Transient state point linearization method in stable area of automobile dynamics system

Abstract

The invention belongs to the field of automobile dynamics analysis, and particularly relates to a transient state point linearization method in a stable area of an automobile dynamics system, which comprises the following steps of: firstly, constructing a high-dimensional nonlinear automobile dynamics model, and analyzing and solving the stable area through a phase trajectory; secondly, carrying out simulation experiment data acquisition, and solving a linearized automobile dynamics system corresponding to a transient state point by utilizing a generalized dynamic mode decomposition algorithm; and finally, by calculating the root mean square error of the phase trajectory of the original nonlinear dynamic system and the linearization dynamic system, the linearization method effectiveness analysis is carried out, so that the problems that the nonlinear dynamic system analysis method is limited and the Jacobian linearization method is difficult to realize transient state point linearization are solved. A linear model can be provided for nonlinear automobile system analysis, and a bridge is built for applying a linear system theory to nonlinear dynamic system analysis.

Description

Technical Field

[0001] The present invention belongs to the field of automobile dynamics analysis, and specifically relates to a method for linearizing transient state points within a stable region of an automobile dynamics system. The method is based on a generalized dynamic mode decomposition algorithm and realizes the construction of a linearized model of any state point within the stable region of a vehicle system in a data-driven manner. Background Art

[0002] As a complex, high-dimensional, strongly nonlinear dynamic system, common analysis methods for automobiles include phase plane, cell mapping, Lyapunov function, Lyapunov index, dissipated energy and other nonlinear system analysis methods. However, due to their own limitations, these nonlinear analysis methods can only qualitatively analyze the system characteristics of automobiles, and it is difficult to consider the impact of external interference on the system characteristics. Therefore, linearization methods have become another way to analyze nonlinear systems, and constructing accurate and effective linearized automobile models has become a key issue in the field of automobile dynamics system analysis and control.

[0003] At present, the linearization method of nonlinear vehicle dynamics system usually adopts Jacobi linearization. Using Jacobi linearization method, the linearized vehicle dynamics model at the equilibrium point can be obtained. Based on this linearized model, it can be used to analyze the steady-state steering characteristics of the vehicle, providing a basic analysis method for the handling stability analysis and control of the vehicle. However, the Jacobi linearization model based on the equilibrium point is difficult to analyze the transient dynamic characteristics of the vehicle, and the extreme working conditions such as sideslip and sideslip of the vehicle are basically at the transient state point of the vehicle. Therefore, exploring new technical methods to linearize the transient state point of the vehicle and constructing a linearized model based on the transient state point is the basis for vehicle safety analysis, handling stability evaluation and stability control.

[0004] In order to solve the problem of complex nonlinear dynamic systems and limited linearization methods, the Koopman operator theory provides a powerful tool. By combining the Koopman operator theory with the dynamic mode decomposition algorithm, the model simplification and low-order linear model construction of high-dimensional nonlinear dynamic systems can be achieved based on experimental and simulation data.

[0005] In summary, the nonlinear dynamic system analysis method cannot quantitatively evaluate the characteristics of the automobile system. The traditional Jacobi linearization method makes it difficult to construct a linearized model of the transient state points of the nonlinear automobile dynamics system. The Koopman operator theory and dynamic mode decomposition algorithm provide the possibility for the linearization of the transient state points in the stable region of the automobile dynamics system. Summary of the invention

[0006] In order to overcome the above problems, the present invention provides a method for linearizing transient state points in the stable region of a vehicle dynamics system, which is implemented based on a generalized dynamic mode decomposition algorithm, makes up for the deficiency that traditional Jacobi linearization is only effective for equilibrium points, and realizes the linearization of any transient state point of the vehicle dynamics system.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] A method for linearizing transient state points in a stable region of a vehicle dynamics system comprises the following steps:

[0009] S1, respectively constructed high-dimensional nominal nonlinear dynamical system and disturbed nonlinear dynamical system;

[0010] S2. Solution of stable region of automobile system based on phase trajectory analysis:

[0011] S2.1. First, set the initial conditions of the simulation to include the steady-state initial value points and all possible transient state initial value points;

[0012] S2.2, then simulate and solve the nonlinear vehicle dynamics model to obtain the state variable time series data and express it in the phase space;

[0013] S2.3, finally, determine the stable region of the vehicle dynamics system through state variable phase trajectory analysis;

