A high-speed train safe operation control method based on non-repetitive iterative learning

Abstract

The present invention discloses a high-speed train safe operation control method based on non-repetitive iterative learning, specifically: according to the repeated operation mode and non-repetitive characteristics of the train, a high-speed train dynamic model for iterative learning, as well as displacement constraints and speed constraints are established; the expected reference displacement and reference speed are set, and the boundedness of the parameters related to the train operation is analyzed; an error conversion mechanism is established to convert the restricted train operation control problem into an unconstrained form; based on the unconstrained system, a high-speed train non-repetitive iterative learning control algorithm is designed, including control laws and parameter learning rules; a train operation simulation platform is built to test the algorithm and obtain the expected parameter values; and the train non-repetitive iterative learning control algorithm is deployed to the train operation control system. The present invention breaks through the limitation of the traditional train iterative learning control method requiring strict repeatability, and provides an active safety guarantee mechanism based on displacement constraints and speed constraints, which has stronger practicality and reliability.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent rail transportation, and in particular relates to a high-speed train safe operation control method based on non-repetitive iterative learning. Background Art

[0002] Thanks to its powerful carrying capacity, extremely fast running speed, and good user experience, high-speed trains have become an important support for social and economic development. Among the core components of high-speed train systems, the train automatic operation control system is one of the most critical equipment to ensure the safe and efficient operation of high-speed railways. Its main goal is to plan / formulate the traction and braking operation strategies of the train according to the railway department's operating timetable. However, due to factors such as air damping and mechanical coupling at high speeds, the operating dynamics of high-speed trains are very complex, including time-varying parameters, external disturbances, unmodeled dynamics, etc., so it is extremely difficult to achieve precise control of displacement and speed.

[0003] In recent years, with the continuous increase in operating speed and the continuous reduction in headway, the safety margin of high-speed trains has been continuously compressed. Under the influence of the line environment and adjacent vehicles, the running state of the train (such as displacement, speed, etc.) needs to be strictly constrained to ensure driving safety. For example, when passing through speed-limited sections, such as bridges and tunnels, the actual running speed of the train cannot exceed the maximum speed limit. Similarly, in the emerging mobile block signal system, the displacement of the train needs to be limited to prevent collisions.

[0004] According to the operation schedule formulated by the railway department, the operation process of high-speed trains includes many periodic characteristics, which are specifically manifested in: repeatability of the operation line (such as tunnels, ramps, curves, etc.), invariance of the dynamic model structure, similarity of traction and braking conditions between carriages, etc. The repeated operation mode of the train has accumulated a wealth of prior knowledge, and the iterative learning control method can make full use of this knowledge to support the intelligent operation of the train. However, although the operation process of high-speed trains has obvious periodic characteristics, there are also non-repetitive dynamic changes caused by passenger flow changes, environmental weather, etc. Specifically, the train's vehicle weight, drag coefficient, and external disturbance may be different in each operation, which will not only reduce the performance of the iterative learning control system, but even threaten the safety of the train in serious cases. So far, there is a lack of a train iterative learning precise tracking control method that can adapt to non-repetitive characteristics and meet displacement / speed constraints. Summary of the invention

[0005] In view of the above problems, the present invention provides a high-speed train safe operation control method based on non-repetitive iterative learning.

[0006] A high-speed train safe operation control method based on non-repetitive iterative learning of the present invention comprises the following steps:

[0007] Step 1: Based on the repetitive operation mode and non-repetitive characteristics of the train, a high-speed train dynamics model for iterative learning, as well as displacement constraints and speed constraints, is established.

[0008] Step 2: Set the expected reference displacement and reference speed of the high-speed train, and analyze the boundedness of the parameters related to the train operation.

[0009] Step 3: Establish an error conversion mechanism to transform the constrained train operation control problem into an unconstrained form.

[0010] Step 4: Based on the unconstrained system, design a non-repetitive iterative learning control algorithm for high-speed trains, including control laws and parameter learning rules.

[0011] Step 5: Build a train operation simulation platform and conduct algorithm testing to obtain the expected parameter values.

