CN115407788B - Fixed-time convergence second-order sliding mode control method and control system for underwater high-speed navigation body - Google Patents
Fixed-time convergence second-order sliding mode control method and control system for underwater high-speed navigation body Download PDFInfo
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- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
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Abstract
The invention provides a control method and a control system for a second-order sliding mode of fixed-time convergence of an underwater high-speed navigation body, which are characterized in that firstly, an underwater high-speed navigation body dynamics model is established, a second-order sliding mode control algorithm is based on the second-order sliding mode, a second-order sliding mode controller of the underwater high-speed navigation body with the fixed-time convergence is designed, the stability of the controller is proved through Lyapunov, and finally, mathematical simulation verification is carried out; the invention can effectively control the depth, has high control precision and quick convergence time, and effectively weakens the buffeting effect of the sliding mode controller, so that the depth can smoothly and quickly reach the appointed depth.
Description
Technical Field
The invention belongs to the technical field of power energy, and particularly relates to a fixed time convergence second-order sliding mode control method and a fixed time convergence second-order sliding mode control system for an underwater high-speed navigation body.
Background
The supercavitation means that when the navigation body sails under water at a high speed, the surrounding liquid pressure is reduced due to the higher speed, a layer of supercavitation is formed after gasification, the projectile body is wrapped by the cavitation and is separated from the surrounding liquid, and the supercavitation technology can effectively reduce the resistance of the navigation body in the navigation process, so that the navigation speed is greatly improved, and the supercavitation technology is a hot spot for current research. Compared with the traditional all-wet navigation body, the stress mode of the underwater high-speed navigation body is completely different, and the system has strong nonlinearity and strong time-varying characteristics due to the mutual coupling of the cavitation bubbles and the cavitation bubbles only under the action of the front-end cavitation device, the tail rudder, the gravity and the tail sliding force, so that the design of the controller is greatly challenged, and the existence of external interference and system uncertainty also brings new difficulties to the design of the controller.
Disclosure of Invention
Aiming at the problems, the invention provides a method and a system for controlling a fixed-time convergence second-order sliding mode of an underwater high-speed navigation body; firstly, an underwater high-speed navigation body dynamics model is established, then a controller with fixed time convergence is designed based on a second-order sliding mode control algorithm, lyapunov stability is proved, and finally mathematical simulation verification is carried out.
The invention is realized by the following technical scheme:
a fixed time convergence second order sliding mode control method for an underwater high-speed navigation body comprises the following steps:
the method specifically comprises the following steps:
step 1: establishing an underwater high-speed navigation body dynamics model;
step 2: designing an underwater high-speed navigation body second-order sliding mode controller converging at fixed time based on a second-order sliding mode control algorithm;
step 3: performing stability demonstration on the second-order sliding mode controller obtained in the step 2 through a Lyapunov function;
step 4: based on steps 1 to 3, mathematical simulation analysis is performed.
Further, in step 1, the process comprises,
step 1.1: in the process of underwater high-speed navigation of the supercavitation navigation body, most of the projectile body is wrapped by cavitation bubbles and is only controlled by the control force F of the cavitation device cav Gravity F g Stress F of tail rudder fin And the sliding force F due to contact of the projectile with the cavity wall plane These forces and the effect on the moment of stress, the mathematical model is as follows:
wherein z, θ, w, q represent the depth, pitch angle, vertical velocity and pitch angle velocity of the vehicle, respectively, V represents the axial velocity of the vehicle, m is the mass of the vehicle, J y For moment of inertia of the craft, L c For the distance from the head of the navigation body to the mass center, L f For the tail-to-centroid distance of the vehicle,
step 1.2: the mathematical model in step 1.1 is rewritten into the form of a state equation:
in the formula ,δc 、δ f Represents the rudder deflection angle of the cavitation device and the rudder deflection angle of the tail rudder, F p (t, τ) represents the magnitude of the tail-biting force experienced by the vehicle;
step 1.3: the specific form of the matrix of the model is:
wherein ,g is gravity acceleration, R n The cavitation radius is the cavitation radius, ρ is the density of water, σ is the cavitation number, n is the similarity coefficient, and I (t, τ) is the tail vane wetting rate.
