based on input and output data of a linear time-varying system. The method comprises: establishing a linear time-varying system with unknown parameters; filtering the linear time-varying system with unknown parameters to obtain filtering variables; designing an integral auxiliary vector; reconstructing the linear time-varying system based on the filtering variables and the integral auxiliary vector; establishing a virtual variable and an augmented unknown parameter column vector estimation error relationship based on the reconstructed linear time-varying system; constructing auxiliary variables based on the virtual variable and the augmented unknown parameter column vector estimation error relationship; constructing a cost function based on the auxiliary variables; and obtaining an estimated value of the unknown parameter based on the cost function. The present invention introduces an adaptive learning optimal gain method to construct a cost function, which is then used to obtain an estimated value of the unknown parameter. Compared with the traditional gradient method and the method without the optimal gain, the present invention has a high accuracy rate and an optimal convergence performance.

Description

Technical Field

[0001] The invention relates to an adaptive parameter estimation method and system based on input and output data of a linear time-varying system, and belongs to the field of adaptive parameter estimation. Background Art

[0002] Adaptive control has been developed for decades. It has attracted extensive attention from industry and academia due to its ability to effectively handle system parameter uncertainty, and has triggered a large number of studies. The core technology of adaptive control lies in adaptive parameter estimation, which enables online adjustment of the adaptive controller through its ability to accurately estimate the unknown parameters of the controlled system.

[0003] There are a lot of research results on adaptive parameter estimation methods. Its early work is based on the gradient descent algorithm and the least squares method. The algorithm updates the unknown parameters by minimizing the observation / prediction error generated by the observer / predictor. However, this type of parameter estimation method has a slow convergence speed and poor robustness to noise and interference. In the subsequent development, Narendra and Ioannou successively proposed the σ-correction method and the e-correction method to ensure the robustness of the parameter estimation algorithm. Although these correction methods make the parameter estimation error bounded, they also lead to the parameter error can only converge to the residual set, but cannot converge to zero, that is, the parameter estimation cannot converge to the true value. In the subsequent development, researchers have proposed a large number of parameter estimation algorithms to improve the convergence performance and application scope of parameter estimation. An adaptive finite time parameter estimation algorithm is proposed to ensure the convergence time of parameter estimation. A parameter estimation error extraction method based on filtering operation is used in the adaptive parameter estimation algorithm to avoid directly measuring the derivative of the system state with respect to time. However, the above adaptive parameter estimation algorithm cannot obtain the optimal convergence performance (i.e., minimizing the predefined estimation error cost function).

[0004] Furthermore, the current design of adaptive laws is mostly aimed at the steady-state parameters of the system, that is, the system parameters will not change accordingly with the changes in the working environment and the operating time of the equipment. However, under actual working conditions, the temperature and humidity of the working environment, as well as the use time of the equipment, will induce changes in system parameters, thereby generating time-varying parameters (for example, in the hydraulic system, the change in leakage, the change in hydraulic oil viscosity caused by temperature, and the change in the position of the hydraulic rod cause the change in parameters). Some adaptive laws with unknown time-varying parameters use the polynomial expansion method, which will generate a large amount of calculation. In addition, since the polynomial expansion transforms the estimation problem of unknown time-varying parameters into the problem of estimating steady-state parameters, this method will have problems such as underfitting. On the other hand, the construction of existing adaptive laws mostly depends on the full state of the system. However, this requirement is usually difficult to achieve in actual working conditions. Because the internal states of most systems cannot be directly measured (for example, in some application scenarios, it is impossible to measure all the state information of the hydraulic system), if additional sensors are installed, it will inevitably cause the engineering cost to rise. Moreover, as complex electromechanical systems develop towards smaller, more precise, and more powerful performance, installing additional sensors will inevitably increase the size of the mechanical structure under limited mechanical structure size, which is difficult to meet the current development trend of electromechanical systems. Therefore, without adding additional system sensors, using the limited input and output data of the system, for the time-varying parameters of the system, designing a time-varying parameter adaptive law, accurately obtaining the unknown time-varying parameters of the system and achieving the optimal convergence performance, it has important theoretical reference value and practical engineering significance for further promoting the application of adaptive control in actual industrial systems and obtaining the unknown parameters inside the electromechanical system. Summary of the invention

[0005] The present invention provides an adaptive parameter estimation method based on linear time-varying system input and output data, which is used for estimating system time-varying parameters based on the linear time-varying system input and output data that varies with time.

