A method and system for robust control of heterogeneous vehicle platoon under DoS attack

Abstract

A robust control method and system for heterogeneous vehicle platoons under DoS attacks is proposed. The method includes: constructing a discrete local disturbance observer that relies only on the vehicle's own acceleration measurement and nominal dynamics term to estimate the total disturbance in real time for each following vehicle; using a two-mode Markov chain to describe the random switching state of the communication link under a DoS attack; constructing an augmented state vector and establishing a mode-dependent augmented closed-loop system by combining Markov mode transition characteristics; selecting Lyapunov weight matrices for different communication modes to construct mode-dependent Lyapunov functions; deriving sufficient conditions for the stochastic exponential stability of the augmented closed-loop system and satisfying dissipative performance by combining a strict dissipative supply rate derivation, and giving sufficient conditions for the chordal stability of the finite vehicle platoon; and jointly solving for the control gain of the normal communication mode, the control gain of the DoS attack mode, the preceding vehicle cooperation gain, and the disturbance observer gain.

Description

Technical Field

[0001] This invention relates to the fields of intelligent transportation and vehicle engineering technology, specifically to a robust control method and system for heterogeneous vehicle queues under DoS attacks. Background Technology

[0002] Vehicle platooning control is a key technology in intelligent transportation systems and connected autonomous driving. It enables a lead vehicle and multiple following vehicles to travel at the desired speed and spacing through inter-vehicle communication and cooperative control, thereby improving road traffic efficiency, reducing energy consumption and improving traffic safety.

[0003] In a platoon of connected vehicles, following vehicles typically need to obtain status information such as the position, speed, acceleration, and control input of the preceding or lead vehicle via a forward communication link, and then combine this information with their own vehicle's status to form coordinated control input. This control method improves the platoon's response speed, but it also tightly couples vehicle dynamics with the wireless communication network.

[0004] Real-world communication networks are susceptible to packet loss, random latency, signal interference, and denial-of-service (DoS) attacks. DoS attacks, in particular, disrupt communication channels, preventing vehicles from receiving timely information from the vehicle ahead. This causes intermittent failures in the preceding vehicle's coordination, resulting in the vehicle control law switching between normal and disrupted communication states. If the controller does not account for this switching characteristic, transient errors in the vehicle platoon may be amplified, potentially even compromising platoon stability.

[0005] On the other hand, actual vehicle platoons typically consist of different types of vehicles, each with variations in mass, damping, air resistance, rolling resistance, transmission parameters, and actuator time constants. These heterogeneous vehicle parameters, combined with road disturbances, model mismatch, and unmodeled inputs, generate integrated disturbances within the vehicle platoon that propagate along the platoon's direction.

[0006] Existing research on vehicle platooning anti-DoS (Denial of Service) and robust control typically addresses communication failures, vehicle heterogeneity, and external disturbances separately. There is a lack of control methods that integrate DoS random switching, vehicle heterogeneous parameters, disturbance observation errors, and mode-dependent controllers into a single closed-loop model. Furthermore, controllers and disturbance observers often employ step-by-step tuning, making it difficult to guarantee the consistency between closed-loop dissipation performance and error propagation performance. Summary of the Invention

[0007] To address the aforementioned problems, a robust control method and system for heterogeneous vehicle platoons under DoS attacks is proposed. By employing a two-modal Markov chain to describe the stochastic switching process between normal communication and DoS attacks, vehicle heterogeneous parameter perturbations and external disturbances are uniformly grouped into a total disturbance. A local disturbance observer relying solely on the vehicle's own acceleration information is constructed, and mode-dependent control laws are designed for both normal communication mode and DoS attack mode. This invention can ensure stable platoon following even when preceding vehicle coordination information fails randomly, vehicle parameters exhibit heterogeneity, and unknown disturbances affect the vehicle system. It also provides solvable performance constraints on disturbance input and error propagation.

[0008] To achieve the above objectives, the present invention includes the following steps:

[0009] Firstly, a robust control method for heterogeneous vehicle queues under DoS attacks includes the following steps:

[0010] S1. Establish a discrete-time model for heterogeneous vehicle queues;

[0011] S2. For the total disturbance of each following vehicle, construct a discrete local disturbance observer that relies only on the vehicle's own acceleration measurement and nominal dynamics term to estimate the total disturbance in real time.

[0012] S3. A two-modal Markov chain is used to describe the random switching state of the communication link under a DoS attack.

[0013] S4. Construct an augmented state vector from the following error state of the vehicle, the local coordination state of the preceding vehicle, the disturbance observation error of the vehicle and the disturbance observation error of the preceding vehicle, and combine it with the Markov mode transfer characteristics to establish a mode-dependent augmented closed-loop system.