[0014] S3. Linearization of transient state points of nominal dynamic system based on control dynamic mode decomposition algorithm:

[0015] S3.1. Firstly, the simulation test data of the transient state point of the vehicle dynamics system is collected, and then a snapshot data matrix containing the system state quantity and control quantity is constructed;

[0016] S3.2, then use the control dynamic mode decomposition algorithm to solve the linearized system matrix corresponding to the transient state point;

[0017] S4. Linearization of transient state points of disturbed dynamic systems based on generalized dynamic mode decomposition algorithm:

[0018] S4.1. Firstly, the simulation test data of the transient state point of the vehicle dynamics system is collected, and then a snapshot data matrix including the system state quantity, control quantity and interference quantity is constructed;

[0019] S4.2. Then use the generalized dynamic mode decomposition algorithm to solve the disturbed linearized system matrix corresponding to the transient state point.

[0020] As a more optimal technical solution of the present invention, the simulation test data collection of the transient state points of the vehicle dynamics system in step S3.1 is specifically as follows:

[0021] Collect system measurement and control input timing data to form data matrices X, X′, and Y, where Y is the control input matrix:

[0022]

[0023] The data matrices X and Υ are stacked to construct the matrix Ω, which is defined as the input space matrix.

[0024] As a more optimal technical solution of the present invention, the simulation test data collection of the transient state points of the vehicle dynamics system in step S4.1 is specifically as follows:

[0025] Collect system measurement, control input and interference input timing data to form data matrices X, X′, Y and W; where W is the interference input matrix:

[0026]

[0027] The data matrices X, Υ, and W are stacked to construct the matrix Ω, which is defined as the input space matrix.

[0028] As a more optimal technical solution of the present invention, the step S4.2 is specifically as follows:

[0029] First, calculate the singular value decomposition of the input space Ω and get the decomposition Ω = UΣV * .

[0030] Secondly, calculate the singular value decomposition of the output space X′ and get the decomposition

[0031] Finally, the approximate value of the linear operator is calculated and the result is as follows:

[0032]

[0033] Each transient state point of the nonlinear dynamic system is transformed into a corresponding linear dynamic system; the state space expression is:

[0034]

[0035] The beneficial effects are as follows:

[0036] The present invention applies the generalized dynamic modal decomposition algorithm to the linearization of transient state points of the vehicle dynamics system. By collecting the simulation data of the vehicle dynamics model or the actual vehicle test data, the transient state point linearization model of the vehicle dynamics system is constructed in a data-driven manner, solving the problem that the Jacobi linearization method is only effective for equilibrium points. The construction of the transient state point linearization model is helpful to realize the transient handling stability evaluation and handling stability control of the vehicle, and can provide a model basis for vehicle safety analysis, structural parameter optimization and auxiliary driving controller design. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic flow chart of a method for linearizing transient state points in a stable region of an automobile dynamics system of the present invention;

[0038] Figure 2 is a schematic diagram of a car model in Embodiment 1 of the present invention;

[0039] Figure 3 is a phase trajectory diagram of the automobile system state points in Embodiment 1 of the present invention;

[0040] Figure 4 is a stable region diagram determined by the phase trajectory in Example 1 of the present invention;

[0041] Figure 5 is a linearization error diagram of the lateral velocity at a transient state point in the nominal vehicle dynamics system in Example 1 of the present invention

[0042] Figure 6 is a linearization error diagram of the yaw rate at a transient state point in the nominal vehicle dynamics system in Example 1 of the present invention

[0043] Figure 7 is a linearization error diagram of the lateral velocity at a transient state point in the disturbed vehicle dynamics system in Example 1 of the present invention

[0044] Figure 8 is a linearization error diagram of the yaw rate at a transient state point in the disturbed vehicle dynamics system in Example 1 of the present invention DETAILED DESCRIPTION

[0045] The method of the present invention is further described in detail by the following examples and drawings.

[0046] The present invention provides a method for linearizing transient state points in the stable region of an automobile dynamics system, which combines the Koopman operator theory with the dynamic mode decomposition algorithm to achieve model simplification and low-order linear model construction of a high-dimensional nonlinear dynamic system based on test and simulation data. Specifically, the method comprises the following steps:

[0047] S1, respectively constructed high-dimensional nominal nonlinear dynamical system and disturbed nonlinear dynamical system;

[0048] S2. Solving the stable region of the automobile system based on phase trajectory analysis;

[0049] S3, linearization of transient state points of nominal dynamic system based on control dynamic mode decomposition algorithm;

[0050] S4. Linearize transient state points of disturbed dynamic systems based on generalized dynamic mode decomposition algorithm.