Further, in step 2, the process comprises,
step 2.1: definition x 1 ＝[z θ] T ，x 2 ＝[w q] T Control input u= [ delta ] c δ f ] T The model can be rewritten as affine:
each system matrix isC 1 ＝[g 0] T ,
The design slip form surface is as follows:
wherein ：k 1 、k 2 the constant is V, and the navigation speed of the navigation body is V;
step 2.2: in order to weaken buffeting, a second-order sliding mode approach law is designed:
wherein S= [ S ] 1 s 2 ] T Is a sliding die surface; z= [ Z ] 1 z 2 ] T An augmented state for the system; m is a positive constant, reflects the sliding mode approach law order, and has m more than or equal to 2; lambda (lambda) 1 ≥0、λ 2 The gain is equal to or more than 0;
the following control laws can be derived:
further, in step 3, the process comprises,
step 3.1: performing stability demonstration, and enabling:
then for i=1, 2 there is:
the finishing method can obtain:
in the formula ：
taking the Lyapunov function as:
in the formula ：is a positive definite matrix;
the Lyapunov function is derived from:
in the formula ,when lambda is satisfied 1 ＞0，/>When Q is a positive definite matrix;
then there are:
in the formula ：λQmax Is the maximum eigenvalue of Q, lambda Qmin Is the minimum eigenvalue of Q; then there are:
step 3.2: order theIt can be converted into:
solving the above method to obtain a convergence time boundary:
when (when)Then there are:
thus, the state error can converge to zero within a finite time, the maximum convergence time being
An underwater high-speed navigation body fixed time convergence second order sliding mode control system:
the system comprises a model building module, a sliding mode controller design module, a stability proving module and a simulation analysis module:
the model building module is used for building an underwater high-speed navigation body dynamics model;
the sliding mode controller design module is used for designing a second-order sliding mode controller of the underwater high-speed navigation body, which converges in a fixed time, based on a second-order sliding mode control algorithm;
the stability proving module is used for proving the stability of the second-order sliding mode controller obtained in the step 2 through a Lyapunov function;
and the simulation analysis module is used for carrying out mathematical simulation analysis.
Further, the method comprises the steps of,
the model building module further comprises a mathematical model analysis module, a state equation building module and a matrix building module;
mathematical model analysis module: in the process of the supercavitation navigation body navigating under water at high speed, most of the projectile body is wrapped by cavitation, and only the cavitation control force F is applied cav Gravity F g Stress F of tail rudder fin And the sliding force F due to contact of the projectile with the cavity wall plane These forces and the effect on the moment of stress, the mathematical model is as follows:
wherein z, θ, w, q represent the depth, pitch angle, vertical velocity and pitch angle velocity of the vehicle, respectively, V represents the axial velocity of the vehicle, m is the mass of the vehicle, J y For moment of inertia of the craft, L c For the distance from the head of the navigation body to the mass center, L f For the tail-to-centroid distance of the vehicle,
the state equation establishment module: the mathematical model is rewritten into the form of a state equation:
in the formula ,δc 、δ f Represents the rudder deflection angle of the cavitation device and the rudder deflection angle of the tail rudder, F p (t,τ) represents the magnitude of the tail slapping force exerted by the vehicle;
and a matrix establishment module: the specific form of the matrix of the model is:
wherein ,g is gravity acceleration, R n The cavitation radius is the cavitation radius, ρ is the density of water, σ is the cavitation number, n is the similarity coefficient, and I (t, τ) is the tail vane wetting rate.
