System kinetic parameter real-time estimation method and system based on short-time increment

Abstract

The system dynamic parameter real-time estimation method based on the short-time increment comprises the following steps: S1, solving a complex system dynamic model expression with unknown parameters or functions, discretizing a control simulation process of the complex system dynamic model expression, and defining a large step length and a small step length of simulation; s2, selecting a proper one-step optimal prediction model through an autocorrelation function and a partial autocorrelation function of the state variable sequence and a model selection criterion; s3, at the starting moment of each large step length, solving the starting moment of the next large step length and each small step length in the large step length through the one-step optimal prediction model selected in the step S2; s4, acting an input control quantity increment at each small step time in the large step, and measuring a state variable at the starting time of each small step; and S5, calculating unknown parameters of the dynamical model according to the difference between the predicted value and the actual measured value of each small-step state variable. According to the method, the dynamic parameters of the system are estimated through a one-step optimal prediction method, and estimation while control is realized, so that the dynamic parameters of the system can be accurately estimated on the premise that the system is not greatly influenced.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent robots, and in particular relates to a method and system for real-time estimation of system dynamics parameters based on short-time increments. Background Art

[0002] As an important branch of modern science and technology, robotics has achieved remarkable development achievements. With the continuous progress of mechatronics, automation control and computer science, robots have gradually penetrated into various fields, greatly promoting the development of social intelligence and automation. However, with the increase in task complexity and task requirements, new transmission and drive mechanisms as well as intelligent and soft materials have begun to be used in robotics. Flexibility, softness, deformability, miniaturization and intelligent control have become important directions for the development of robots. It is also particularly difficult to establish accurate dynamic models and effective motion control of robots.

[0003] At present, the dynamics modeling methods of robot systems mainly include the following three categories: the first category directly uses Newton's classical mechanics and material mechanics to derive dynamic equations, such as using Lagrange equations, Hamilton equations, Cosserat rod theory, etc. This type of method can obtain relatively accurate dynamic equations for simple robot systems, but it faces great difficulties in modeling complex robot systems, and this method is difficult to consider the impact of external environment and material aging on the robot dynamic model. The second type is a data-driven modeling method, which first gives the robot's dynamic constraints and equation structure, and then uses deep learning to obtain its position parameters or equations. This type of method overcomes the problem of being unable to model directly due to the complexity of the system to a certain extent, but the learning process will be affected by hyperparameters, and may be underfitting or overfitting, resulting in its extrapolation not meeting the requirements. The third type of method fits a dynamic model during the robot task process, which is not affected by environmental changes, external disturbances, etc. A typical method is to fit the dynamic model parameters based on RBF neural network. RBF neural network has been proven to have high fitting accuracy in a large number of scenarios and can meet the modeling requirements. However, when the freedom degree of the robot model is too high, the RBF neural network will also face slow convergence, and it is necessary to combine a new and more accurate real-time estimation method of system dynamics parameters to achieve more accurate real-time dynamic modeling. Summary of the invention

[0004] The purpose of the present invention is to address the defects in the prior art and to propose a method and system for real-time estimation of system dynamics parameters based on short-time increments.

[0005] A method for real-time estimation of system dynamics parameters based on short-time increments of the present invention comprises the following steps:

[0006] S1. Solve the complex system dynamics model expression with unknown parameters or functions, discretize its control simulation process, and define the large and small step sizes of the simulation;

[0007] S2, select a suitable one-step optimal prediction model through the autocorrelation function, partial autocorrelation function and model selection criteria of the state variable sequence;

[0008] S3, at the start time of each large step, the predicted value of the state variable at the start time of the next large step and at the start time of each small step between the large step is solved by the one-step optimal prediction model selected in step S2;

[0009] S4, applying the input control amount increment at each small step within the large step, measuring the state variables at the start of each small step, and updating the predicted values ​​of the state variables at the start of the next large step and subsequent small steps in real time;

[0010] S5. Calculate the unknown parameters of the dynamic model based on the difference between the predicted value of each small step state variable and the actual measured value.