[0051] Example 1

[0052] Reference Figure 1 In this embodiment, a method for linearizing transient state points in the stable region of a vehicle dynamics system based on a generalized dynamic modal decomposition algorithm is provided. The method takes the five-degree-of-freedom plane motion differential equation of a vehicle as an example. However, the effectiveness of the method is not limited to the five-degree-of-freedom vehicle dynamics model, but is applicable to all nonlinear vehicle dynamics systems. The specific implementation method is described in detail as follows:

[0053] Step 1: Construction of nonlinear vehicle dynamics model

[0054] 1.1 Construction of nominal five-DOF vehicle dynamics model

[0055] The two-degree-of-freedom vehicle dynamics model is a classic model for studying vehicle stability. This model assumes that the longitudinal velocity of the vehicle remains constant. However, in the actual operation of the vehicle, it may be in extreme working conditions. At this time, the longitudinal motion and lateral motion of the vehicle are coupled, and part of the longitudinal velocity is converted back into lateral velocity. Therefore, the two-degree-of-freedom model cannot reveal the lateral and longitudinal coupling characteristics of the vehicle's planar motion, and cannot reflect the real vehicle motion phenomenon.

[0056] The present invention adopts a five-degree-of-freedom vehicle dynamics model. The complete five-degree-of-freedom model includes the longitudinal movement of the vehicle along the X-axis, the lateral movement along the Y-axis, the rotational movement around the Z-axis, and the rotational movement of the front and rear wheels. Figure 2 shown.

[0057] The differential equation of the five-degree-of-freedom vehicle dynamics model is:

[0058]

[0059] where v x is the longitudinal velocity of the vehicle's center of mass; v y is the lateral velocity of the vehicle's center of mass; ω is the vehicle's yaw angular velocity; ω f ,ω r are the front wheel angular velocity and the rear wheel angular velocity respectively; m is the vehicle mass; I z is the moment of inertia of the vehicle around the Z axis; C x , Cy are longitudinal and lateral drag coefficients respectively; A x , A y are the longitudinal and lateral frontal areas respectively; ρ air is the air density; J is the rotational inertia of the tire; R e is the tire rotation radius; T df 、T dr are the driving torques acting on the front and rear wheels respectively; l f , l r The distance from the center of mass to the front and rear axes respectively; F sf 、F sr are the lateral forces of the front and rear wheels respectively; F lf 、F lr are the front and rear wheel longitudinal forces respectively. In this embodiment, only the rear wheel drive is considered, so T df =0, T dr =T d .

[0060] 1.2 Construction of five-DOF vehicle dynamics model for side wind interference

[0061] Crosswind interference is the most common external interference scenario during vehicle driving. Based on the above nominal five-degree-of-freedom vehicle dynamics model, this embodiment further constructs a planar five-degree-of-freedom vehicle dynamics model under crosswind interference conditions. The air force and torque generated by the crosswind acting on the vehicle body are simplified and expressed in the corresponding vehicle dynamics model differential equation.

[0062] The differential equation of the side wind interference vehicle dynamics model constructed is:

[0063]

[0064] Among them, F w is the lateral force on the vehicle during driving; γ is the windward angle of the external side wind; l w is the distance from the crosswind action point to the center of mass of the vehicle. In this embodiment, only the influence of the crosswind with a windward angle γ=90° on the vehicle is considered.

[0065] 1.3 Tire dynamics model

[0066] Tires play an important role in automobile movement and are the main source of nonlinear characteristics of automobiles. In this embodiment, the "magic formula" tire model is used to calculate tire force for the tire dynamics model. The tire model is fitted from actual tire test data and uses trigonometric functions to construct a tire force calculation formula. It can accurately express the longitudinal and lateral forces of the tire with a set of calculation formulas. The calculation formula is:

[0067] F=Dsin(Carctan(Bx-E(Bx-arctanBx)))#(3)

[0068] In the formula, B is the stiffness factor; C is the shape factor; D is the peak factor; E is the curvature factor; x is the slip rate or sideslip angle of the tire; and F is the steady-state longitudinal force or lateral force of the tire.