[0006] The technical solution of the present invention is: an adaptive parameter estimation method based on input and output data of a linear time-varying system, comprising: establishing a linear time-varying system containing unknown parameters; performing a filtering operation on the linear time-varying system containing unknown parameters to obtain filtering variables; designing an integral auxiliary vector; reconstructing the linear time-varying system based on the filtering variables and the integral auxiliary vector; establishing a relationship between the estimation error of a virtual variable and an augmented unknown parameter column vector based on the reconstructed linear time-varying system; constructing auxiliary variables based on the relationship between the estimation error of a virtual variable and an augmented unknown parameter column vector; constructing a cost function based on the auxiliary variables; and obtaining an estimated value of the unknown parameter based on the cost function.

[0007] The establishment of a linear time-varying system with unknown parameters comprises:

[0008] Set up an initial linear time-varying system with unknown time-varying parameters:

[0009]

[0010] y(t)=C T x(t)

[0011] Where x(t) is the system state and is an n-dimensional column vector, is the derivative of the system state x(t); u(t) and y(t) are the input and output of the system respectively; A(t) is the system matrix, B(t) is the control matrix, and C is the output matrix;

[0012] Transform the initial linear time-varying system:

[0013]

[0014] y(t)=C T x(t)

[0015] Among them, A k =A0-KC T is the gain matrix; is the filter parameter vector, and k i >0, is a normal number, i=1,…,n; A0 is the intermediate matrix, θ1(t) and θ2(t) are unknown parameter vectors.

[0016] The system matrix, control matrix, and output matrix are expressed as follows:

[0017]

[0018] The intermediate matrix and unknown parameter vector are expressed as follows:

[0019]

[0020] Among them, a i (t), b i (t) is the unknown parameter; t is time; I n-1 is the n-1 dimensional identity matrix.

[0021] The α i (t), β i (t) are all unknown time-varying parameters; or any unknown parameter is an unknown time-varying parameter: that is, α i When (t) is an unknown time-varying parameter, then β i (t) is the unknown constant parameter, β i When (t) is an unknown time-varying parameter, α i (t) is an unknown constant parameter.

[0022] The integral auxiliary vector is:

[0023]

[0024] in, is the integration variable, is the derivative of the unknown parameter vector θ1(t) with respect to time t; is the derivative of the unknown parameter vector θ2(t) with respect to time t.

[0025] The linear time-varying system is reconstructed based on the filtering variables and the integral auxiliary vector, and the expression is:

[0026]

[0027] Where x(t) is the system state and is an n-dimensional column vector; P(t) and Q(t) are filter variables based on the system output y(t), W(t) is a filter variable based on the system input u(t), P(t) is an n-dimensional column vector, Q(t) and W(t) are n×n-dimensional matrices; θ1(t) and θ2(t) are unknown parameter vectors; is the auxiliary vector of integration.

[0028] The linear time-varying system reconstructed according to the present invention is used to establish the error relationship between the virtual variable and the augmented unknown parameter column vector:

[0029]

[0030] The auxiliary variable is constructed based on the estimated error relationship between the virtual variable and the augmented unknown parameter column vector.

[0031]

[0032] Among them, S(t) is a dummy variable; E(t) = x(t) - P(t) is an intermediate variable; is an n×2n-dimensional augmented regression matrix; x(t) is the system state and is an n-dimensional column vector; P(t) and Q(t) are filter variables based on the system output y(t), W(t) is a filter variable based on the system input u(t), P(t) is an n-dimensional column vector, Q(t) and W(t) are n×n-dimensional matrices; is the estimated vector of the augmented unknown parameter column vector Θ(t), is the estimation error of the augmented unknown parameter column vector Θ(t); is the integral auxiliary vector; C is the output matrix.