[0012] Step 6: Deploy the high-speed train non-iterative learning control algorithm into the train operation control system, and set the controller parameters and parameter learning gains to the expected parameter values, so as to achieve precise control of the displacement and speed of the high-speed train and ensure the safe operation of the train.

[0013] Furthermore, step 1 is specifically as follows:

[0014] According to Newton's law, high-speed trains are subject to a variety of forces during operation, including air resistance f a (·), mechanical resistance f m (·), additional resistance f d (·), and the dynamic model of high-speed train is established as follows:

[0015]

[0016] Where t represents time, m(t) is the mass of the train, u(t) represents the control input, i.e., the traction force, s(t) and v(t) represent the displacement and velocity of the train, respectively, which satisfy are the drag coefficients, and ω(t) represents the external disturbance.

[0017] By integrating the iteration index i into the above train dynamics model, the high-speed train dynamics model for iterative learning control is established as follows:

[0018]

[0019] Among them, s i (t) and v i (t) represent the displacement and speed of the train during the i-th operation, u i(t) is the control input signal for the i-th operation, m i (t), c 0,i (t), c v,i (t), c v,i (t) is the unknown iterative parameter, ω i (t) is the non-repeating external disturbance in the ith run, f d (·) is an unknown state-dependent continuous function.

[0020] In order to ensure the running safety of the train, two constraints are imposed on the i-th displacement s i (t) and speed v i (t), that is, the displacement constraints and velocity constraints are as follows:

[0021] s l (t)≤s i (t)≤s p (t)

[0022] v l (t)≤v i (t)≤v p (t)

[0023] where s l (t) and s p (t) represent the lower bound and upper bound of the displacement, respectively, v l (t) and v p (t) represent the lower bound and upper bound of the speed constraint respectively, which are flexibly set according to the tracking interval in the operation diagram and the speed limit of the section of the operation line.

[0024] Furthermore, step 2 is specifically as follows:

[0025] According to the operation diagram specified by the railway department, the expected reference displacement and reference speed of the high-speed train are defined as s r (t) and v r (t); Since the train always departs from the same station, the initial values ​​of displacement and speed are the same for each run; that is, the displacement s for any i-th run i (t) and speed v i The initial value of (t) and the displacement s at any j-th run j (t) and speed v j The initial value of (t) is the same, that is, s i (0) = s j (0), v i (0) = v j (0).

[0026] Furthermore, set the reference displacement s r(t) and reference speed v r The initial values ​​of (t) are equal to the displacement s during the i-th run. i (t) and speed v i The initial value of (t), i.e., s r (0) = s i (0), v r (0) = v i (0).

[0027] At the same time, from the physical properties of the train, we can know that the train operation related parameters, including the iterative parameter m i (t), c 0,i (t), c v,i (t), c a,i (t), and the non-repeating external disturbance ω i (t), is bounded throughout the entire run.

[0028] Furthermore, step 3 is specifically as follows:

[0029] The displacement error and velocity error are defined as e s,i (t) = s i (t)-s r (t), e v,i (t) = v i (t)-v r (t), according to the displacement constraint and velocity constraint, the displacement error constraint and velocity error constraint are as follows:

[0030] λ s,l (t)≤e s,i (t)≤λ s,p (t)

[0031] λ v,l (t)≤e v,i (t)≤λ v,p (t)

[0032] Among them, λ s,l (t) and λ s,p (t) represent the constraint lower bound and constraint lower bound of displacement error, respectively, λ v,l (t) and λ v,p (t) represent the lower bound and upper bound of the velocity error respectively.

[0033] In order to relax the restrictions of safety constraints on controller design, the following error conversion mechanism is established to achieve the displacement error e s,i (t) to the unconstrained state x 1,i (t), speed error e v,i (t) to the unconstrained state x 2,i (t) is a one-to-one mapping.

[0034]

[0035] in and is a strictly smoothly increasing function, and Respectively represent their inverse functions; from the above formula, we can get the function and Satisfy the following characteristics:

[0036]

[0037] It can be concluded that as long as the unconstrained state x 1,i (t) and x 2,i (t) is bounded, then the displacement error constraint and velocity error constraint must hold; at the same time, when the unconstrained state x 1,i (t) and x 2,i (t) converge to the desired unconstrained state and When the displacement error e s,i (t) and the velocity error e v,i (t) will converge to 0 respectively.