[0011] Preferably, S1 specifically includes the following steps:

[0012] The expression for solving complex system dynamics models with unknown parameters or functions is as follows:

[0013]

[0014] Among them, x, represents the state variables and their first-order derivatives of the system dynamics, u is the input of the control system, f(x) represents the sum of the terms in the dynamic equation that are independent of the input u, and g(x) represents the The linear change matrix of the input quantity u, that is, the partial derivative of x with respect to u;

[0015] The control simulation process of system dynamics is regarded as a discrete time process. Assume that the number of degrees of freedom of the system dynamics is n, and one large step time contains 2n small steps. In the simulation process, the state variable at the start of the k-th large step is set to x(k), and the state variable at the start of the l-th small step during the k-th large step is set to x(k; l-1), where l is an integer in the range of 1 to 2n. Let each large step time be T, and each small step time be Discretize the system dynamics model and use replace have

[0016] Preferably, S2 specifically includes the following steps:

[0017] Define the autocorrelation function of the state variable sequence and partial autocorrelation function Predict the system state value at the start of the next large step;

[0018] The AIC model selection criterion AIC = 2r-2ln (L) is used to select the order of the time prediction series model, where r is the number of model parameters and L is the maximum likelihood function value of the model. The selected autoregressive model order p and / or moving average model order q should make the AIC value as small as possible, and then the model parameters are selected to maximize the likelihood function.

[0019]

[0020] Where θ is the model parameter array, including autoregressive model parameters and / or moving average model parameters, y = [x(1), x(2), …, x(N)] T is the observed value sequence of the state variable, W is the design matrix containing the lag term and the white noise term, and ∑ is the covariance matrix of the error term.

[0021] Preferably, S3 specifically includes the following steps:

[0022] Using the one-step time series prediction model obtained in step S2, the state variable x(k) at the start of the current large step, and the state variables x(k-1), x(k-2), ... at the start of the previous large step, calculate the predicted value of the state variable at the start of the next large step

[0023] For the system state value at the start of the next large step and the system state value at the start of the current large step, linear interpolation is performed on the system state value at the start of each small step in the current large step as the system state prediction value of each small step, that is, during the current large step, the estimated value of the state variable at the start of each small step is expressed as follows:

[0024]

[0025] Preferably, S4 specifically includes the following steps:

[0026] Define the vector γ i =[0,…,0,1,0,…0] T ,i=1,2,…,n, that is γ i is an n-dimensional column vector, in which all elements except i are 1 and the others are 0; for the l+1th small step (l=0,1,…,2n-1) during the large step, if l is an even number, let l=2m,m=0,1,…,n-1, and let the control input increment during the small step be δu k,l =αm+1 γ m+1 , if l is an odd number, let l = 2m + 1, m = 0, 1, ..., n-1, and let the control input increment during the small step length be δu k,l =-α m+1 γ m+1 , where α i >0, i=1,2,…,n is the predetermined increment coefficient. At this time, assuming u k is the theoretical value of the input during the k-th large step calculated by step S5 in the previous large step. For the l+1th small step during the k-th large step, the control input u k,l =u k +δu k,l ;

[0027] The state variable measured at the end of each odd-numbered small step in this large step is x(k; 2m+1). Suppose the estimated value of the state variable at this time is Then the state variable estimation error is Therefore, the first-order derivative estimation error of the state variable is Discretize it, we have

[0028]

[0029] At this time, since the 2m+1th small step has ended, Adjust to its true value x(k;2m).