Further, the method comprises the steps of,
the sliding mode controller design module further comprises a sliding mode surface design module and a sliding mode approach law design module;
and a sliding mode surface design module: definition x 1 ＝[z θ] T ，x 2 ＝[w q] T Control input u= [ delta ] c δ f ] T The model can be rewritten as affine:
each system matrix isC 1 ＝[g 0] T ,
The design slip form surface is as follows:
wherein ：k 1 、k 2 the constant is V, and the navigation speed of the navigation body is V;
the sliding mode approach law design module: the method is used for weakening buffeting and designing a second-order sliding mode approach law:
wherein S= [ S ] 1 s 2 ] T Is a sliding die surface; z= [ Z ] 1 z 2 ] T An augmented state for the system; m is a positive constant, reflects the sliding mode approach law order, and has m more than or equal to 2; lambda (lambda) 1 ≥0、λ 2 The gain is equal to or more than 0;
the following control laws can be derived:
further, the method comprises the steps of,
the stability proving module further comprises a Lyapunov module and a time boundary calculating module;
lyapunov module: performing stability demonstration, and enabling:
then for i=1, 2 there is:
the finishing method can obtain:
in the formula ：
taking the Lyapunov function as:
in the formula ：is a positive definite matrix;
the Lyapunov function is derived from:
in the formula ,when lambda is satisfied 1 ＞0，/>When Q is a positive definite matrix;
then there are:
in the formula ：λQmax Is the maximum eigenvalue of Q, lambda Qmin Is the minimum eigenvalue of Q; then there are:
and a time boundary calculation module: order theCan be converted into：
Solving the above method to obtain a convergence time boundary:
when (when)Then there are:
thus, the state error can converge to zero within a finite time, the maximum convergence time being
An electronic device comprising a memory storing a computer program and a processor implementing the steps of any one of the methods described above when the processor executes the computer program.
A computer readable storage medium storing computer instructions which, when executed by a processor, implement the steps of the method of any of the preceding claims.
The invention has the beneficial effects that
The invention can effectively control the depth, has high control precision and quick convergence time, and effectively weakens the buffeting effect of the sliding mode controller, so that the depth can smoothly and quickly reach the appointed depth.
Drawings
FIG. 1 is a diagram of a stress analysis of an underwater high-speed vehicle;
FIG. 2 is a vehicle depth profile;
FIG. 3 is a vertical velocity profile of a vehicle;
FIG. 4 is a graph of pitch angle of a vehicle;
FIG. 5 is a graph of pitch rate of a vehicle;
FIG. 6 is a graph of a taxiing force profile for a vehicle;
FIG. 7 is a graph of cavitation rudder deflection angle;
fig. 8 is a tail rudder deflection angle graph.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
With reference to fig. 1 to 8.
A fixed time convergence second order sliding mode control method for an underwater high-speed navigation body comprises the following steps:
the method specifically comprises the following steps:
step 1: establishing an underwater high-speed navigation body dynamics model;
step 2: designing an underwater high-speed navigation body second-order sliding mode controller converging at fixed time based on a second-order sliding mode control algorithm;
step 3: performing stability demonstration on the second-order sliding mode controller obtained in the step 2 through a Lyapunov function;
step 4: based on steps 1 to 3, mathematical simulation analysis is performed.
In step 1, as shown in fig. 1,
step 1.1: in the process of underwater high-speed navigation of the supercavitation navigation body, most of the projectile body is wrapped by cavitation bubbles and is only controlled by the control force F of the cavitation device cav Gravity F g Stress F of tail rudder fin And the sliding force F due to contact of the projectile with the cavity wall plane These forces and the effect on the moment of stress, the mathematical model is as follows:
wherein z, θ, w, q each represent the vehicleDepth, pitch angle, vertical speed and pitch angle speed, V denotes the axial speed of the vehicle, m is the mass of the vehicle, J y For moment of inertia of the craft, L c For the distance from the head of the navigation body to the mass center, L f For the tail-to-centroid distance of the vehicle,
step 1.2: the mathematical model in step 1.1 is rewritten into the form of a state equation:
in the formula ,δc 、δ f Represents the rudder deflection angle of the cavitation device and the rudder deflection angle of the tail rudder, F p (t, τ) represents the magnitude of the tail-biting force experienced by the vehicle;
step 1.3: the specific form of the matrix of the model is:
wherein ,g is gravity acceleration, R n The cavitation radius is the cavitation radius, ρ is the density of water, σ is the cavitation number, n is the similarity coefficient, and I (t, τ) is the tail vane wetting rate.