[0038] For the unconstrained state x 1,i (t) and x 2,i (t) is derived, we can get:

[0039]

[0040] Integrating the above equation with the train dynamics model for iterative learning, the following unconstrained system is established:

[0041]

[0042] The known state-related functions φ1(·), φ2(·), φ3(·), h1(·), and h2(·) are defined as follows:

[0043]

[0044] The unconstrained system will be used to design an iterative learning control algorithm for high-speed trains.

[0045] Furthermore, step 4 is specifically as follows:

[0046] Define the auxiliary error signal as z i (t) = γ0(x 1,i (t)-x 1,r (t))+(x 2,i (t)-x 2,r(t)), where γ0 represents the controller parameter; according to the Hurwitz stability polynomial theorem, if and only if the irreducible state x 1,i (t) and x 2,i (t) converge to the desired unconstrained state x 1,r (t) and x 2,r (t), the auxiliary error signal z i (t) converges to 0; Based on the unconstrained system in step 3, a non-repeated iterative learning control algorithm for high-speed trains can be designed, including the following control law:

[0047]

[0048] And the parameter learning rule:

[0049]

[0050] where μ i (t) and η i (t) represents the auxiliary control signal during the i-th operation, represents the parameter estimation at the i-th run, γ0 represents the controller parameter, q0, q l , q4 is the parameter learning gain, ∈0, ∈ l is the parameter of the hyperbolic tangent function, is the projection operation, represents the auxiliary variable, and ψ(·) represents the Gaussian basis function of the neural network.

[0051] In addition, the parameter estimates The initial values ​​are set to where θ0 is an arbitrarily small positive real number.

[0052] Furthermore, step 5 is specifically as follows:

[0053] A train operation simulation platform is built based on MATLAB simulation software, and the mass of the train in the i-th operation is set to m i (t) = (3.45 + 0.8r) × 10 5 kg, the resistance is c 0,i (t)=-[2977+275sin(0.0037t)r]N, c v,i (t)=-[25.17+2.5sin(0.0037t)r]N·s / m, c a,i (t)=-[0.3864+0.04sin(0.0037t)r]N·s 2 / m 2 , the external disturbance is ω i(t) = -1000w(t)N, where r and w(t) are random numbers between 0 and 1 generated by a computer; the high-speed train non-repetitive iterative learning control algorithm designed in step 4 is tested and verified on a train operation simulation platform; by adjusting the controller parameters and parameter learning gain, the displacement s on the train operation simulation platform is i (t) and speed v i (t) can accurately track the desired reference displacement s respectively r (t) and reference speed v r (t), and the displacement and speed are always within the safe area; specifically, the expected parameter values ​​obtained from the train operation simulation platform are: γ0 = 0.5, γ1 = 20, q0 = 10, q1 = 10 2 q2=10 -3 q3=10 -5 , q4=0.1, ∈0=∈1=∈2=∈3=0.1.

[0054] The beneficial technical effects of the present invention are:

[0055] 1. The repetitive operation mode of high-speed trains provides great potential for iterative learning control methods, but non-repetitive uncertainties caused by transport loads, random disturbances, etc. may weaken the controller's capabilities. This invention breaks through the limitation that traditional iterative learning control methods require the controlled object to meet strict repeatability, and provides a new technology for high-speed train operation control.

[0056] 2. The present invention integrates displacement constraints and speed constraints into the control system, so that the control algorithm has active safety assurance capabilities, laying a foundation for further improving the line traffic density and operating speed, and has obvious significance for promoting the efficient and coordinated development of high-speed railways.

[0057] 3. The present invention can be extended to the application scenarios of other rail transportation vehicles such as heavy-load locomotives, urban rail trains, maglev trains, etc., and can be used to formulate safe and efficient traction and braking strategies, so it has good scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a block diagram of the high-speed train safe operation control principle based on non-repetitive iterative learning of the present invention.

[0059] Figure 2 This is a flow chart for implementing the high-speed train safe operation control based on non-repetitive iterative learning of the present invention.