[0069] Tire slip rate is mainly used to calculate the longitudinal force of the tire. The calculation formula is:

[0070]

[0071] In the formula, k f , k r are the slip rates of the front and rear wheels respectively; v xf 、v xr are the longitudinal speeds of the wheel center in the front and rear wheel planes respectively.

[0072] The tire slip angle is mainly used to calculate the lateral force of the tire. The calculation formula is:

[0073]

[0074] In the formula, α f , α r are the side slip angles of the front and rear wheels respectively; v yf 、v yr are the lateral speeds of the wheel center in the planes of the front and rear wheels respectively.

[0075] When a car is running, there is a coupling relationship between longitudinal motion and lateral motion. This coupling relationship also exists in the tire dynamics model, that is, the "adhesion ellipse" relationship of tire force. In order to fully describe the lateral and longitudinal coupling characteristics of automobile tire forces, the mixed slip characteristics of the tire should be considered, and the calculation formula is:

[0076]

[0077] In the formula, G x , G y are tire force mixed slip correction function; r x,1 、r x,2 、r y,1 、r y,2 are tire mixed slip correction coefficients; F lf0 、F lr0 are the front and rear tire longitudinal forces in steady state, F sf0 、F sr0 are the lateral forces of the front and rear tires in steady state, respectively.

[0078] Step 2: Analyze the stable region of the automobile system based on phase trajectory

[0079] 2.1 Solution of the phase trajectory of the automobile system state points

[0080] For the nominal five-degree-of-freedom vehicle dynamics model, set the simulation initial conditions: longitudinal velocity v x =10m / s, lateral speed v y =[-10,10]m / s, yaw rate ω =[-1,1]rad / s, front and rear wheel rotation angular velocity ω f ,ω r =v x / R e , select the tire force parameters under low adhesion road conditions.

[0081] Substitute the above simulation initial conditions into the constructed five-degree-of-freedom vehicle dynamics model, and set the simulation time to 10 seconds. The state quantity time series data of each state variable within the simulation time range is obtained by solving the model, and it is plotted on the x-axis coordinate as the lateral velocity v y , the y-axis coordinate is the yaw angular velocity ω, and the z-axis coordinate is the longitudinal velocity v x The phase trajectory of the automobile system state variables obtained by solving the above model is as follows: Figure 3 shown.

[0082] 2.2 Solution of Stable Region of Automobile System

[0083] As a typical nonlinear dynamic system, the vehicle needs to first determine the stable region and stable state point of the vehicle dynamic system. In the embodiment of the present invention, a method for determining the stable region of the vehicle dynamic system based on phase trajectory is adopted.

[0084] Within a given range of initial conditions, the motion state of the automobile system can be roughly divided into two categories: one is that the various state quantities of the automobile can converge to a stable linear motion state relatively quickly and smoothly after experiencing a small amplitude "oscillation". These state points are "stable state points", such as Figure 3 The red phase trajectory in the middle; the other type is that after the various state quantities of the car have experienced violent "shocks", they finally maintain straight driving or reverse driving at a smaller longitudinal speed. These state points are "instability state points", such as Figure 3 Phase trajectory in medium blue.

[0085] The stable state point and the unstable state point are distinguished by the intensity of the "oscillation" of the time series data of the state variables of the automobile system. The set of all stable state points within the range of the simulation initial value conditions is the stable region of the automobile dynamics system, such as Figure 4 shown.

[0086] Step 3: Linearize the transient state points of the nominal dynamic system based on the control dynamic mode decomposition algorithm

[0087] Dynamic mode decomposition is data-driven in nature. It first collects multiple snapshot pairs of the system state over time and arranges these snapshot pairs into two data matrices X and X′:

[0088]

[0089] The dynamic mode decomposition algorithm finds the best fitting linear operator A that relates the two snapshot matrices in time:

[0090] X′≈AX#(9)

[0091] The best fit operator A establishes a linear dynamical system that optimally advances the snapshot measurements forward in time. Mathematically, the best fit operator A is defined as:

[0092]

[0093] The control dynamic modal decomposition algorithm is an extension of the dynamic modal decomposition algorithm that disambiguates the natural dynamic system from the drive effects. By collecting sampled measurements of the drive input, an accurate and efficient linear model related to the dynamic modal decomposition is identified. In control dynamic modal decomposition, the three measurements are assumed to be correlated. The goal of control dynamic modal decomposition is to analyze the relationship between future system measurements and current measurements and current controls. For each of the three measurements, a pair of linear operators provides the following relationship:

[0094] x k+1 ≈Ax k +Bu k #(11)

[0095] Operators A and B are the optimal solutions for the three sets of data and are also the matrices of the linear dynamics system.