[0030] Preferably, S5 specifically includes the following steps:

[0031] From the kinetic equation expression

[0032]

[0033] have to

[0034]

[0035] And by

[0036]

[0037] Combining the above two equations, we get

[0038]

[0039] Assume that within the same large step size, the value of g is constant, that is g(x(k;2m))=g(x(k)); then we have approximately

[0040]

[0041] By δu k,2m From the definition of g(x(k)), we know that the value of the m+1th column of g(x(k)) is After a large step, g(x(k)) can be completely obtained, and substituting it into the controller equation can calculate the theoretical value of the input under the next large step;

[0042] When l is an even number, let l = 2m, m = 1, ..., n-1. At the beginning of the l+1th small step, the actual state value x(k; l) at the current moment is obtained, and the predicted value of the state variable at the beginning of the next large step and subsequent small steps is modified according to the values ​​of x(k; 2m) and x(k). At this time, the predicted value of the state variable at the next large step is modified to x(k+1) = The predicted values ​​of the current and subsequent small steps are modified to 2m, 2m+1,…, 2n. If the large step length has not ended, enter the subsequent small step length and return to step S4. If the large step length is ended, the system dynamics parameters are estimated in real time, enter the next large step length and return to step S3.

[0043] The present invention also relates to a system for real-time estimation of system dynamics parameters based on short-time increments, comprising a computer module, which applies the above-mentioned method for real-time estimation of system dynamics parameters based on short-time increments.

[0044] Beneficial Effects

[0045] The present invention proposes a real-time estimation method for system dynamics parameters based on short-time increments. The system dynamics parameters are estimated by a one-step optimal prediction method, realizing "estimation while controlling", so that the system dynamics parameters can be estimated more accurately without being significantly affected.

[0046] 1. The overall logic and principle of the method of the present invention are clear and simple, applicable to a large number of different systems and various working conditions, and have strong generalization.

[0047] 2. The method of the present invention adopts a strategy of "controlling while estimating", which eliminates the need to pre-estimate and measure the dynamic parameters before its application. Due to the real-time nature of the estimation, this method avoids the adverse effects on the control accuracy caused by changes in the dynamic model of the system under different working conditions.

[0048] 3. The method of the present invention has good anti-disturbance performance and can obtain more accurate system parameter estimation when facing external interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A flow chart of the method used in the present invention;

[0050] Figure 2It is a conceptual diagram of large step length and small step length in the present invention;

[0051] Figure 3 This is a block diagram of a soft robot control system in an embodiment of the present invention;

[0052] Figure 4 A schematic diagram of the tracking error of the configuration variables of the soft robot in the simulation test of the present invention;

[0053] Figure 5 Schematic diagram of the 2-norm of the fitting error in the simulation test of the present invention.

[0054] Specific implementation

[0055] The following combination Figures 1 to 5 This embodiment will be described in detail.

[0056] A method for real-time estimation of system dynamics parameters based on short-time increments of the present invention comprises the following steps:

[0057] S1. Solve the complex system dynamics model expression with unknown parameters or functions, discretize its control simulation process, and define the large and small step sizes of the simulation;

[0058] S1 specifically includes the following steps:

[0059] The expression for solving complex system dynamics models with unknown parameters or functions is as follows:

[0060]

[0061] Among them, x, represents the state variables and their first-order derivatives of the system dynamics, u is the input of the control system, f(x) represents the sum of the terms in the dynamic equation that are independent of the input u, and g(x) represents the The linear change matrix of the input quantity u is: Partial derivatives with respect to u;

[0062] The control simulation process of system dynamics is regarded as a discrete time process. Assume that the number of degrees of freedom of the system dynamics is n, and one large step time contains 2n small steps. In the simulation process, the state variable at the start of the k-th large step is set to x(k), and the state variable at the start of the l-th small step during the k-th large step is set to x(k; l-1), where l is an integer in the range of 1 to 2n. Let each large step time be T, and each small step time be Discretize the system dynamics model and use replace have

[0063] S2, select a suitable one-step optimal prediction model through the autocorrelation function, partial autocorrelation function and model selection criteria of the state variable sequence;

[0064] S2 specifically includes the following steps:

[0065] Define the autocorrelation function of the state variable sequence and partial autocorrelation function Predict the system state value at the start of the next large step;

[0066] The AIC model selection criterion AIC = 2r-2ln (L) is used to select the order of the time prediction series model, where r is the number of model parameters and L is the maximum likelihood function value of the model. The selected autoregressive model order p and / or moving average model order q should make the AIC value as small as possible, and then the model parameters are selected to maximize the likelihood function.