[0014] S5. Select Lyapunov weight matrices for different communication modes and construct mode-dependent Lyapunov functions; combine with the strict dissipative supply rate derivation to obtain sufficient conditions for the stochastic exponential stability of the augmented closed-loop system and satisfy dissipative performance, and further give sufficient conditions for the chordal stability of the finite vehicle queue.

[0015] S6. Based on the LMI synthesis conditions of stochastic exponential stability and strict dissipation, and combined with the observer pole constraint, jointly solve the control gain of normal communication mode, control gain of DoS attack mode, cooperative gain of the preceding vehicle, and gain of the disturbance observer.

[0016] Preferably, in S2, the updates to the internal state and perturbation estimate of the local perturbation observer include:

[0017] The total disturbance estimate is obtained by combining the observer's internal state and the vehicle's acceleration after observer gain correction. The observer's internal state is recursively updated based on the internal state at the previous sampling time, as well as the difference between the nominal acceleration dynamics term, the vehicle's execution input, and the total disturbance estimate.

[0018] As a preferred embodiment, in S2, the disturbance observation errors of both the vehicle and the preceding vehicle are jointly determined by the observation error at the previous sampling time and the total disturbance change at adjacent sampling times; by adjusting the observer gain and combining it with the sampling period, the convergence speed of the observation error subsystem is constrained.

[0019] Preferably, S2 includes:

[0020] The following pole constraints are set to constrain the convergence rate of the observation error subsystem:

[0021]

[0022] in, Indicates the sampling period. This represents the observer gain; both the lower and upper bounds of the pole constraints are preset scalars, satisfying that the lower bound is greater than 0, the upper bound is less than 1, and the lower bound is less than the upper bound.

[0023] Preferably, S4 includes a control law related to the communication mode design:

[0024] The control input consists of the vehicle's following error feedback item and the preceding vehicle's coordination feedback item. When communication is normal, both types of feedback participate in the control. During a DoS attack, the preceding vehicle's coordination feedback item automatically exits, and only the vehicle's error feedback is retained to avoid using unavailable preceding vehicle information.

[0025] As a preferred embodiment, in S4, constructing the augmented closed-loop system includes: defining the augmented state as consisting of the following error state of the vehicle itself, the local coordination state of the preceding vehicle, the disturbance observation error of the vehicle itself, and the disturbance observation error of the preceding vehicle, while taking the auxiliary control input of the preceding vehicle and the total disturbance change as external inputs; the augmented state at the next sampling moment is evolved from the current augmented state through the closed-loop system matrix corresponding to the communication mode, and the external input under the action of the external input matrix is ​​superimposed.

[0026] As a preferred embodiment, S5 includes:

[0027] S51. Define the stochastic exponential stability objective as follows: when there is no external input, the mathematical expectation of the energy of the closed-loop augmented state decays exponentially with increasing sampling time.

[0028] The strict dissipation performance is defined to satisfy the following condition: within a given finite time range, the expected cumulative energy of the carousel error output should be less than the upper bound of the expected cumulative energy of the external input after weighting by the dissipation performance index; where Lyapunov weight matrices are selected for different communication modes to measure the augmented state energy.

[0029] S52. Extract the spacing error and velocity error from the augmented state as the following error output; form a weighted performance output for dissipation performance evaluation by weighting the output;

[0030] S53. Define the supply rate: using the weighted performance output energy as the term to be suppressed and the external input energy as the allowable input term, the difference between the two is used to evaluate the augmented closed-loop system's ability to attenuate external disturbances.

[0031] S54. Based on the closed-loop augmented system and the supply rate, obtain sufficient conditions for the closed-loop augmented system to be stable and to satisfy dissipation performance.

[0032] As a preferred option, S5 also includes:

[0033] S55. Supplementary finite vehicle queue chord stability constraint: When the initial augmented state is zero and the external input energy satisfies a given upper bound, the following error energy of the next vehicle shall not exceed the error output energy of the previous vehicle.

[0034] Secondly, a robust control system for heterogeneous vehicle queuing under DoS attacks includes:

[0035] The vehicle dynamics modeling module is used to establish discrete-time models of heterogeneous vehicle platoons.

[0036] The local disturbance observer module is used to construct a discrete local disturbance observer that relies only on the vehicle's own acceleration measurement and nominal dynamics term for the total disturbance of each following vehicle, and to estimate the total disturbance in real time.

[0037] The DoS attack modeling module is used to describe the random switching state of communication links under a DoS attack using a two-modal Markov chain.

[0038] The augmented closed-loop system module is used to construct an augmented state vector by unifying the following error state of the vehicle, the local coordination state of the preceding vehicle, the disturbance observation error of the vehicle and the disturbance observation error of the preceding vehicle, and to establish a mode-dependent augmented closed-loop system by combining the Markov mode transfer characteristics.