[0060] Figure 3 The displacement and displacement error are obtained by the present invention on the train operation simulation platform.

[0061] Figure 4It is the speed and speed error obtained by the present invention on the train operation simulation platform. DETAILED DESCRIPTION

[0062] The present invention is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0063] The control principle of the high-speed train safe operation control method based on non-repetitive iterative learning of the present invention is as follows: Figure 1 As shown in Figure 1, it specifically includes two modules: active safety assurance module and iterative learning control module. The control implementation flow chart is shown in Figure 1. Figure 2 As shown in the figure, it includes 6 steps: establishing a high-speed train dynamics model, setting the expected reference displacement and reference speed, designing a one-to-one mapping error conversion mechanism, designing a non-repetitive iterative learning control algorithm, building a train operation simulation platform and testing it, and deploying the algorithm to the train operation control system. The specific steps are as follows:

[0064] Step 1: Based on the repetitive operation mode and non-repetitive characteristics of the train, a high-speed train dynamics model for iterative learning, as well as displacement constraints and speed constraints, is established.

[0065] According to Newton's law, high-speed trains are subject to a variety of forces during operation, including air resistance f a (·), mechanical resistance f m (·), additional resistance f d (·), and the dynamic model of high-speed train is established as follows:

[0066]

[0067] Where t represents time, m(t) is the mass of the train, u(t) represents the control input, i.e., the traction force, s(t) and v(t) represent the displacement and velocity of the train, respectively, which satisfy c a (t), c0(t), c v (t) are the drag coefficients, and ω(t) represents the external disturbance.

[0068] By integrating the iteration index i into the above train dynamics model, the high-speed train dynamics model for iterative learning control is established as follows:

[0069]

[0070] Among them, s i (t) and v i (t) represent the displacement and speed of the train during the i-th operation, u i (t) is the control input signal for the i-th operation, m i (t), c 0,i (t), cv,i (t), c v,i (t) is the unknown iterative parameter, ω i (t) is the non-repeating external disturbance in the ith run, f d (·) is an unknown state-dependent continuous function.

[0071] In order to ensure the running safety of the train, two constraints are imposed on the i-th displacement s i (t) and speed v i (t), that is, the displacement constraints and velocity constraints are as follows:

[0072] s l (t)≤s i (t)≤s p (t)

[0073] v l (t)≤v i (t)≤v p (t)

[0074] where s l (t) and s p (t) represent the lower bound and upper bound of the displacement, respectively, v l (t) and v p (t) represent the lower bound and upper bound of the speed constraint respectively, which are flexibly set according to the tracking interval in the operation diagram and the speed limit of the section of the operation line.

[0075] Step 2: Set the expected reference displacement and reference speed of the high-speed train, and analyze the boundedness of the parameters related to the train operation.

[0076] According to the operation diagram specified by the railway department, the expected reference displacement and reference speed of the high-speed train are defined as s r (t) and v r (t); Since the train always departs from the same station, the initial values ​​of displacement and speed are the same for each run; that is, the displacement s for any i-th run i (t) and speed v i The initial value of (t) and the displacement s at any j-th run j (t) and speed v j The initial value of (t) is the same, that is, s i (0) = s j (0), v i (0) = v j (0).

[0077] Furthermore, set the reference displacement s r (t) and reference speed v rThe initial values ​​of (t) are equal to the displacement s during the i-th run. i (t) and speed v i The initial value of (t), i.e., s r (0) = s i (0), v r (0) = v i (0).

[0078] At the same time, from the physical properties of the train, we can know that the train operation related parameters, including the iterative parameter m i (t), c 0,i (t), c v,i (t), c a,i (t), and the non-repeating external disturbance ω i (t), is bounded throughout the entire run.

[0079] Step 3: Establish an error conversion mechanism to transform the constrained train operation control problem into an unconstrained form.