[0033] Based on the auxiliary variables, the cost function is constructed:

[0034]

[0035] in, is an auxiliary variable; m is a normal number; l is a normal number; is a 2n×2n dimensional positive definite diagonal matrix; express The initial value of is the estimation vector of the augmented unknown parameter column vector Θ(t).

[0036] The method of obtaining the estimated value of the unknown parameter based on the cost function includes: obtaining the expression of the augmented unknown parameter column vector estimation vector and the optimal gain based on the cost function; obtaining the adaptive law of the augmented unknown parameter column vector based on the expression of the augmented unknown parameter column vector estimation vector and the optimal gain; obtaining the estimated value of the unknown parameter based on the adaptive law of the augmented unknown parameter column vector.

[0037] The step of obtaining an estimated value of an unknown parameter based on a cost function includes:

[0038] Constructing the cost function Partial derivative relation Obtain the expression of the augmented unknown parameter column vector estimation vector and the optimal gain;

[0039] Derivative the expression of the augmented unknown parameter column vector estimation vector, and obtain the adaptive law of the augmented unknown parameter column vector:

[0040]

[0041] Integrate the adaptive law of the augmented unknown parameter column vector to obtain the estimated value of the augmented unknown parameter column vector Θ(t) Thus, the estimated values ​​of the unknown parameter vectors θ1(t) and θ2(t) required for the linear time-varying system can be obtained. and Where m is a positive constant; represents the optimal gain, is a 2n×2n dimensional positive definite diagonal matrix, l is a positive constant, is the n×2n-dimensional augmented regression matrix, C is the output matrix, is an auxiliary variable.

[0042] According to another aspect of the present invention, there is also provided an adaptive parameter estimation based on the input and output data of a linear time-varying system, comprising: a first establishment module for establishing a linear time-varying system containing unknown parameters; a first acquisition module for performing a filtering operation on the linear time-varying system containing unknown parameters to obtain filtering variables; a design module for designing an integral auxiliary vector; a reconstruction module for reconstructing the linear time-varying system based on the filtering variables and the integral auxiliary vector; a second establishment module for establishing an estimation error relationship between virtual variables and augmented unknown parameter column vectors based on the reconstructed linear time-varying system; a first construction module for constructing auxiliary variables based on the estimation error relationship between virtual variables and augmented unknown parameter column vectors; a second construction module for constructing a cost function based on the auxiliary variables; and a second acquisition module for obtaining estimated values ​​of the unknown parameters based on the cost function.

[0043] The beneficial effects of the present invention are:

[0044] 1. The present invention only uses system input data and output data to construct an adaptive law, which gets rid of the dependence on the full state of the system. This enables the present invention to achieve parameter estimation of unknown parameters of the hydraulic system in application scenarios where the full state information of the hydraulic system cannot be collected, and the estimation method has the advantage of being simple to implement.

[0045] 2. The adaptive law proposed in the present invention is constructed using parameter estimation error information, which can further improve the accuracy of time-varying parameter estimation and thus improve system control performance.

[0046] 3. In the adaptive law proposed in the present invention, the adaptive learning gain Γ is derived from the optimal cost function, which gets rid of the artificial parameter selection, making the present invention easier to use.

[0047] 4. The adaptive learning gain Γ designed in the present invention can be effectively adjusted according to the size of the regression vector, which effectively suppresses the deterioration of the time-varying parameter estimation performance caused by the excessive amplitude of the regression vector, and enables the parameter estimation of the unknown time-varying parameters of the hydraulic system caused by leakage, temperature, hydraulic rod displacement and other reasons of the present invention to have optimal convergence performance.

[0048] In summary, the present invention introduces an adaptive learning optimal gain method to construct a cost function, which is then used to obtain an estimated value of an unknown parameter. Compared with the traditional gradient method and the method without the optimal gain, the present invention has high accuracy and optimal convergence performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flowchart for the implementation of the adaptive time-varying parameter estimation method based on system input and output data provided by the present invention

[0050] Figure 2This is a diagram showing the effect of parameter estimation using the method proposed in Example 1 of the present invention;

[0051] Figure 3 This is a parameter estimation effect diagram without the optimal learning gain Γ in Application Example 1 of the present invention;

[0052] Figure 4 This is a diagram showing the effect of parameter estimation using the traditional gradient method in Application Example 1 of the present invention;