[0067]

[0068] Where θ is the model parameter array, including autoregressive model parameters and / or moving average model parameters, y = [x(1), x(2), …, x(N)] T is the observed value sequence of the state variable, W is the design matrix containing the lag term and the white noise term, and Σ is the covariance matrix of the error term.

[0069] S3, at the start time of each large step, the predicted value of the state variable at the start time of the next large step and at the start time of each small step between the large step is solved by the one-step optimal prediction model selected in step S2; S3 specifically includes the following steps:

[0070] Using the one-step time series prediction model obtained in step S2, the state variable x(k) at the start of the current large step, and the state variables x(k-1), x(k-2), ... at the start of the previous large step, calculate the predicted value of the state variable at the start of the next large step

[0071] For the system state value at the start of the next large step and the system state value at the start of the current large step, linear interpolation is performed on the system state value at the start of each small step in the current large step as the system state prediction value of each small step, that is, during the current large step, the estimated value of the state variable at the start of each small step is expressed as follows:

[0072]

[0073] S4, applying the input control amount increment at each small step within the large step, measuring the state variables at the start of each small step, and updating the predicted values ​​of the state variables at the start of the next large step and subsequent small steps in real time;

[0074] S4 specifically includes the following steps:

[0075] Define the vector γ i =[0,…,0,1,0,…0] T ,i=1,2,…,n, that is γ i is an n-dimensional column vector, in which all elements except i are 1 and the others are 0; for the l+1th small step (l=0,1,…,2n-1) during the large step, if l is an even number, let l=2m,m=0,1,…,n-1, and let the control input increment during the small step be δu k,l =α m+1 γ m+1 , if l is an odd number, let l = 2m + 1, m = 0, 1, ..., n-1, and let the control input increment during the small step length be δu k,l =-α m+1 γ m+1 , where α i >0, i=1,2,…,n is the predetermined increment coefficient. At this time, assuming u k is the theoretical value of the input during the k-th large step calculated by step S5 in the previous large step. For the l+1th small step during the k-th large step, the control input u k,l =u k +δu k,l ;

[0076] The state variable measured at the end of each odd-numbered small step in this large step is x(k; 2m+1). Suppose the estimated value of the state variable at this time is The state variable estimation error is Then there is

[0077]

[0078] At this time, since the 2m+1th small step has ended, Adjust to its true value x(k;2m).

[0079] S5. Calculate the unknown parameters of the dynamic model based on the difference between the predicted value of each small step state variable and the actual measured value.

[0080] S5 specifically includes the following steps:

[0081] The function g satisfies the following formula:

[0082]

[0083] Assume that within the same large step size, the value of g is constant, that is g(x(k;2m))=g(x(k)); then we have approximately

[0084]

[0085] By δu k,2m From the definition of g(x(k)), we know that the value of the m+1th column of g(x(k)) is After a large step, g(x(k)) can be completely obtained, and substituting it into the controller equation can calculate the theoretical value of the input under the next large step;

[0086] When l is an even number, let l = 2m, m = 1, ..., n-1. At the beginning of the l+1th small step, the actual state value x(k; l) at the current moment is obtained, and the predicted value of the state variable at the beginning of the next large step and subsequent small steps is modified according to the values ​​of x(k; 2m) and x(k). At this time, the predicted value of the state variable at the next large step is modified to The predicted values ​​of the current and subsequent small steps are modified to If the large step length has not ended, enter the subsequent small step length and return to step S4. If the large step length has ended, the system dynamics parameters are estimated in real time, enter the next large step length, and return to step S3.