[0080] The displacement error and velocity error are defined as e s,i (t) = s i (t)-s r (t), e v,i (t) = v i (t)-v r (t), according to the displacement constraint and velocity constraint, the displacement error constraint and velocity error constraint are as follows:

[0081] λ s,l (t)≤e s,i (t)≤λ s,p (t)

[0082] λ v,l (t)≤e v,i (t)≤λ v,p (t)

[0083] Among them, λ s,l (t) and λ s,p (t) represent the constraint lower bound and constraint lower bound of displacement error, respectively, λ v,l (t) and λ v,p (t) represent the lower bound and upper bound of the velocity error respectively.

[0084] In order to relax the restrictions of safety constraints on controller design, the following error conversion mechanism is established to achieve the displacement error e s,i (t) to the unconstrained state x 1,i (t), speed error e v,i (t) to the unconstrained state x 2,i (t) is a one-to-one mapping.

[0085]

[0086] in and is a strictly smoothly increasing function, and Respectively represent their inverse functions; from the above formula, we can get the function and Satisfy the following characteristics:

[0087]

[0088] It can be concluded that as long as the unconstrained state x 1,i (t) and x 2,i (t) is bounded, then the displacement error constraint and velocity error constraint must hold; at the same time, when the unconstrained state x 1,i (t) and x 2,i (t) converge to the desired unconstrained state and When the displacement error e s,i (t) and the velocity error e v,i (t) will converge to 0 respectively.

[0089] For the unconstrained state x 1,i (t) and x 2,i (t) is derived, we can get:

[0090]

[0091] Integrating the above equation with the train dynamics model for iterative learning, the following unconstrained system is established:

[0092]

[0093] The known state-related functions φ1(·), φ2(·), φ3(·), h1(·), and h2(·) are defined as follows:

[0094]

[0095] The unconstrained system will be used to design an iterative learning control algorithm for high-speed trains.

[0096] Step 4: Based on the unconstrained system, design a non-repetitive iterative learning control algorithm for high-speed trains, including control laws and parameter learning rules.

[0097] Define the auxiliary error signal as z i (t) = γ0(x 1,i (t)-x 1,r (t))+(x 2,i(t)-x 2,r (t)), where γ0 represents the controller parameter; according to the Hurwitz stability polynomial theorem, if and only if the irreducible state x 1,i (t) and x 2,i (t) converge to the desired unconstrained state x 1,r (t) and x 2,r (t), the auxiliary error signal z i (t) converges to 0; Based on the unconstrained system in step 3, a non-repeated iterative learning control algorithm for high-speed trains can be designed, including the following control law:

[0098]

[0099] And the parameter learning rule:

[0100]

[0101] where μ i (t) and η i (t) represents the auxiliary control signal during the i-th operation, represents the parameter estimation at the i-th run, γ0 represents the controller parameter, q0, q l , q4 is the parameter learning gain, ∈0, ∈ l is the parameter of the hyperbolic tangent function, is the projection operation, represents the auxiliary variable, and ψ(·) represents the Gaussian basis function of the neural network.

[0102] In addition, the parameter estimates The initial values ​​are set to where θ0 is an arbitrarily small positive real number.

[0103] Step 5: Build a train operation simulation platform and conduct algorithm testing to obtain the expected parameter values.

[0104] A train operation simulation platform is built based on MATLAB simulation software, and the mass of the train in the i-th operation is set to m i (t) = (3.45 + 0.8r) × 10 5 kg, the resistance is c 0,i (t)=-[2977+275sin(0.0037t)r]N, c v,i (t)=-[25.17+2.5sin(0.0037t)r]N·s / m, c a,i (t)=-[0.3864+0.04sin(0.0037t)r]N·s 2 / m 2 , the external disturbance is ω i(t) = -1000w(t)N, where r and w(t) are random numbers between 0 and 1 generated by a computer; the high-speed train non-repetitive iterative learning control algorithm designed in step 4 is tested and verified on a train operation simulation platform. The displacement and displacement error related results obtained on the train operation simulation platform are as follows Figure 3 As shown in Figure 1, it specifically includes the displacement curves of the train during the first and 30th runs, as well as the absolute values ​​of the displacement errors at 400s, 800s, 1200s, and 1600s during the entire iterative run. The speed and speed error related results obtained on the train operation simulation platform are shown in Figure 1. Figure 4 As shown, it specifically includes the speed curves of the train during the 1st and 30th runs, as well as the absolute values ​​of the speed errors at 400s, 800s, 1200s, and 1600s during the entire iterative running process.