In the step 2 of the process, the process is carried out,
step 2.1: definition x 1 ＝[z θ] T ，x 2 ＝[w q] T Control input u= [ delta ] c δ f ] T The model can be rewritten as affine:
each system inThe matrix isC 1 ＝[g 0] T ,
The design slip form surface is as follows:
wherein ：k 1 、k 2 the constant is V, and the navigation speed of the navigation body is V;
step 2.2: in order to weaken buffeting, a second-order sliding mode approach law is designed:
wherein S= [ S ] 1 s 2 ] T Is a sliding die surface; z= [ Z ] 1 z 2 ] T An augmented state for the system; m is a positive constant, reflects the sliding mode approach law order, and has m more than or equal to 2; lambda (lambda) 1 ≥0、λ 2 The gain is equal to or more than 0;
the following control laws can be derived:
in the step (3) of the process,
step 3.1: performing stability demonstration, and enabling:
then for i=1, 2 there is:
the finishing method can obtain:
in the formula ：
taking the Lyapunov function as:
in the formula ：is a positive definite matrix;
the Lyapunov function is derived from:
in the formula ,when lambda is satisfied 1 ＞0，/>When Q is a positive definite matrix;
then there are:
in the formula ：λQmax Is the maximum eigenvalue of Q, lambda Qmin Is the minimum eigenvalue of Q; then there are:
/>
step 3.2: order theIt can be converted into:
solving the above method to obtain a convergence time boundary:
when (when)Then there are:
thus, the state error can converge to zero within a finite time, the maximum convergence time being
An underwater high-speed navigation body fixed time convergence second order sliding mode control system:
the system comprises a model building module, a sliding mode controller design module, a stability proving module and a simulation analysis module:
the model building module is used for building an underwater high-speed navigation body dynamics model;
the sliding mode controller design module is used for designing a second-order sliding mode controller of the underwater high-speed navigation body, which converges in a fixed time, based on a second-order sliding mode control algorithm;
the stability proving module is used for proving the stability of the second-order sliding mode controller obtained in the step 2 through a Lyapunov function;
and the simulation analysis module is used for carrying out mathematical simulation analysis.
The model building module further comprises a mathematical model analysis module, a state equation building module and a matrix building module;
mathematical model analysis module: in the process of the supercavitation navigation body navigating under water at high speed, most of the projectile body is wrapped by cavitation, and only the cavitation control force F is applied cav Gravity F g Stress F of tail rudder fin And the sliding force F due to contact of the projectile with the cavity wall plane These forces and the effect on the moment of stress, the mathematical model is as follows:
wherein z, θ, w, q represent the depth, pitch angle, vertical velocity and pitch angle velocity of the vehicle, respectively, V represents the axial velocity of the vehicle, m is the mass of the vehicle, J y For moment of inertia of the craft, L c For the distance from the head of the navigation body to the mass center, L f For the tail-to-centroid distance of the vehicle,
the state equation establishment module: the mathematical model is rewritten into the form of a state equation:
in the formula ,δc 、δ f Represents the rudder deflection angle of the cavitation device and the rudder deflection angle of the tail rudder, F p (t, τ) represents the magnitude of the tail-biting force experienced by the vehicle;
and a matrix establishment module: the specific form of the matrix of the model is:
wherein ,g is gravity acceleration, R n Is a cavitation device halfDiameter ρ is the density of water, σ is the cavitation number, n is the similarity coefficient, and I (t, τ) is the tail vane wetting rate.
The sliding mode controller design module further comprises a sliding mode surface design module and a sliding mode approach law design module;
and a sliding mode surface design module: definition x 1 ＝[z θ] T ，x 2 ＝[w q] T Control input u= [ delta ] c δ f ] T The model can be rewritten as affine:
each system matrix isC 1 ＝[g 0] T ,
The design slip form surface is as follows:
wherein ：k 1 、k 2 the constant is V, and the navigation speed of the navigation body is V;
the sliding mode approach law design module: the method is used for weakening buffeting and designing a second-order sliding mode approach law:
wherein S= [ S ] 1 s 2 ] T Is a sliding die surface; z= [ Z ] 1 z 2 ] T An augmented state for the system; m is a positive constant, reflects the sliding mode approach law order, and has m more than or equal to 2; lambda (lambda) 1 ≥0、λ 2 The gain is equal to or more than 0;
the following control laws can be derived:
the stability proving module further comprises a Lyapunov module and a time boundary calculating module;
lyapunov module: performing stability demonstration, and enabling:
then for i=1, 2 there is:
the finishing method can obtain:
in the formula ：
taking the Lyapunov function as:
in the formula ：is a positive definite matrix;
the Lyapunov function is derived from:
in the formula ,when lambda is satisfied 1 ＞0，/>When Q is a positive definite matrix;
then there are:
in the formula ：λQmax Is the maximum eigenvalue of Q, lambda Qmin Is the minimum eigenvalue of Q; then there are:
/>
and a time boundary calculation module: order theIt can be converted into:
solving the above method to obtain a convergence time boundary:
when (when)Then there are:
thus, the state error can converge to zero within a finite time, the maximum convergence time being
In step 4, the control parameters are takenm＝8，k 1 ＝4，k 2 =0.4, and design the desired depth to be z d =3, mathematical simulation analysis was performed;
as can be seen from the simulation result of the drawing, the second-order sliding mode control can effectively control the depth, has high control precision and quick convergence time, effectively weakens the buffeting effect of the sliding mode controller, and enables the depth to smoothly and quickly reach the designated depth.
