An intelligent vehicle tracking control method based on sliding mode control

Abstract

The present invention relates to the establishment of an automotive model containing disturbances, attacks, time delays, and parameter uncertainties, as well as the design of a tracking algorithm. The present invention discloses the modeling of an intelligent vehicle system considering disturbances, attacks, time delays, and parameter uncertainties, as well as the design of a sliding mode tracking algorithm for intelligent vehicles. Its technology includes the modeling of an automotive system considering disturbances, attacks, time delays, and parameter uncertainties, the design of a sliding mode surface, and the proof of sliding mode dynamic stability, the design of a sliding mode controller, and the proof of the reachability of the sliding mode surface. The present invention establishes a dynamic model of an intelligent vehicle with disturbances, attacks, time delays, and parameter uncertainties for an intelligent vehicle system. In view of the system characteristics, a sliding mode controller based on an integral sliding mode surface is designed, and the stability of its control is analyzed and proved. The present invention can effectively solve the problem that the intelligent vehicle system can stably track the desired signal in the presence of disturbances, attacks, time delays, and parameter uncertainties in the system model.

Description

Technical Field

[0001] The present invention designs the establishment of a vehicle model containing disturbances, attacks, time delays, and parameter uncertainties, as well as a tracking algorithm. Background Art

[0002] Intelligent connected vehicles are a typical network control system. In recent years, people's transportation demands have been increasing continuously. Intelligent connected vehicles are becoming a research hotspot due to their advantages of reducing energy consumption, alleviating traffic pressure, and reducing traffic accidents. The main purpose of intelligent connected vehicle control is to make vehicles drive safely at a set desired distance and speed. In actual situations, the system will inevitably encounter interference, or even malicious attacks by hackers, and due to network transmission reasons, there are also factors such as time delays in the actual system. These factors will reduce the system performance and even cause serious accidents. Therefore, how to design a control strategy so that the vehicle can still maintain normal driving to avoid accidents when suffering from the above situations has become an urgent problem to be solved. Regarding hacker attacks, the literature ["Data-Driven FalseData-Injection Attack Design and Detection in Cyber-Physical Systems" (Z. Zhao, Y. Huang, Z. Zhen and Y. Li, IEEE Transactions on Cybernetics, vol. 51, no. 12, pp. 6179-6187, Dec. 2021.)] studied the data-driven false data injection attack design and detection in cyber-physical systems and proposed a data-driven design scheme for undetectable false data injection attacks against cyber-physical systems. Regarding parameter uncertainties and time delays, the literature ["Robust predictive control of a supercavitatingvehicle based on time-delay characteristics and parameter uncertainty" (Y. Han, Z. Xu, H. Guo, Ocean Engineering, Volume 237, 2021.)] studied the time delays, disturbances, and parameter uncertainty problems faced by supercavitating vehicles and designed a robust predictive controller with anti-interference performance. However, although all the above-mentioned literatures have achieved good results in related aspects, there are few studies that consider all factors, which inspired the research work of this patent. Summary of the Invention

[0003] The problem to be solved by the present invention is to establish an automobile model considering disturbances, attacks, time delays, and parameter uncertainties, and to design a sliding mode control tracking algorithm.

[0004] The algorithm adopted by the present invention to solve the above problems is as follows: for an intelligent vehicle system with disturbances, attacks, time delays, and parameter uncertainties, an automobile dynamics model is established; in order to make the system state slide along a predetermined trajectory, an integral sliding surface is designed, and the conditions for the dynamic stability of the sliding mode are given; according to the system characteristics, a sliding mode control strategy is designed and its stability is analyzed.

[0005] Modeling of an intelligent vehicle system considering disturbances, attacks, time delays, and parameter uncertainties, and a sliding mode tracking control algorithm for intelligent vehicles. It includes modeling of an automobile system considering disturbances, attacks, time delays, and parameter uncertainties, design of a sliding surface, proof of the dynamic stability of the sliding mode, design of a sliding mode controller, and proof of the reachability of the sliding surface.

[0006] The establishment of the intelligent vehicle system model under disturbances, attacks, time delays, and parameter uncertainties adds disturbances, attacks, time delays, and parameter uncertainties to the establishment of the original system model.

[0007] The design of the sliding surface and the proof of the dynamic stability of the sliding mode involve designing an integral sliding surface Combining Lyapunov stability theory and linear matrix inequalities, etc., the system stability conditions are given.

[0008] The design of the sliding mode controller and the proof of the reachability of the sliding surface utilize the sliding mode reaching law and Solve to obtain the sliding mode controller, and use Lyapunov stability theory to prove the stability of the designed controller. Description of the Drawings

[0009] Figure 1 It is a schematic structural diagram of the control system of the present invention Detailed Embodiments

[0010] The technical solution of the present invention will be described in detail below with reference to the drawings.

