A short-time increment-based system dynamics parameter real-time estimation method and system

Abstract

The short-time increment-based system dynamics parameter real-time estimation method comprises the following steps: S1, solving a complex system dynamics model expression with unknown parameters or functions, discretizing a control simulation process, and defining a large step and a small step of the simulation; S2, selecting a one-step optimal prediction model through an autocorrelation function, a partial autocorrelation function and a model selection criterion of a state variable sequence; S3, at a starting moment of each large step, solving a next large step starting moment and each small step in the large step through the one-step optimal prediction model selected in step S2; S4, applying an input control amount increment at each small step moment in the large step, and measuring a state variable at a starting moment of each small step; and S5, calculating unknown parameters of the dynamics model according to a difference between a predicted value and an actual measured value of each small step state variable. The method estimates the system dynamics parameters through the one-step optimal prediction, realizes "estimation while controlling", and can accurately estimate the system dynamics parameters under the premise that the system is not greatly affected.

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 a key branch of modern science and technology, robotics has achieved remarkable development. With the continuous advancement of mechatronics, automated control, and computer science, robotics has gradually penetrated various fields, significantly promoting the development of intelligent and automated society. However, with the increasing complexity and demands of tasks, 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 in the development of robotics. This has made it particularly difficult to establish accurate dynamic models and effective motion control for robots.

[0003] Currently, there are three main approaches to modeling the dynamics of robotic systems. The first approach directly uses Newtonian classical mechanics and material mechanics to derive dynamic equations, such as the Lagrangian equations, Hamiltonian equations, and Cosserat rod theory. While these approaches can produce relatively accurate dynamic equations for simple robotic systems, they face significant challenges in modeling complex robotic systems and often struggle to account for the effects of the external environment and material aging on the robot's dynamics model. The second approach is data-driven modeling, which first defines the robot's dynamic constraints and equation structure and then uses deep learning to obtain position parameters or equations. These approaches, to some extent, overcome the problem of direct modeling due to system complexity. However, the learning process is affected by hyperparameters and can result in underfitting or overfitting, resulting in suboptimal generalization. The third approach fits a dynamic model during the robot's mission, unaffected by environmental changes and external disturbances. A typical approach uses RBF neural networks to fit dynamic model parameters. RBF neural networks have been proven to have high fitting accuracy in a wide range of scenarios and meet modeling requirements. However, when the degree of freedom of the robot model is too high, the RBF neural network will also face slow convergence, and it is necessary to combine it with a new and more accurate real-time estimation method of system dynamic 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 the control simulation process, and define the large and small step sizes of the simulation;

[0007] S2, select the appropriate 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 an input control variable increment at each small step within the large step, measuring the state variable at the start of each small step, and updating the predicted value of the state variable 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 and the actual measured value of each small step state variable.

[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 variation matrix of the input 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 is 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. 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 observation 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 to serve 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 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 all other elements 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 The theoretical value of the input during the k-th large step is calculated by step S5 in the previous large step. Then, 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). Let the estimated value of the state variable at this time be 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] According to the kinetic equation

[0032]

[0033] have to

[0034]

[0035] Also 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 The definition of g(x(k)) shows that the value of the m+1 column 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. Then, at the beginning of the l+1th small step, the actual state value x(k; l) at the current moment is obtained. According to the values ​​of x(k; 2m) and x(k), the predicted state variable values ​​at the beginning of the next large step and subsequent small steps are modified. At this time, the predicted state variable value of 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 through 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 "control-while-estimation" strategy, which does not require pre-estimation and measurement of its dynamic parameters before its application. Due to the real-time nature of the estimation, this method avoids the adverse impact on its control accuracy caused by changes in the system's dynamic model under different working conditions.

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

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

[0050] Figure 2This 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 Schematic diagram of the tracking error of the soft robot configuration variables 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] DETAILED DESCRIPTION

[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 the 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 is Discretize the system dynamics model and use replace have

[0063] S2, select the appropriate 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. 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 sequence of state variable observations, 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 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 to serve 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 an input control variable increment at each small step within the large step, measuring the state variable at the start of each small step, and updating the predicted value of the state variable at the start of the next large step and subsequent small steps in real time;

[0074] S4 specifically includes the following steps:

[0075] Define 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 all other elements 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 The theoretical value of the input during the k-th large step is calculated by step S5 in the previous large step. Then, 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). Let the estimated value of the state variable at this time be 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 and the actual measured value of each small step state variable.

[0080] S5 specifically includes the following steps:

[0081] The function g satisfies the following formula:

[0082]

[0083] Assume that the value of g is constant in the same large step, i.e. g(x(k;2m))=g(x(k));at this time the approximation is

[0084]

[0085] From the definition of δu k,2m , the value of g(x(k)) in the m+1 column is After experiencing a large step, g(x(k)) can be completely obtained, and by substituting it into the controller equation, the theoretical value of the input quantity in the next large step can be calculated;

[0086] When l is even, let l=2m, m=1,…,n-1, at the beginning of the l+1 small step, the actual state value x(k;l) at the current time is obtained, and the predicted value of the state variable at the beginning of the next large step and the subsequent small step 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 beginning of the next large step is modified as The predicted values of the current and subsequent small steps are modified as If the large step is not over, enter the subsequent small step, return to step S4, if the large step is over, the system dynamics parameters are estimated in real time, enter the next large step, and return to step S3.