An electronic device comprising a memory storing a computer program and a processor implementing the steps of any one of the methods described above when the processor executes the computer program.
A computer readable storage medium storing computer instructions which, when executed by a processor, implement the steps of the method of any of the preceding claims.
The above detailed description of the method and the system for controlling the fixed time convergence second order sliding mode of the underwater high-speed navigation body is provided, the principle and the implementation mode of the invention are explained, and the above description of the embodiment is only used for helping to understand the method and the core idea of the invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Claims (4)
1. A fixed time convergence second order sliding mode control method for an underwater high-speed navigation body is characterized by comprising the following steps of:
the method specifically comprises the following steps:
step 1: establishing an underwater high-speed navigation body dynamics model;
in step 1, step 1.1: in the process of underwater high-speed navigation of the supercavitation navigation body, most of the projectile body is wrapped by cavitation bubbles and is only controlled by the control force F of the cavitation device c Gravity F g Stress F of tail rudder fin And the sliding force F due to contact of the projectile with the cavity wall p These forces and the effect on the moment of stress, the mathematical model is as follows:
wherein z, θ, w, q represent the depth, pitch angle, vertical velocity and pitch angle velocity of the vehicle, respectively, V represents the axial velocity of the vehicle, m is the mass of the vehicle, J y For moment of inertia of the craft, L c For the distance from the head of the navigation body to the mass center, L f For the tail-to-centroid distance of the vehicle,
step 1.2: the mathematical model in step 1.1 is rewritten into the form of a state equation:
in the formula ,δc 、δ f Represents the rudder deflection angle of the cavitation device and the rudder deflection angle of the tail rudder, F p (t, τ) represents the magnitude of the tail-biting force experienced by the vehicle;
step 1.3: the specific form of the matrix of the model is:
wherein ,g is gravity acceleration, R n The cavitation radius is the cavitation radius, ρ is the density of water, σ is the cavitation number, n is the similarity coefficient, and I (t, τ) is the tail vane wetting rate;
step 2: designing an underwater high-speed navigation body second-order sliding mode controller converging at fixed time based on a second-order sliding mode control algorithm;
in the step 2 of the process, the process is carried out,
step 2.1: definition x 1 ＝[z θ] T ，x 2 ＝[w q] T Control input u= [ delta ] c δ f ] T The model can be rewritten as affine:
each system matrix isC 1 ＝[g 0] T ,/>
The design slip form surface is as follows:
wherein ：k 1 、k 2 the constant is V, and the navigation speed of the navigation body is V;
step 2.2: in order to weaken buffeting, a second-order sliding mode approach law is designed:
wherein S= [ S ] 1 s 2 ] T Is a sliding die surface; z is Z＝[z 1 z 2 ] T An augmented state for the system; m is a positive constant, reflects the sliding mode approach law order, and has m more than or equal to 2; lambda (lambda) 1 ≥0、λ 2 The gain is equal to or more than 0;
the following control laws can be derived:
step 3: performing stability demonstration on the second-order sliding mode controller obtained in the step 2 through a Lyapunov function;
in the step (3) of the process,
step 3.1: performing stability demonstration, and enabling:
then for i=1, 2 there is:
the finishing method can obtain:
in the formula ：
taking the Lyapunov function as:
in the formula ：is a positive definite matrix;
the Lyapunov function is derived from:
in the formula ,when lambda is satisfied 1 ＞0，/>When Q is a positive definite matrix;
then there are:
in the formula ：λQmax Is the maximum eigenvalue of Q, lambda Qmin Is the minimum eigenvalue of Q; then there are:
step 3.2: order theIt can be converted into:
solving the above method to obtain a convergence time boundary:
when (when)v 0 Not less than 0, the following are:
thus, the stateThe error can be converged to zero in a limited time, and the maximum convergence time is
Step 4: based on steps 1 to 3, mathematical simulation analysis is performed.