[0096] 3.1 Transient state point simulation test data collection

[0097] For the transient state point in the stable region of the automobile system, the control input u=[δ f T d ]. Collect system measurement and control input timing data to form data matrices X, X′ and Y. Among them, Y is the control input matrix:

[0098]

[0099] The data matrices X and Υ are stacked to construct the matrix Ω, which is defined as the input space matrix.

[0100] 3.2 Solution of transient state point linearization system

[0101] Through the simulation of the nominal dynamics model, the state quantity time series data and control quantity time series data of the transient state point are obtained, and the linearization system of the transient state point is solved by constructing the data matrix. The solution process is as follows:

[0102] First, calculate the singular value decomposition of the input space matrix Ω and obtain the decomposition Ω = UΣV * .

[0103] Secondly, calculate the singular value decomposition of the output space matrix X′ and get the decomposition

[0104] Finally, the approximate value of the linear operator is calculated and the result is as follows:

[0105]

[0106] After the above calculations, each transient state point of the nonlinear dynamic system is transformed into a corresponding linear vehicle dynamic system. The state space expression is:

[0107]

[0108] Step 4: Linearize the transient state points of the disturbed dynamic system based on the generalized dynamic mode decomposition algorithm

[0109] 4.1 Introduction to Generalized Dynamic Mode Decomposition Algorithm

[0110] The generalized dynamic mode decomposition algorithm is also proposed based on the dynamic mode decomposition algorithm, which eliminates the ambiguity between the natural dynamic system, the driving effect and the external disturbance. Under the new algorithm framework, sampled measurements of control inputs and disturbance inputs can be collected and an accurate and efficient linear model related to the dynamic mode decomposition algorithm and the characteristic system realization algorithm can be identified.

[0111] The generalized dynamic mode decomposition algorithm is a further extension of the dynamic mode decomposition algorithm, incorporating the effects of control and disturbance. The new algorithm separates the effects of control input and external disturbance on the system. The linearized system of the generalized dynamic mode decomposition algorithm can be expressed as:

[0112] x k+1 ≈Ax k +Bu k +B w w k #(15)

[0113] Where operators A, B and B w It is the best fitting coefficient of the acquired data and also the linearization matrix of the disturbed nonlinear system.

[0114] 4.2 Transient state point simulation test data collection

[0115] For transient state points within the stable region of the automotive system, in addition to applying control input, the disturbance input w = [w 0 ]. Collect system measurement, control input and interference input timing data to form data matrices X, X′, Y and W. Where W is the interference input matrix:

[0116]

[0117] The data matrices X, Υ, and W are stacked to construct the matrix Ω, which is defined as the input space matrix.

[0118] 4.3 Solution of transient state point linearization system

[0119] Through the interference dynamics model simulation, the state quantity time series data, control quantity time series data and interference quantity time series data of the transient state point are obtained. By constructing the data matrix, the linearization system of the transient state point is solved. The solution process is as follows:

[0120] First, calculate the singular value decomposition of the input space Ω and get the decomposition Ω = UΣV * .

[0121] Secondly, calculate the singular value decomposition of the output space X′ and get the decomposition

[0122] Finally, the approximate value of the linear operator is calculated and the result is as follows:

[0123]

[0124] After the above calculations, each transient state point of the nonlinear dynamic system is transformed into a corresponding linear dynamic system. The state space expression is:

[0125]

[0126] Step 5: Verification of the effectiveness of the transient state point linearization method

[0127] 5.1 Simulation Verification

[0128] The embodiments of the present invention respectively use a dynamic mode decomposition algorithm and a generalized dynamic mode decomposition algorithm to perform transient state point linearization on a nominal dynamic model and a disturbed dynamic model, and calculate a linearization error.