[0087] The present invention relates to a system dynamics parameter real-time estimation system based on short-time increment, comprising a computer module, and the module applies the system dynamics parameter real-time estimation method based on short-time increment. Example

[0088] The method of the present invention is applied to an arm-type continuous soft robot (hereinafter referred to as "robot") to perform real-time estimation of the dynamic model and tracking of configuration variables. Using the piecewise constant curvature assumption, the soft robot is regarded as two segments of space arcs smoothly spliced ​​together, and each arc has three parameters (degrees of freedom). Two of the parameters are the two-dimensional coordinates of the end of the arc on the cross section of the head end, indicating the bending direction and bending angle of the arc; the other represents the change in the length of the arc, indicating the stretching and compression of the arc. Three control input quantities are defined for each arc, two of which are the torques in two perpendicular directions on the end cross section, and the other is the axial tension. In this way, the robot will be regarded as a six-degree-of-freedom and six-control quantity just-driven system dynamics, and the specific steps are as follows:

[0089] Step 1: Using the Lagrangian dynamics equation and the differential element method, the approximate expression of the robot system dynamics model is:

[0090]

[0091] Among them, q is the robot parameter array, also known as the robot configuration variable array, and u is the control input array, both of which are six-dimensional column vectors. K, D, G(q), and A(q) are all undetermined kinetic parameters. Define the state variables The system dynamics can be expressed as of the form, where

[0092]

[0093] g(x)=[0,(-B(q) -1 A(q)0 T ] T

[0094] Step 2: Consider the control simulation process of system dynamics as a discrete time process. The number of degrees of freedom (control input dimension) of the system dynamics is n = 6. The concepts of large step length and small step length are proposed, where a large step length contains 2n = 12 small steps. Consider the control simulation process of robot system dynamics as a discrete time process. Let each large step length T = 0.01s, then each small step length is During the entire simulation process, the state variable at the start of the kth large step is set to x(k), and the state variable at the start of the lth small step during the kth large step is set to x(k; l-1), where l is an integer in the range of 1 to 2n. In particular, x(k; 0) = x(k). Discretize the system dynamics model and use replace have

[0095] Step 3: Use the autocorrelation function and partial autocorrelation function According to the truncation and tailing of the autocorrelation function and partial autocorrelation function, the autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) models are reasonably selected to predict the system state value at the start of the next large step.

[0096] Step 4: Use the AIC model selection criterion AIC = 2r-2ln (L) to select the order of the time prediction series model, where r is the number of model parameters and L is the maximum likelihood function value of the model. The selected autoregressive model order p and / or moving average model order q should make the AIC value as small as possible;

[0097] Step 5: Select model parameters so that the likelihood function

[0098]

[0099] Maximize. Where θ is the model parameter array, including autoregressive model parameters and / or moving average model parameters, y=[x(1),x(2),…,x(N)] T is the sequence of observed values ​​of the state variables, W is the design matrix containing the lag term and the white noise term, and ∑ is the covariance matrix of the error term;

[0100] Step 6: Using the one-step time series prediction model obtained in steps 3 to 5, the state variable x(k) at the start of the current large step, and the state variables x(k-1), x(K-2), ... at the start of the previous large step, calculate the predicted value of the state variable at the start of the next large step

[0101] Step 7: For the system state value at the start of the next large step obtained in step 6 and the system state value at the start of the current large step, linear interpolation is performed on the system state value at the start of each small step in the current large step as the system state prediction value of each small step, that is, during the current large step, the estimated value of the state variable at the start of each small step is expressed as follows:

[0102]

[0103] Step 8: Define the vector γ i =[0,…,0,1,0,…0] T ,i=1,2,…,n, that is γ i is an n-dimensional column vector, in which all elements except the i-th element are 1 and the rest are 0. For the l+1th small step (l=0,1,…,2n-1) during the large step, if l is an even number, let l=2m, m=0,1,…,n-1, and let the control input increment during the small step be δu k,l =α m+1 γ m+1 , if l is an odd number, let l = 2m + 1, m = 0, 1, ..., n-1, and let the control input increment during the small step length be δu k,l =-α m+1 γ m+1 , where α i >0, i=1,2,…,n is the predetermined increment coefficient. At this time, assuming u k is the theoretical value of the input during the k-th large step calculated by step 10. Then, for the l+1th small step during the k-th large step, the control input u k,l =u k +δu k,l ;

[0104] Step 9: At the end of each odd-numbered small step, the actual state variable x(k; 2m+1) needs to be measured. Suppose the estimated value of the state variable at this time is Then the value of the m+1th column of g(x(k)) is In this way, after a large step, g(x(k)) can be completely obtained, and substituting it into the controller equation can calculate the theoretical value of the input quantity under the next large step.