2. An underwater high-speed navigation body fixed time convergence second order sliding mode control system is characterized in that:
the system comprises a model building module, a sliding mode controller design module, a stability proving module and a simulation analysis module:
the model building module is used for building an underwater high-speed navigation body dynamics model;
the model building module further comprises a mathematical model analysis module, a state equation building module and a matrix building module;
mathematical model analysis module: in the process of the supercavitation navigation body navigating under water at high speed, most of the projectile body is wrapped by cavitation, and only the cavitation control force F is applied c Gravity F g Stress F of tail rudder fin And the sliding force F due to contact of the projectile with the cavity wall p These forces and the effect on the moment of stress, the mathematical model is as follows:
wherein z, θ, w, q represent the depth, pitch angle, vertical velocity and pitch angle velocity of the vehicle, respectively, V represents the axial velocity of the vehicle, m is the mass of the vehicle, J y For moment of inertia of the craft, L c For the distance from the head of the navigation body to the mass center, L f For the tail-to-centroid distance of the vehicle,
the state equation establishment module: the mathematical model is rewritten into the form of a state equation:
in the formula ,δc 、δ f Represents the rudder deflection angle of the cavitation device and the rudder deflection angle of the tail rudder, F p (t, τ) represents the magnitude of the tail-biting force experienced by the vehicle;
and a matrix establishment module: the specific form of the matrix of the model is:
wherein ,g is gravity acceleration, R n The cavitation radius is the cavitation radius, ρ is the density of water, σ is the cavitation number, n is the similarity coefficient, and I (t, τ) is the tail vane wetting rate;
the sliding mode controller design module is used for designing a second-order sliding mode controller of the underwater high-speed navigation body, which converges in a fixed time, based on a second-order sliding mode control algorithm; the sliding mode controller design module further comprises a sliding mode surface design module and a sliding mode approach law design module;
and a sliding mode surface design module: definition x 1 ＝[z θ] T ，x 2 ＝[w q] T Control input u= [ delta ] c δ f ] T The model can be rewritten as affine:
each system matrix isC 1 ＝[g 0] T ,/>
The design slip form surface is as follows:
wherein ：k 1 、k 2 the constant is V, and the navigation speed of the navigation body is V;
the sliding mode approach law design module: the method is used for weakening buffeting and designing a second-order sliding mode approach law:
wherein S= [ S ] 1 s 2 ] T Is a sliding die surface; z= [ Z ] 1 z 2 ] T An augmented state for the system; m is a positive constant, reflects the sliding mode approach law order, and has m more than or equal to 2; lambda (lambda) 1 ≥0、λ 2 The gain is equal to or more than 0;
the following control laws can be derived:
the stability proving module is used for proving the stability of the second-order sliding mode controller obtained by the sliding mode controller design module through the Lyapunov function; the stability proving module further comprises a Lyapunov module and a time boundary calculating module;
lyapunov module: performing stability demonstration, and enabling:
then for i=1, 2 there is:
the finishing method can obtain:
in the formula ：
taking the Lyapunov function as:
in the formula ：is a positive definite matrix;
the Lyapunov function is derived from:
in the formula ,when lambda is satisfied 1 ＞0，/>When Q is a positive definite matrix;
then there are:
in the formula ：λQmax Is the maximum eigenvalue of Q, lambda Qmin Is the minimum eigenvalue of Q; then there are:
and a time boundary calculation module: order theIt can be converted into:
solving the above method to obtain a convergence time boundary:
when (when)v 0 Not less than 0, the following are:
thus, the state error can converge to zero within a finite time, the maximum convergence time being
And the simulation analysis module is used for carrying out mathematical simulation analysis.
3. An electronic device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of claim 1 when executing the computer program.
4. A computer readable storage medium storing computer instructions which, when executed by a processor, implement the steps of the method of claim 1.
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