[0011] As Figure 1 shown, the present invention relates to the establishment of an automobile model considering disturbances, attacks, time delays, and parameter uncertainties, and the design of a tracking algorithm. It includes modeling of an automobile system considering disturbances, attacks, time delays, and parameter uncertainties, design of a sliding surface, proof of the dynamic stability of the sliding mode, design of a sliding mode controller, and proof of the reachability of the sliding surface.

[0012] Model Establishment

[0013] Consider a row of n vehicles moving on a horizontal road, where x, v, and a represent the position, speed, and acceleration of each vehicle respectively, and the desired headway of the vehicle is defined as q d , the desired speed is v d , and the desired acceleration is a d , then the desired state vector is:

[0014] x d = [q d , v d , a d T (1)

[0015] The dynamic model of the vehicle is modeled as:

[0016]

[0017] where r is the engine input of the vehicle, and n(v) and e(v,a) are given by the following formulas:

[0018]

[0019] where σ is the specific mass of air, and S, κ, c, m, δ, and q are the cross-sectional area, drag coefficient, mechanical resistance, mass, engine time constant, and engine input of the vehicle respectively, represents the air resistance. Without loss of generality, each vehicle here can be different.

[0020] To facilitate the analysis, the following control law is set using feedback linearization:

[0021]

[0022] Furthermore, we get:

[0023]

[0024] Define the state variable x(t) = [x, v, a] T , and the output vector y(t) = [x, v, a] T . The state-space equation of a single-vehicle system can be written as:

[0025]

[0026] where and

[0027] Using coordinate transformation to move the desired state of the vehicle to zero, we get:

[0028]

[0029] ​where \(x(t)=x(t)-x\) d .

[0030] Adding perturbations, attacks, time delays, and parameter uncertainties, we get:

[0031]

[0032] where \(\Delta A\) is the uncertain parameter term, \(h(t)\) is the perturbation term, and \(H\) is a matrix of appropriate dimension. \(\Delta A\) satisfies \(\Delta A(t)=\Lambda g(t)\Xi\), and the nonlinear term \(g(t)\) satisfies \(g T (t)g(t)\leq I\), and \(d(t)\) satisfies \(0\leq d(t)\lt\infty\). u f (t)=\omega(t)\varphi(x(t),t)\), where \(\omega(t)\) represents the injection pattern of the attack and satisfies \(\|\omega(t)\|\leq\mu\), and \(\varphi(x(t),t)\) represents the system information exploited by the attacker and satisfies \(\|\varphi(x(t),t)\|\leq\Phi(x(t),t)\).

[0033] Sliding mode function design

[0034] Design an integral sliding surface as follows:

[0035]

[0036] where \(K\) represents the sliding mode parameter matrix to be designed and will be solved later; the matrix \(G\) will be designed such that \((GB) -1 exists and \((GB) -1 \gt0\).

[0037] Let We can solve for the following equivalent control law:

[0038] u eq (t)=(K-(GB) -1 G\Delta A(t))x(t)-(GB) -1 GA d x(t - d(t)-u f (t)-(GB) -1 GHh(t)(11)

[0039] Substituting the equivalent control law into the system state equation, we get the following sliding mode dynamics:

[0040]

[0041] where and Proof of sliding mode dynamic stability

[0042] When the perturbation \(h(t) = 0\), there exist a positive definite matrix \(P\gt0\) and a matrix \(K\) that satisfy the following conditions:

[0043]

[0044] Then the sliding mode dynamics is stable. Select the Lyapunov function as:

[0045]

[0046] Derive V(t) along the state trajectory of the sliding mode, and we get:

[0047]

[0048] Let ο(t) = [x(t), x(t - d(t))] T We get:

[0049]

[0050] According to the inequality We can obtain:

[0051] Ω2 ≤ λ m (Ω2)·I < 0 (16)

[0052] where λ m (Ω2) represents the maximum eigenvalue of Ω2. Further, we can obtain:

[0053]

[0054] From Dynkin's formula, we can get:

[0055]

[0056] Let When t → ∞, we get:

[0057]

[0058] According to the definition, when the disturbance h(t) = 0, the sliding mode dynamics is stable.

[0059] For the vehicle system, if there exist a positive definite matrix P, a scalar and an H∞ suppression factor σ > 0, and satisfy the following linear matrix inequality:

[0060]

[0061] where The sliding mode parameter matrix K can be solved by K = ZP. Then the sliding mode dynamics is asymptotically stable.

[0062] Select the function:

[0063]

[0064] Furthermore, we obtain:

[0065]

[0066] Let ξ = [x(t), x(t - d(t)), h(t)] T We get:

[0067]

[0068] where

[0069] Let It can be deduced from the lemma that:

[0070]

[0071] Using the Schur complement theorem, we can obtain:

[0072]

[0073] where Ω4 is given by the following equation:

[0074]

[0075] Further simplify and multiply Ω4 by the diagonal matrix on the left and right and substitute K = ZP -1 into it to get:

[0076]

[0077] The proof is completed.