[0105] Step 10: When l is an even number, let l = 2m, m = 1, ..., n-1. At the beginning of the l+1th small step, the actual state value x(k; l) at the current moment is obtained, and the predicted value of the state variable at the beginning of the next large step and subsequent small steps is modified according to the values ​​of x(k; 2m) and x(k). At this time, the predicted value of the state variable at the next large step is modified to The predicted values ​​of the current and subsequent small steps are modified to If the large step length has not ended, enter the subsequent small step length and return to step 8;

[0106] Step 11: Estimate the value of f(x(k)) in real time through RBF neural network;

[0107] Step 12: Substitute the estimated f(x(k)) in step 7 and the estimated g(x(k)) in step 5 into the core control system (such as the sliding mode controller) to calculate the theoretical value of the input of the next large step. This large step ends, enters the next large step, and returns to step 1.

[0108] Simulation experiment

[0109] The above embodiment is applied in a simulation environment to test the algorithm of the present invention. The simulation content is to track the trajectory of the configuration variables of a two-segment arm soft robot. In order to verify the effectiveness of the algorithm, a sliding mode controller is used in the simulation, and interference is added to the control input to simulate the external disturbance to which the soft robot is subjected in reality. Figure 4 and Figure 5 They are schematic diagrams of the 2-norm of the soft robot configuration variable tracking error and g(x) fitting error in the simulation. As can be seen from the figure, the soft robot configuration variable tracking error reaches a stable state after 0.5s, and the order of magnitude of the tracking error in the stable state is about 10 -5 ~10 -4 The 2-norms of the fitting errors of m and g(x) are also small, both being kept below 5. This shows that the present invention has a relatively good effect on the dynamic model fitting of complex systems such as soft robots.

[0110] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

[0111] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A real-time estimation method for system dynamics parameters based on short-time increments, It is characterized in that The method comprises the following steps: S1. Solve the complex system dynamics model expression with unknown parameters or functions, discretize its control simulation process, and define the large and small step sizes of the simulation; S2, select a suitable one-step optimal prediction model through the autocorrelation function, partial autocorrelation function and model selection criteria of the state variable sequence; S3, at the start time of each large step, the predicted value of the state variable at the start time of the next large step and at the start time of each small step between the large step is solved by the one-step optimal prediction model selected in step S2; S4, applying the input control amount increment at each small step within the large step, measuring the state variables at the start of each small step, and updating the predicted values ​​of the state variables at the start of the next large step and subsequent small steps in real time; S5. Calculate the unknown parameters of the dynamic model based on the difference between the predicted value of each small step state variable and the actual measured value.