[0053] Figure 5 Parameter estimation error diagram of application example 1 of the present invention;

[0054] Figure 6 This is a diagram showing the estimation effect of unknown parameters of a hydraulic actuator according to the second embodiment of the present invention;

[0055] Figure 7 This is a diagram showing the effect of estimating unknown parameters of a hydraulic actuator without the optimal learning gain algorithm in Application Example 2 of the present invention;

[0056] Figure 8 This is a diagram showing the effect of estimating unknown parameters of a hydraulic actuator using the traditional gradient method in Application Example 2 of the present invention;

[0057] Fig. 9 This is a comparison diagram of errors of estimating unknown parameters of a hydraulic actuator using three methods in Application Example 2 of the present invention.

[0058] Fig.10 This is a comparison diagram of the errors of parameter estimation of the unknown time-varying parameter a1 using three methods in Application Example 2 of the present invention. DETAILED DESCRIPTION

[0059] The invention is further described below in conjunction with the accompanying drawings and embodiments, but the content of the invention is not limited to the scope of the embodiments.

[0060] Example 1: Figure 1-5 As shown, an adaptive parameter estimation method based on the input and output data of a linear time-varying system includes: establishing a linear time-varying system with unknown parameters; performing a filtering operation on the linear time-varying system with unknown parameters to obtain filtering variables; designing an integral auxiliary vector; reconstructing the linear time-varying system based on the filtering variables and the integral auxiliary vector; establishing a relationship between the estimation error of a dummy variable and an augmented unknown parameter column vector based on the reconstructed linear time-varying system; constructing auxiliary variables based on the relationship between the estimation error of a dummy variable and an augmented unknown parameter column vector; constructing a cost function based on the auxiliary variables; and obtaining an estimated value of the unknown parameter based on the cost function.

[0061] Furthermore, the present invention provides optional specific implementation modes as follows:

[0062] Step 1. Establish a second-order linear time-varying system with unknown time-varying parameters:

[0063]

[0064] Where x1(t) and x2(t) are the system states; u(t) and y(t) are the input and output of the system respectively; the unknown time-varying parameters are a1(t) = -5 + sin(t), a2(t) = -25 + 8 sin(2t), b1(t) = -1 + 0.1 sin(t), b2(t) = 2 + 2 sin(t);

[0065] The linear time-varying system is transformed into the following form:

[0066]

[0067] where x(t) = [x1(t), x2(t)] T is the system state vector, A k =A0-KC T is the gain matrix, K = [100,500] T is a filtering parameter vector composed of positive numbers, the intermediate matrix A0, vector C and unknown parameter vectors θ1(t) and θ2(t) are respectively:

[0068]

[0069] Step 2: For the linear time-varying system, select its input u(t) and output y(t) to perform the following K filtering operation:

[0070]

[0071] Among them, P(t) and Q(t) are filter variables based on the system output y(t), W(t) is the filter variable based on the system input u(t), P(t) is an n-dimensional column vector, Q(t) and W(t) are n×n-dimensional matrices; P(0), Q(0), and W(0) are the initial values ​​of the filter variables P(t), Q(t), and W(t), respectively. n is the n-dimensional identity matrix;

[0072] Step 3, design the following integral auxiliary variables:

[0073]

[0074] in, is the integration variable, and are the derivatives of the unknown time-varying parameter vectors θ1(t) and θ2(t) with respect to time t;

[0075] Step 4. According to formula (3) and formula (4), a new system expression is designed as follows:

[0076]

[0077] To verify that the reconstructed system formula (5) has the same expression as the original system formula (2), the system is differentiated to obtain: It can be seen from the formula that using the filter variables P(t), Q(t), W(t) and the integral auxiliary variable The reconstructed system formula (5) has the same expression as the original system formula (2);

[0078] Step 5. Let E(t) = x(t) - P(t), and take the derivative of the variable E(t):

[0079]

[0080] Integrate both ends of equation (6) to obtain:

[0081]

[0082] in, and are all augmented regression matrices of n×2n dimensions, Θ(t)=[θ1 T (t),θ2 T (t)] T is a 2n-dimensional augmented unknown parameter column vector;