[0039] The stability analysis module is used to select Lyapunov weight matrices for different communication modes and construct mode-dependent Lyapunov functions; combined with the rigorous dissipative supply rate derivation, sufficient conditions for the stochastic exponential stability of the augmented closed-loop system and satisfaction of dissipative performance are obtained, and sufficient conditions for the chordal stability of the finite vehicle queue are further given.

[0040] The LMI solver module is used to solve the LMI synthesis conditions for stochastic exponential stability and strict dissipation, and, in conjunction with the observer pole constraint, jointly solves the control gain of normal communication mode, the control gain of DoS attack mode, the cooperative gain of the preceding vehicle, and the gain of the disturbance observer.

[0041] The aforementioned robust control system for heterogeneous vehicle queues under DoS attacks is used to implement the robust control method and steps for heterogeneous vehicle queues under DoS attacks as described in the first aspect.

[0042] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0043] 1. Unlike traditional technologies that separately address DoS communication failures, vehicle heterogeneous disturbances, disturbance observation compensation, and controller gain design, this invention adopts an integrated control technology solution of "Markov chain communication mode modeling + local disturbance observer + LMI joint solution". This allows the control gain, leading vehicle cooperative gain, and disturbance observer gain under normal communication mode and DoS attack mode to be jointly determined within the same augmented closed-loop system, and under the same stochastic exponential stability and strict dissipation constraints. Furthermore, it analyzes the error propagation characteristics through the finite vehicle queue chord stability criterion, thereby avoiding the inconsistency between control performance and disturbance observation performance caused by step-by-step design. This enables the vehicle queue to maintain stable car following even when stochastic DoS attacks, vehicle parameter heterogeneity, and external disturbances coexist, and suppresses the propagation of car following error along the queue.

[0044] 2. Unlike traditional technologies where control laws or disturbance compensation rely on the communication information of the preceding vehicle and are prone to reduced control effectiveness during DoS attacks due to the unavailability of the preceding vehicle's status, this invention employs a local disturbance observer that relies solely on the vehicle's own acceleration information and nominal dynamics terms. It also combines this with a mode-dependent control law designed for both normal communication mode and DoS attack mode. This allows the vehicle to improve its car-following response capability by utilizing the preceding vehicle's cooperative state when communication is normal, and to allow the preceding vehicle's cooperative term to exit the control law when a DoS attack renders the preceding vehicle's information unavailable. Simultaneously, it maintains continuous operation of disturbance estimation and compensation for the vehicle, thereby reducing the risk of transient error amplification caused by random communication interruptions and improving the tolerance of heterogeneous vehicle platoons to DoS attacks and combined disturbances.

[0045] 3. A Markov chain is used to describe the communication mode switching caused by a DoS attack, enabling the controller to switch between two modes: normal communication and attack failure. The local disturbance observer only relies on the information of the vehicle itself and can continue to compensate for the overall disturbance when the communication of the preceding vehicle is blocked. The controller and the observer are jointly solved through LMI to avoid performance inconsistencies caused by step-by-step design. Even when random DoS attacks, heterogeneous vehicle parameters, and external disturbances coexist, the vehicle platoon can still maintain stable following and has good anti-disturbance performance and attack tolerance. Attached Figure Description

[0046] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0047] Figure 2 This is a DoS mode switching sequence diagram for the first following vehicle in Embodiment 1 of the present invention;

[0048] Figure 3 This is a closed-loop transient response diagram within a typical maneuvering window of Embodiment 1 of the present invention, wherein, Figure 3 (a) Input and acceleration for the navigator vehicle Figure 3 (b) represents the distance error between each following vehicle. Figure 3 (c) represents the speed error of each following vehicle. Figure 3 (d) represents the acceleration of each following vehicle;

[0049] Figure 4 This is a magnified view of the final error response and error envelope diagram of Embodiment 1 of the present invention.

[0050] Figure 5 This is a graph showing the energy ratio analysis of finite vehicle queuing errors in Embodiment 1 of the present invention.

[0051] Figure 6 This is a DoS handover and disturbance observer response diagram of Embodiment 1 of the present invention;

[0052] Figure 7 This is a comparison diagram of the full formation error envelope under different operating conditions in Embodiment 1 of the present invention. Detailed Implementation

[0053] To make the technical means, inventive features, objectives, and effects of the invention readily understandable, the invention is further described below with reference to specific illustrations. However, the invention is not limited to the embodiments described below.

[0054] It should be noted that the structures, proportions, sizes, etc., illustrated in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0055] Example 1:

[0056] like Figure 1 As shown, the method flow of the present invention includes discrete-time modeling of heterogeneous vehicle queues, construction of local disturbance observers, DoS communication mode modeling, design of mode-dependent control laws, establishment of stability and string stability criteria, and joint solution of LMI, thereby forming a complete control flow from system modeling to controller and observer gain solution.