[0087] The present application relates to a kind of based on short-time increment system dynamics parameter real-time estimation system, including a computer module, the module application above-mentioned based on short-time increment system dynamics parameter real-time estimation method. Embodiment

[0088] The method of the application 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 the configuration variable. By using the piecewise constant curvature assumption, the soft robot is regarded as being smoothly spliced by two segments of spatial circular arcs, each of which has three parameters (degrees of freedom). Two of the parameters are the two-dimensional coordinates of the end of the circular arc on the cross section at the head, representing the bending direction and bending angle of the circular arc; the other represents the length change of the circular arc, representing the stretching and compression of the circular arc. Each circular arc defines three control input quantities, two of which are the moments 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 six-control-quantity exact drive system dynamics, and the specific steps are as follows:

[0089] Step 1: using the Lagrange dynamics equation and the infinitesimal method, the general expression of the robot system dynamics model is obtained as

[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 in the form of

[0092]

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

[0094] Step 2: Consider the control simulation process of the 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. A large step length contains 2n = 12 small steps. Consider the control simulation process of the 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 properties 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 series forecast 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 minimize the AIC value.

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

[0098]

[0099] maximize ||y - Wθ||2, where θ is a column vector of model parameters, including autoregressive model parameters or / and moving average model parameters, y = [x(1), x(2),..., x(N)] T is a sequence of state variable observations, W is a design matrix including lagged terms and white noise terms,∑ is a covariance matrix of error terms;

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

[0101] Step 7: Linearly interpolating the system state value at the beginning of the next large step obtained in step 6 and the system state value at the beginning of the current large step, the system state prediction value at the beginning of each small step in the current large step is obtained, i.e. the state variable estimation value at the beginning of each small step during the current large step is expressed as follows:

[0102]

[0103] Step 8: Defining the vector γ i = [0,..., 0, 1, 0,..., 0] T , i = 1, 2,..., n, i.e. γ i is an n-dimensional column vector, whose elements are all 0 except the i-th element which is 1. For the l+1-th small step (l = 0, 1,..., 2n-1) during this large step, if l is even, 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 odd, let l = 2m+1, 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 , where α i > 0, i = 1, 2,..., n is a predetermined increment coefficient. At this time, assuming that u k is the theoretical value of the input during the k-th large step calculated by step 10 in the k-1-th large step, then for the l+1-th small step during the k-th large step, the control input u k,l during this period is 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. Let the estimated value of the state variable at this time be 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. Then, at the beginning of the l+1th small step, calculate the actual state value x(k; l) at the current moment, and modify the state variable prediction value at the beginning of the next large step and subsequent small steps according to the values ​​of x(k; 2m) and x(k). At this time, the state variable prediction value of 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 f(x(k)) estimated in step 7 and the g(x(k)) estimated in step 5 into the core control system (such as the sliding mode controller) to calculate the theoretical value of the input quantity for the next large step. This large step ends, enters the next large step, and returns to step 1.

[0108] Simulation experiment

[0109] The above-described embodiment was applied in a simulation environment to test the algorithm of the present invention. The simulation involved tracking the trajectory of a two-segment, arm-type soft robot with configurational variables. To verify the effectiveness of the algorithm, a sliding mode controller was used in the simulation, and disturbances were added to the control input to simulate the external disturbances that the soft robot would experience in reality. Figure 4 and Figure 5 The following 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 examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

[0111] The present invention may 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 method for real-time estimation of system dynamics parameters based on short-time increments, characterized in that: The method comprises the following steps: S1. Solve the complex system dynamics model expression with unknown parameters or functions, discretize the control simulation process, and define the large and small step sizes of the simulation; S2, select the appropriate 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 an input control variable increment at each small step within the large step, measuring the state variable at the start of each small step, and updating the predicted value of the state variable at the start of the next large step and subsequent small steps in real time; S5, calculating the unknown parameters of the dynamic model based on the difference between the predicted value and the actual measured value of each small step state variable; 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 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 is Discretize the system dynamics model and use replace have 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. 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 sequence of observed values ​​of the state variables, W is the design matrix containing the lag term and the white noise term, and δ is the covariance matrix of the error term; 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 to serve 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: S4 specifically includes the following steps: Define 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 all other elements are 0; for the l+1th small step during the large step, l=0,1,…,2n-1, if l is an even number, let l=2m,m=0,1,…,n-1, 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 The theoretical value of the input during the k-th large step is calculated by step S5 in the previous large step. Then, 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). Let the estimated value of the state variable at this time be 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); 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, g(x(k;2m))=g(x(k)); then we have approximately By δu k,2m The definition of g(x(k)) shows that the value of the m+1 column 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. Then, at the beginning of the l+1th small step, the actual state value x(k; l) at the current moment is obtained. According to the values ​​of x(k; 2m) and x(k), the predicted state variable values ​​at the beginning of the next large step and subsequent small steps are modified. At this time, the predicted state variable values ​​of the next large step are 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 is ended, the system dynamics parameters are estimated in real time, enter the next large step length, and return to step S3.

2. A real-time estimation system for system dynamics parameters based on short-time increments, characterized in that: The method comprises a computer module, wherein the module applies the real-time estimation method of system dynamics parameters based on short-time increments as claimed in claim 1.

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