[0083] Step 6. Define the following virtual variable S(t) to extract the unknown time-varying parameter error information:

[0084]

[0085] in, is the estimated value of the augmented unknown parameter column vector Θ(t), is the estimation error of the augmented unknown time-varying parameter column vector Θ(t);

[0086] Step 7, in the formula Multiply both sides by vector C T , construct the following auxiliary variables

[0087]

[0088] Step 8. In order to ensure that the adaptive law can be applied to different time-varying parameters and eliminate the problem of weakened parameter estimation caused by excessive amplitude of the regression vector, the optimal control idea is introduced to construct the following cost function:

[0089]

[0090] Among them, m = 1 is used to adjust the learning rate of the adaptive law, and the forgetting factor l = 50 is used to ensure that the cost function is bounded. is an identity matrix;

[0091] Step 9: For formula (10), Find the partial derivative, that is We can get:

[0092]

[0093] in,

[0094] Step 10. Derivative equation (11) gives the adaptive law of time-varying parameters:

[0095]

[0096] Step 11. Integrate equation (12) to obtain the estimated value of the augmented unknown time-varying parameter vector Θ(t) Thus, the estimated values ​​of the unknown time-varying parameters θ1(t) and θ2(t) required by the original system can be obtained. and

[0097] According to the above implementation process, the unknown time-varying parameters of the system are estimated online using only the input and output data of the system, and simulated in Matlab software to verify the engineering application of the present invention. The simulation results of this case can be obtained as follows Figure 2-Figure 5 . Figure 2 The figure shows the estimation effect of the proposed method for unknown time-varying parameters. Figure 3 This is the estimated effect diagram of the unknown time-varying parameters without the optimal learning gain algorithm, that is, Figure 4 This is a diagram showing the estimation effect of the traditional gradient method for unknown time-varying parameters. Figure 5 This is a comparison chart of the errors of the above three methods for estimating unknown time-varying parameters. Figure 2 and Figure 3 The comparison shows that compared with the adaptive law of traditional learning gain, the adaptive law using optimal learning gain still has better performance when the regression vector amplitude changes greatly. Figure 2 and Figure 4 By comparison, it can be seen that compared with the traditional gradient method, the adaptive law constructed with unknown parameter errors makes the parameter estimation algorithm converge more accurately. Figure 5It can be seen that the transient and steady-state performances of the method proposed in the present invention, such as convergence speed, overshoot, and convergence error, are better than those of the method without the optimal gain Γ and the traditional gradient method. The simulation of the above implementation case shows that the parameter estimation method proposed in the present invention has better performance in estimating unknown time-varying parameters under the premise of getting rid of the dependence on the internal state of the system.

[0098] It should be noted that in actual engineering applications, there are many mathematical models of electromechanical systems that can be described as a type of linear time-varying system with unknown time-varying parameters, for example, the viscosity parameter of the hydraulic oil in the hydraulic servo system will change with the increase of the oil temperature, and the length parameter of the mechanical arm in the flexible mechanical arm system will change with the change of the air pressure, etc. Further, an optional specific implementation process is given as Example 2.

[0099] Example 2: Figure 1 , Figure 6-10 As shown, for a double-rod hydraulic actuator system with an unknown and time-varying hydraulic oil viscosity coefficient, the above-mentioned adaptive parameter estimation method based on input and output data of a linear time-varying system is applied to the system. The specific steps of the method are as follows:

[0100] Step 1. Establish the following hydraulic actuator system model:

[0101]

[0102] Where x1(t), x2(t), x3(t) are the system states; u(t) = 7sin(3t) + sin(20t)V is the input voltage of the system, y(t) is the output displacement of the system; k s =15000N / m is the total spring stiffness coefficient, b(t)=700e -0.02t N / (m / s) is the viscosity coefficient of the hydraulic oil, m1=80kg is the load mass, β=700Mpa is the effective bulk elastic modulus of the hydraulic oil, A=3.2656×10 -4 m 2 is the effective area of ​​the piston, V1=6.5312×10 -5 m 3 is the volume of the hydraulic cylinder cavity, ω=0.0001(m 3 / s) / V1 is the input conversion efficiency.