[0078] Design of the controller and reachability analysis of the sliding mode surface

[0079] The controller is designed as follows:

[0080]

[0081] Next, it is proved that the designed control law can satisfy the reachability of the sliding mode surface.

[0082] For the vehicle system (GB) -1 When > 0, the sliding mode control law can ensure that the system state trajectory converges to the sliding mode surface S(t) = 0 in finite time.

[0083] Select the Lyapunov function as:

[0084]

[0085] Take the derivative of V(t) and substitute it to get:

[0086]

[0087] Furthermore, we obtain:

[0088] ||ω(t)φ(x(t),t)|| - μΦ(x(t),t)sign(S(t)) ≥ 0 (29)

[0089] Then

[0090]

[0091] According to the Lyapunov stability condition, from it can be concluded that the sliding mode control law can ensure that the system state trajectory converges to the sliding mode surface S(t) = 0 in finite time.

Claims

1. An intelligent vehicle tracking control method based on sliding mode control, which considers the tracking control of an intelligent vehicle system with disturbances, attacks, time delays, and parameter uncertainties, is characterized in that: Intelligent vehicle system modeling, sliding mode surface design, proof of sliding mode dynamic stability, sliding mode controller design, and proof of reachability of the sliding mode surface under perturbations, attacks, time delays, and parameter uncertainties. The specific model is as follows: Consider a row of n vehicles moving on a horizontal road, where x, v, and a represent the position, speed, and acceleration of each vehicle respectively. Define the desired spacing between vehicles as q d , the desired speed as v d , and the desired acceleration as a d . Then the desired state vector is: x d = [q d , v d , a d T ​ The dynamic model of the vehicle is modeled as: where r is the engine input of the vehicle, and n(v) and e(v,a) are given by the following formulas: e(v) = 1 / δm where σ is the specific mass of air, and S, κ, c, m, δ, and q are the cross-sectional area, drag coefficient, mechanical resistance, mass, engine time constant, and engine input of the vehicle, respectively, denotes the aerodynamic drag; without loss of generality, each vehicle here can be different. For the convenience of analysis, the following control law is set using feedback linearization: Furthermore, we get: Define the state variable \(x(t)=[x, v, a]\) T , and the output vector \(y(t)=[x, v, a]\) T , then the state - space equation of a single - vehicle system can be written as: Among them and By using coordinate transformation to move the desired state of the vehicle to zero, we obtain: where \(x(t)=x(t)-x\) d , adding disturbances, attacks, time delays, and parameter uncertainties gives: where ΔA is an uncertain parameter term, h(t) is a perturbation term, H is a matrix of appropriate dimension, ΔA satisfies ΔA(t) = Λg(t)Ξ, the nonlinear term g(t) satisfies g T (t)g(t) ≤ I, d(t) satisfies 0 ≤ d(t) < ∞, u f (t) = ω(t)φ(x(t), t), ω(t) represents the injection pattern of the attack and satisfies ||ω(t)|| ≤ μ, φ(x(t), t) represents the system information exploited by the attacker and satisfies ||φ(x(t), t)|| ≤ Φ(x(t), t).

2. The intelligent vehicle tracking control method based on sliding mode control according to claim 1, which is for the intelligent vehicle system modeling with disturbances, attacks, time delays and parameter uncertainties, is characterized in that: The parameter uncertainty ΔA considered in the system satisfies ΔA(t) = Λg(t)Ξ, where Λ and Ξ are known matrices of appropriate dimensions, and the nonlinear term g(t) satisfies g T (t)g(t) ≤ I. The time-delay term d(t) considered in the system satisfies 0 ≤ d(t) < ∞, The attack considered in the system is modeled as u f (t) = ω(t)φ(x(t), t), where ω(t) represents the injection pattern of the attack and φ(x(t), t) represents the system information exploited by the attacker. Here, ω(t) satisfies ||ω(t)|| ≤ μ, and φ(x(t), t) satisfies ||φ(x(t), t)|| ≤ Φ(x(t), t). The perturbation considered in the system is nonlinearly bounded.

3. The intelligent vehicle tracking control method based on sliding mode control, the design of the sliding mode surface and the proof of the dynamic stability of the sliding mode, is characterized in that: The designed integral sliding surface is where K represents the sliding mode parameter matrix to be designed, and the matrix G will be designed such that (GB) -1 exists and (GB) -1 > 0. Combining the Lyapunov stability theorem and linear matrix inequalities, the stability conditions of the sliding surface are obtained.

4. The intelligent vehicle tracking control method based on sliding mode control, the design of the sliding mode controller and the proof of the reachability of the sliding mode surface according to claim 1, characterized in that: The designed sliding mode controller is \(u(t)=(K - (GB) -1 G\Delta A(t))x(t)-\mu\varPhi(x(t),t)\text{sign}(S(t))-\eta(GB) -1 \text{sign}(S(t))-(GB) -1 GHh(t)-(GB) -1 GA d x(t - d(t)), and then the Lyapunov stability theorem is used to prove the stability of the designed controller.

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