2. The method for real-time estimation of system dynamics parameters based on short-time increment according to claim 1, It is characterized in that S1 specifically includes the following steps: The expression for solving complex system dynamics models with unknown parameters or functions is as follows: Among them, x, represents the state variables and their first-order derivatives of the system dynamics, u is the input of the control system, f(x) represents the sum of the terms in the dynamic equation that are independent of the input u, and g(x) represents the The linear change matrix of the input quantity u is: Partial derivatives with respect to u; The control simulation process of system dynamics is regarded as a discrete time process. Assume that the number of degrees of freedom of the system dynamics is n, and one large step time contains 2n small steps. In the simulation process, the state variable at the start of the k-th large step is set to x(k), and the state variable at the start of the l-th small step during the k-th large step is set to x(k; l-1), where l is an integer in the range of 1 to 2n. Let each large step time be T, and each small step time be Discretize the system dynamics model and use replace have 3. The method for real-time estimation of system dynamics parameters based on short-time increment according to claim 1, It is characterized in that S2 specifically includes the following steps: Define the autocorrelation function of the state variable sequence and partial autocorrelation function Predict the system state value at the start of the next large step; The AIC model selection criterion AIC = 2r-2ln (L) is used to select the order of the time prediction series model, where r is the number of model parameters and L is the maximum likelihood function value of the model. The selected autoregressive model order p and / or moving average model order q should make the AIC value as small as possible, and then the model parameters are selected to maximize the likelihood function. Where θ is the model parameter array, including autoregressive model parameters and / or moving average model parameters, y = [x(1), x(2), ..., x(N)] T is the observed value sequence of the state variable, W is the design matrix containing the lag term and the white noise term, and ∑ is the covariance matrix of the error term.

4. The method for real-time estimation of system dynamics parameters based on short-time increment according to claim 1, It is characterized in that S3 specifically includes the following steps: Using the one-step time series prediction model obtained in step S2, the state variable x(k) at the start of the current large step, and the state variables x(k-1), x(k-2), ... at the start of the previous large step, calculate the predicted value of the state variable at the start of the next large step For the system state value at the start of the next large step and the system state value at the start of the current large step, linear interpolation is performed on the system state value at the start of each small step in the current large step as the system state prediction value of each small step, that is, during the current large step, the estimated value of the state variable at the start of each small step is expressed as follows:

5. The method for real-time estimation of system dynamics parameters based on short-time increment according to claim 1, It is characterized in that S4 specifically includes the following steps: Define the vector γ i =[0,…,0,1,0,…0] T , i=1,2,…,n, that is, γ i is an n-dimensional column vector, in which all elements except i are 1 and the others are 0; for the l+1th small step (l=0,1,…,2n-1) during the large step, if l is an even number, let l=2m, m=0,1,…,n-1, and let the control input increment during the small step be δu k，l =α m+1 γ m+1 , if l is an odd number, let l = 2m + 1, m = 0, 1, ..., n-1, and let the control input increment during the small step length be δu k，l =-α m+1 γ m+1 , where α i >0, i=1,2,…, n is the predetermined increment coefficient. At this time, assuming u k is the theoretical value of the input during the k-th large step calculated by step S5 in the previous large step. For the l+1th small step during the k-th large step, the control input u k，l =u k +δu k,l ; The state variable measured at the end of each odd-numbered small step in this large step is x(k; 2m+1). Suppose the estimated value of the state variable at this time is The state variable estimation error is Then there is At this time, since the 2m+1th small step has ended, Adjust to its true value x(k;2m).

6. The method for real-time estimation of system dynamics parameters based on short-time increment according to claim 1, It is characterized in that S5 specifically includes the following steps: The function g satisfies the following formula: Assume that within the same large step size, the value of g is constant, that is At this time, there is approximately By δu k，2m From the definition of g(x(k)), we know that the value of the m+1th column of g(x(k)) is After a large step, g(x(k)) can be completely obtained, and substituting it into the controller equation can calculate the theoretical value of the input under the next large step; When l is an even number, let l = 2m, m = 1, ..., n-1. At the beginning of the l+1th small step, the actual state value x(k; l) at the current moment is obtained, and the predicted value of the state variable at the beginning of the next large step and subsequent small steps is modified according to the values ​​of x(k; 2m) and x(k). At this time, the predicted value of the state variable at the next large step is modified to The predicted values ​​of the current and subsequent small steps are modified to If the large step length has not ended, enter the subsequent small step length and return to step S4. If the large step length has ended, the system dynamics parameters are estimated in real time, enter the next large step length, and return to step S3.

7. A real-time estimation system for system dynamics parameters based on short-time increments, It is characterized in that It comprises a computer module, which applies the real-time estimation method of system dynamics parameters based on short-time increments as described in any one of claims 1 to 6.

Images