[0103] According to the coordinate conversion The system is written as follows:

[0104]

[0105] in, is the system state vector after coordinate transformation, x(t)=[x1(t),x2(t),x3(t)] T ; T(t) is the coordinate transformation matrix, is the system output, A k =A0-KC T is the gain matrix, K = [10,500,1000] T is a filter parameter vector composed of positive constants, Ψ(t) is a matrix about input u(t) and output y(t), θ(t) is a column vector of unknown system parameters; A0, C and the conversion matrix T(t) are:

[0106]

[0107] The matrix Ψ(t) and the unknown parameter column vector θ(t) are:

[0108]

[0109] and

[0110] Step 2: For the system, select its input u(t) and output y(t) for the following filtering operations:

[0111]

[0112] Where P(t) is the filter variable based on the system input y(t), Q(t) is the filter variable based on the matrix Ψ(t), P(t) is an n-dimensional nematic quantity, and Q(t) is an n×n-dimensional matrix;

[0113] Step 3, design the following integral auxiliary variables:

[0114]

[0115] in, is the integration variable, is the derivative of the unknown time-varying parameter vector θ(t) with respect to time t;

[0116] Step 4. According to formula (15) and formula (16), a new system expression is designed as follows:

[0117]

[0118] Step 5. Let E(t) = x(t) - P(t), and take the derivative of the variable E(t):

[0119]

[0120] Integrate both ends of equation (18) to obtain:

[0121]

[0122] in, and They are all n×n dimensional regression matrices, Θ(t)=θ(t) is the n-dimensional unknown time-varying parameter column vector;

[0123] Step 6. Define the following virtual variable S(t) to extract the unknown time-varying parameter error information:

[0124]

[0125] in, To augment the estimate of the unknown time-varying parameter vector Θ(t), is the estimation error of the augmented unknown time-varying parameter vector Θ(t);

[0126] Step 7, in formula (20) Multiply both sides by vector C T , construct the following auxiliary variables

[0127]

[0128] Step 8. In order to ensure that the adaptive law can be applied to different time-varying parameters and eliminate the problem of weakened parameter estimation caused by excessive amplitude of the regression vector, the optimal control idea is introduced to construct the following cost function:

[0129]

[0130] Among them, m = 1 is used to adjust the learning rate of the adaptive law, and the forgetting factor l = 5 is used to ensure that the cost function is bounded. is an identity matrix;

[0131] Step 9: For formula (22), Find the partial derivative, that is We can get:

[0132]

[0133] in,

[0134] Step 10. Derivative equation (23) yields the adaptive law of time-varying parameters:

[0135]

[0136] Step 11. Integrate equation (24) to obtain the estimated value of the augmented unknown time-varying parameter vector Θ(t) Thus, the estimated value of the unknown time-varying parameter θ(t) required by the original system can be obtained.

[0137] According to the above implementation process, a simulation of a double-rod hydraulic actuator system with unknown and time-varying hydraulic oil viscosity coefficient can be obtained. The results are as follows: Figure 6-Figure 10 . Figure 6 This is a diagram showing the estimation effect of the proposed method on the unknown parameters of the hydraulic actuator. Figure 7 This is a diagram showing the estimation effect of the unknown parameters of the hydraulic actuator without the optimal learning gain algorithm. Figure 8 This is the estimation effect diagram of the unknown parameters of the hydraulic actuator using the traditional gradient method. Fig. 9 This is a comparison chart of the errors of the above three methods for estimating unknown parameters of hydraulic actuators. Fig.10 This is a comparison chart of the error of the three methods for parameter estimation of the unknown time-varying parameter a1. Figure 6 , Figure 7 and Figure 8 It can be seen from the comparison that compared with the adaptive law of traditional learning gain and the traditional gradient method, the adaptive law constructed by the present invention using unknown parameter error and optimal learning gain has better performance in parameter estimation for the dual-rod hydraulic actuator system with unknown and time-varying hydraulic oil viscosity. Fig. 9 and Fig.10 It can be seen that the transient and steady-state performances of the method proposed in the present invention, such as convergence speed, overshoot, and convergence error, are better than those of the method without the optimal gain Γ and the traditional gradient method. The simulation of the above implementation case shows that the parameter estimation method proposed in the present invention has good performance in parameter estimation of the double-rod hydraulic actuator system with unknown and time-varying hydraulic oil viscosity, under the premise of getting rid of the dependence on the internal state of the system. This further verifies the feasibility and practicality of the present invention.