[0105] By adjusting the controller parameters and parameter learning gain, the displacement s of the train running simulation platform is i (t) and speed v i (t) can accurately track the desired reference displacement s respectively r (t) and reference speed v r (t), and the displacement and speed are always within the safe area; specifically, the expected parameter values ​​obtained from the train operation simulation platform are: γ0 = 0.5, γ1 = 20, q0 = 10, q1 = 10 2 q2=10 -3 q3=10 -5 , q4=0.1, ∈0=∈1=∈2=∈3=0.1.

[0106] Step 6: Deploy the high-speed train non-iterative learning control algorithm into the train operation control system, and set the controller parameters and parameter learning gains to the expected parameter values, so as to achieve precise control of the displacement and speed of the high-speed train and ensure the safe operation of the train.

Claims

1. A high-speed train safe operation control method based on non-repetitive iterative learning, characterized in that: The following steps are involved: Step 1: Based on the repetitive operation mode and non-repetitive characteristics of the train, a high-speed train dynamics model for iterative learning, as well as displacement constraints and speed constraints, is established; According to Newton's law, high-speed trains are subject to a variety of forces during operation, including air resistance f a (·), mechanical resistance f m (·), additional resistance f d (·), and the dynamic model of high-speed train is established as follows: Where t represents time, m(t) is the mass of the train, u(t) represents the control input, i.e., the traction force, s(t) and v(t) represent the displacement and velocity of the train, respectively, which satisfy c a (t), c0(t), c v (t) are the drag coefficients, ω(t) represents the external disturbance; By integrating the iteration index i into the above train dynamics model, the high-speed train dynamics model for iterative learning control is established as follows: Among them, s i (t) and v i (t) represent the displacement and speed of the train during the i-th operation, u i (t) is the control input signal for the i-th operation, m i (t), c 0，i (t), c v，i (t), c a，i (t) is the unknown iterative parameter, ω i (t) is the non-repeating external disturbance in the ith run, f d (·) is the unknown state-dependent continuous function; In order to ensure the running safety of the train, two constraints are imposed on the i-th displacement s i (t) and speed v i (t), that is, the displacement constraints and velocity constraints are as follows: s l (t)≤s i (t)≤s p (t) v l ()≤v i (t)≤v p (t) where s l (t) and s p (t) represent the lower bound and upper bound of the displacement, respectively, v l (t) and v p (t) respectively represent the lower bound and upper bound of the speed constraint, which are flexibly set according to the tracking interval in the operation diagram and the speed limit of the section of the operation line; Step 2: Set the expected reference displacement and reference speed of the high-speed train, and analyze the boundedness of the parameters related to the train operation; According to the operation diagram specified by the railway department, the expected reference displacement and reference speed of the high-speed train are defined as s r (t) and v r (t); Since the train always departs from the same station, the initial values ​​of displacement and speed are the same for each run; that is, the displacement s for any i-th run i (t) and speed v i The initial value of (t) and the displacement s at any j-th run j (t) and speed v j The initial value of (t) is the same, that is, s i (0) = s j (0), v i (0) = v j (0); Furthermore, set the reference displacement s r (t) and reference speed v r The initial values ​​of (t) are equal to the displacement s during the i-th run. i (t) and speed v i The initial value of (t), i.e., s r (0) = s i (0), v r (0) = v i (0); At the same time, from the physical properties of the train, we can know that the train operation related parameters, including the iterative parameter m i (t), c 0，i (t), c v，i (t), c a，i (t), and the non-repeating external disturbance ω i (t), is bounded throughout the run; Step 3: Establish an error conversion mechanism to transform the constrained train operation control problem into an unconstrained form; The displacement error and velocity error are defined as e s，i (t) = s i (t)-s r (t), e v，i (t) = v i (t)-v r (t), according to the displacement constraint and velocity constraint, the displacement error constraint and velocity error constraint are as follows: λ s，l (t)≤e s，i (t)≤λ s，p (t) λ v，l (t)≤e v，i (t)≤λ v，p (t) Among them, λ s，l (t) and λ s，p (t) represent the constraint lower bound and constraint lower bound of displacement error, respectively, λ v，l (t) and λ v，p (t) represent the lower bound and upper bound of the velocity error respectively; In order to relax the restrictions of safety constraints on controller design, the following error conversion mechanism is established to achieve the displacement error e s，i (t) to the unconstrained state x 1，i (t), speed error e v，i (t) to the unconstrained state x 2，i One-to-one mapping of (t); in and is a strictly smoothly increasing function, and Respectively represent their inverse functions; from the above formula, we can get the function and Satisfy the following characteristics: It can be concluded that as long as the unconstrained state x 1，i (t) and x 2，i (t) is bounded, then the displacement error constraint and velocity error constraint must hold; at the same time, when the unconstrained state x 1，i (t) and x 2，i (t) converge to the desired unconstrained state and When the displacement error e s，i (t) and the velocity error e v，i (t) will converge to 0 respectively; For the unconstrained state x 1，i (t) and x 2，i (t) is differentiated and we can get: Integrating the above equation with the train dynamics model for iterative learning, the following unconstrained system is established: The known state-related functions φ1(·), φ2(·), φ3(·), h1(·), and h2(·) are defined as follows: The unconstrained system will be used to design iterative learning control algorithms for high-speed trains; Step 4: Based on the unconstrained system, design a non-repetitive iterative learning control algorithm for high-speed trains, including control laws and parameter learning rules; Define the auxiliary error signal as z i (t) = γ0(x 1，i (t)-x 1，r (t))+(x 2，i (t)-x 2，r (t)), where γ0 represents the controller parameter; according to the Hurwitz stability polynomial theorem, if and only if the irreducible state x 1，i (t) and x 2，i (t) converge to the desired unconstrained state x 1，r (t) and x 2，r (t), the auxiliary error signal z i (t) converges to 0; Based on the unconstrained system in step 3, a non-repeated iterative learning control algorithm for high-speed trains can be designed, including the following control law: And the parameter learning rule: where μ i (t) and η i (t) represents the auxiliary control signal during the i-th operation, represents the parameter estimation at the i-th run, γ0 represents the controller parameter, q0, q l , q4 is the parameter learning gain, ∈0, ∈ l is the parameter of the hyperbolic tangent function, is the projection operation, represents the auxiliary variable, ψ(·) represents the Gaussian basis function of the neural network; In addition, the parameter estimates The initial values ​​are set to in is an arbitrarily small positive real number; Step 5: Build a train operation simulation platform and conduct algorithm testing to obtain the expected parameter values; Step 6: Deploy the high-speed train non-iterative learning control algorithm into the train operation control system, and set the controller parameters and parameter learning gains to the expected parameter values, so as to achieve precise control of the displacement and speed of the high-speed train and ensure the safe operation of the train.