[0129] Set the initial conditions for the simulation: longitudinal velocity v x =10m / s, lateral speed range v y =[-10,10]m / s, yaw rate range ω =[-1,1]rad / s, front and rear wheel rotation angular velocity ω f ,ω r=v x / R e , select the tire force parameters under low adhesion road conditions. The external side wind interference input is set to an amplitude of 1500N and a sine input with a random frequency in the range of [0~2]HZ. The following two schemes are used for analysis:

[0130] The first solution is to linearize the transient state points in the stable region of the nominal five-degree-of-freedom vehicle dynamics model based on the control dynamic modal decomposition algorithm.

[0131] The second solution is to linearize the transient state points in the stable region of the disturbed five-degree-of-freedom vehicle dynamics model based on the generalized dynamic mode decomposition algorithm.

[0132] 5.2 Calculation and analysis of linearization error

[0133] In order to analyze the effectiveness of the linearization method proposed in the present invention, the effectiveness of the linearization method is verified by calculating the linearization error. The linearization error calculation formula is as follows:

[0134]

[0135] Calculate the transient state point v in the stable region of the nominal vehicle dynamics system and the disturbed vehicle dynamics system respectively y and the linearization error of ω. Figure 5 As shown in, it is the linearization error diagram of the lateral velocity at the transient state point in the nominal vehicle dynamics system; Figure 6 As shown in, it is the linearization error diagram of the yaw rate at the transient state point in the nominal vehicle dynamics system; Figure 7 As shown in, it is the linearization error diagram of the lateral velocity at the transient state point in the disturbed vehicle dynamics system; Figure 8 The figure shows the linearization error diagram of the yaw rate at the transient state point in the disturbed vehicle dynamics system. After the linearization error analysis of the above two schemes, it can be seen that the linearization model obtained based on the linearization method of the transient state point in the stable region is accurate and effective.

Claims

1. A method for linearizing transient state points in a stable region of a vehicle dynamics system, characterized in that: The steps include: S1, respectively constructed high-dimensional nominal nonlinear dynamical system and disturbed nonlinear dynamical system; S2. Solution of stable region of automobile system based on phase trajectory analysis: S2.

1. First, set the initial conditions of the simulation to include the steady-state initial value points and all possible transient state initial value points; S2.2, then simulate and solve the nonlinear vehicle dynamics model to obtain the state variable time series data and express it in the phase space; S2.3, finally, determine the stable region of the vehicle dynamics system through state variable phase trajectory analysis; S3. Linearization of transient state points of nominal dynamic system based on control dynamic mode decomposition algorithm: S3.

1. Firstly, the simulation test data of the transient state point of the vehicle dynamics system is collected, and then a snapshot data matrix containing the system state quantity and control quantity is constructed; S3.2, then use the control dynamic mode decomposition algorithm to solve the linearized system matrix corresponding to the transient state point; S4. Linearization of transient state points of disturbed dynamic systems based on generalized dynamic mode decomposition algorithm: S4.

1. Firstly, the simulation test data of the transient state point of the vehicle dynamics system is collected, and then a snapshot data matrix including the system state quantity, control quantity and interference quantity is constructed; S4.

2. Then use the generalized dynamic mode decomposition algorithm to solve the disturbed linearized system matrix corresponding to the transient state point.

2. The method for linearizing transient state points in the stable region of a vehicle dynamics system according to claim 1, characterized in that: The simulation test data collection of the transient state points of the vehicle dynamics system in step S3.1 is specifically as follows: Collect system measurement and control input timing data to form data matrices X, X′, and γ, where γ is the control input matrix: The data matrices X and γ are stacked to construct the matrix Ω, which is defined as the input space matrix.

3. The method for linearizing transient state points in the stable region of a vehicle dynamics system according to claim 1, characterized in that: The simulation test data collection of the transient state point of the vehicle dynamics system in step S4.1 is specifically as follows: Collect system measurement, control input and interference input timing data to form data matrices X, X′, γ and W; where W is the interference input matrix: The data matrices X, γ, and W are stacked to construct the matrix Ω, which is defined as the input space matrix.

4. The method for linearizing transient state points in the stable region of a vehicle dynamics system according to claim 1, characterized in that: The step S4.2 is specifically as follows: First, calculate the singular value decomposition of the input space Ω and get the decomposition Ω = UΣV * . Secondly, calculate the singular value decomposition of the output space X′ and get the decomposition Finally, the approximate value of the linear operator is calculated and the result is as follows: Each transient state point of the nonlinear dynamic system is transformed into a corresponding linear dynamic system; the state space expression is:

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