[0138] Embodiment 3: An adaptive parameter estimation based on input and output data of a linear time-varying system, comprising: a first establishment module, used to establish a linear time-varying system containing unknown parameters; a first acquisition module, used to perform a filtering operation on the linear time-varying system containing unknown parameters to obtain filtering variables; a design module, used to design an integral auxiliary vector; a reconstruction module, used to reconstruct the linear time-varying system based on the filtering variables and the integral auxiliary vector; a second establishment module, used to establish an estimation error relationship between virtual variables and augmented unknown parameter column vectors based on the reconstructed linear time-varying system; a first construction module, used to construct auxiliary variables based on the estimation error relationship between virtual variables and augmented unknown parameter column vectors; a second construction module, used to construct a cost function based on the auxiliary variables; and a second acquisition module, used to obtain estimated values ​​of unknown parameters based on the cost function.

[0139] Embodiment 4: An electronic device comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor is used to run the computer program, wherein when the program is run, any one of the above-mentioned adaptive parameter estimation methods based on input and output data of a linear time-varying system is executed.

[0140] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0141] In the above embodiments of the present invention, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0142] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. An adaptive parameter estimation method based on input and output data of a linear time-varying system, characterized in that: include: Set up linear time-varying systems with unknown parameters; Perform filtering operation on the linear time-varying system with unknown parameters to obtain filtering variables; Design integral auxiliary vectors; Reconstruct the linear time-varying system based on the filter variables and integral auxiliary vectors; According to the reconstructed linear time-varying system, the error relationship between the virtual variable and the augmented unknown parameter column vector is established; Construct auxiliary variables based on the estimated error relationship between dummy variables and augmented unknown parameter column vectors; Construct the cost function based on the auxiliary variables; According to the cost function, the estimated value of the unknown parameter is obtained; The establishment of a linear time-varying system with unknown parameters comprises: Set up an initial linear time-varying system with unknown time-varying parameters: y(t)=C T x(t) Where x(t) is the system state and is an n-dimensional column vector, is the derivative of the system state x(t); u(t) and y(t) are the input and output of the system respectively; A(t) is the system matrix, B(t) is the control matrix, and C is the output matrix; Transform the initial linear time-varying system: y(t)=C T x(t) Among them, A k =A0-KC T is the gain matrix; is the filter parameter vector, and k i >0, is a normal number, i=1,…,n; A0 is the intermediate matrix, θ1(t) and θ2(t) are unknown parameter vectors.

2. The adaptive parameter estimation method based on input and output data of a linear time-varying system according to claim 1, characterized in that: The system matrix, control matrix, and output matrix are expressed as follows: The intermediate matrix and unknown parameter vector are expressed as follows: Among them, a i (t), b i (t) is the unknown parameter; t is time; I n-1 is the n-1 dimensional identity matrix.

3. The adaptive parameter estimation method based on input and output data of a linear time-varying system according to claim 1, characterized in that: The integral auxiliary vector is: in, is the integration variable, is the derivative of the unknown parameter vector θ1(t) with respect to time t; is the derivative of the unknown parameter vector θ2(t) with respect to time t.

4. The adaptive parameter estimation method based on input and output data of a linear time-varying system according to claim 1, characterized in that: The linear time-varying system is reconstructed based on the filtering variables and the integral auxiliary vector, and the expression is: Where x(t) is the system state and is an n-dimensional column vector; P(t) and Q(t) are filter variables based on the system output y(t), W(t) is a filter variable based on the system input u(t), P(t) is an n-dimensional column vector, Q(t) and W(t) are n×n-dimensional matrices; θ1(t) and θ2(t) are unknown parameter vectors; is the auxiliary vector of integration.