2. A high-speed train safe operation control method based on non-repetitive iterative learning according to claim 1, characterized in that: The step 5 is specifically as follows: A train operation simulation platform is built based on MATLAB simulation software, and the mass of the train in the i-th operation is set to m i (t) = (3.45 + 0.8r) × 10 5 kg, the resistance is c 0，i (t)=-[2977+275sin(0.0037t)r]N, c v，i (t)=-[25.17+2.5sin(0.0037t)r]N·s / m, c a，i (t)=-[0.3864+0.04sin(0.0037t)r]N·s 2 / m 2 , the external disturbance is ω i (t) = -1000w(t)N, where r and w(t) are random numbers between 0 and 1 generated by a computer; the high-speed train non-repetitive iterative learning control algorithm designed in step 4 is tested and verified on a train operation simulation platform; by adjusting the controller parameters and parameter learning gain, the displacement s on the train operation simulation platform is i (t) and speed v i (t) can accurately track the desired reference displacement s respectively r (t) and reference speed v r (t), and the displacement and speed are always within the safe area; specifically, the expected parameter values ​​obtained from the train operation simulation platform are: γ0 = 0.5, γ1 = 20, q0 = 10, q1 = 10 2 q2=10 -3 q3=10 -5 , q4=0.1, ∈0=∈1=∈2=∈3=0.1.

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