5. The adaptive parameter estimation method based on input and output data of a linear time-varying system according to claim 1, characterized in that: The linear time-varying system reconstructed according to the present invention is used to establish the error relationship between the virtual variable and the augmented unknown parameter column vector: The auxiliary variable is constructed based on the estimated error relationship between the virtual variable and the augmented unknown parameter column vector. Among them, S(t) is a dummy variable; E(t) = x(t) - P(t) is an intermediate variable; is an n×2n-dimensional augmented regression matrix; x(t) is the system state and is an n-dimensional column vector; P(t) and Q(t) are filter variables based on the system output y(t), W(t) is a filter variable based on the system input u(t), P(t) is an n-dimensional column vector, Q(t) and W(t) are n×n-dimensional matrices; is the estimated vector of the augmented unknown parameter column vector Θ(t), is the estimation error of the augmented unknown parameter column vector Θ(t); is the integral auxiliary vector; C is the output matrix.

6. The adaptive parameter estimation method based on input and output data of a linear time-varying system according to claim 1, characterized in that: Based on the auxiliary variables, the cost function is constructed: in, is an auxiliary variable; m is a normal number; is a positive constant; is a 2n×2n dimensional positive definite diagonal matrix; express The initial value of is the estimation vector of the augmented unknown parameter column vector Θ(t).

7. The adaptive parameter estimation method based on input and output data of a linear time-varying system according to claim 1, characterized in that: The step of obtaining an estimated value of an unknown parameter based on a cost function includes: According to the cost function, the expression of the augmented unknown parameter column vector estimation vector and the optimal gain is obtained; According to the expression of the estimation vector of the augmented unknown parameter column vector and the optimal gain, the adaptive law of the augmented unknown parameter column vector is obtained; According to the adaptive law of augmenting the unknown parameter column vector, the estimated value of the unknown parameter is obtained.

8. The adaptive parameter estimation method based on input and output data of a linear time-varying system according to claim 7, characterized in that: The step of obtaining an estimated value of an unknown parameter based on a cost function includes: Constructing the cost function Partial derivative relation Obtain the expression of the augmented unknown parameter column vector estimation vector and the optimal gain; Derivative the expression of the augmented unknown parameter column vector estimation vector, and obtain the adaptive law of the augmented unknown parameter column vector: Integrate the adaptive law of the augmented unknown parameter column vector to obtain the estimated value of the augmented unknown parameter column vector Θ(t) Thus, the estimated values ​​of the unknown parameter vectors θ1(t) and θ2(t) required for the linear time-varying system can be obtained. and Where m is a positive constant; represents the optimal gain, is a 2n×2n dimensional positive definite diagonal matrix, is a normal number, is the n×2n-dimensional augmented regression matrix, C is the output matrix, is an auxiliary variable.

9. An adaptive parameter estimation system based on input and output data of a linear time-varying system, characterized in that: include: A first building module is used to build a linear time-varying system with unknown parameters; A first acquisition module is used to perform a filtering operation on a linear time-varying system containing unknown parameters to obtain a filtering variable; Design module, used to design integral auxiliary vector; A reconstruction module is used to reconstruct the linear time-varying system based on the filter variables and the integral auxiliary vector; The second building module is used to build a relationship between the virtual variable and the augmented unknown parameter column vector estimation error based on the reconstructed linear time-varying system; The first construction module is used to construct auxiliary variables based on the estimated error relationship between the dummy variables and the augmented unknown parameter column vector; The second construction module is used to construct a cost function based on auxiliary variables; The second acquisition module is used to obtain an estimated value of an unknown parameter according to a cost function; The establishment of a linear time-varying system with unknown parameters comprises: Set up an initial linear time-varying system with unknown time-varying parameters: y(t)=C T x(t) Where x(t) is the system state and is an n-dimensional column vector, is the derivative of the system state x(t); u(t) and y(t) are the input and output of the system respectively; A(t) is the system matrix, B(t) is the control matrix, and C is the output matrix; Transform the initial linear time-varying system: y(t)=C T x(t) Among them, A k =A0-KC T is the gain matrix; is the filter parameter vector, and k i >0, is a normal number, i=1,…,n; A0 is the intermediate matrix, θ1(t) and θ2(t) are unknown parameter vectors.

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