[0057] A robust control method for heterogeneous vehicle queues under DoS attacks includes the following steps:

[0058] S1. Establish a discrete-time model for heterogeneous vehicle queues; specifically including:

[0059] S11, Consider the lead car numbered 0 and the cars numbered 1 to 1. The longitudinal convoy of following vehicles, the first The following timing strategy is adopted for the following vehicles:

[0060]

[0061] in, Let r represent the vehicle length, r represent the stationary safety distance, and h represent the time-distance constant. Indicates the first A following vehicle The speed of time.

[0062] S12, Definition of the The following distance and speed errors of the following vehicles are as follows:

[0063]

[0064]

[0065] in, Indicates the first The location of the car and These represent the position and speed of the vehicle in front, respectively.

[0066] S13. According to the discrete kinematics relationship, the spacing error and velocity error satisfy:

[0067]

[0068]

[0069] in, Indicates the sampling period. Indicates the first The following vehicle accelerates.

[0070] S14, No. The continuous-time longitudinal dynamics model of the following vehicle is as follows:

[0071]

[0072]

[0073]

[0074] in, For vehicle quality, For transmission ratio, The actual driving force is g, where g is the acceleration due to gravity. The rolling resistance coefficient, The damping coefficient is... The air drag coefficient, For the actuator time constant, Input is executed for the vehicle.

[0075] S15. Combine parameter mismatch, rolling resistance variation, air resistance variation, and unmodeled external inputs into a total disturbance. The acceleration channel is written as:

[0076]

[0077] in, Indicates by the first The nominal acceleration dynamics term is determined by the speed and acceleration of the following vehicle. Indicates the first The input coefficients in the acceleration channel are used to execute the input of the vehicle following the vehicle. Indicates the first The following vehicle executes the input. This represents the total disturbance resulting from vehicle parameter mismatch, drag variation, and the aggregation of unmodeled external inputs.

[0078] S16. Applying forward Euler discretization to the above acceleration channel formula, we obtain:

[0079]

[0080] in, , and They are respectively , and exist Discrete values ​​at time points.

[0081] S17. The vehicle's underlying actuator is considered as a first-order acceleration tracking element capable of nominal inverse compensation, controlled by auxiliary commands. and disturbance estimates Generate actual actuator inputs such that the nominal acceleration channel satisfies:

[0082]

[0083] Define the perturbation observation error We can obtain:

[0084]

[0085] in, Indicates the first Assist commands for following vehicles, Indicates the total disturbance The estimated value, This represents the nominal first-order acceleration tracking time constant. This indicates the error in perturbation observation.

[0086] S18. To enable the auxiliary control input to have first-order execution characteristics, a filtering instruction is introduced. :

[0087]

[0088] in, This is the auxiliary control input to be designed.

[0089] S19. Define the following vehicle following error state and local cooperation state as follows:

[0090]

[0091]

[0092] in, Indicates the first The following vehicle's following error status is composed of distance error, speed error, acceleration, and auxiliary commands. This represents a local cooperative state consisting of acceleration and auxiliary commands.

[0093] Make the preceding vehicle coordinated. ,when When =1, Right now It consists of the navigator's acceleration and its filtering commands; corresponding to the auxiliary input of the preceding vehicle. The movement command is given by the navigator. Then the... The discrete model of the following vehicle is:

[0094]

[0095] Among them, matrix , , and They are respectively:

[0096]

[0097]

[0098]

[0099] The preceding vehicle's partial condition meets the following requirements:

[0100]

[0101] in, , and They are respectively:

[0102]

[0103]

[0104] S2. For the total disturbance of each following vehicle, construct a discrete local disturbance observer that relies only on the vehicle's own acceleration measurement and nominal dynamics term to estimate the total disturbance in real time.

[0105] S21, Regarding the total disturbance Construct the following discrete local perturbation observer:

[0106]

[0107]

[0108] The aforementioned local disturbance observer indicates that the total disturbance estimate is obtained by combining the observer's internal state and the vehicle's acceleration after observer gain correction; the observer's internal state is recursively updated based on the internal state at the previous sampling time, as well as the difference between the nominal acceleration dynamics term, the vehicle's execution input, and the total disturbance estimate.

[0109] in, Indicates the first A following vehicle The total disturbance estimate at time 10:00. This represents the internal state variables of the local disturbance observer. Indicates the gain of the observer to be designed. Indicates the first A following vehicle The acceleration at any given moment. This observer relies only on the vehicle's own acceleration and nominal dynamics, and does not depend on communication information from the vehicle ahead. Therefore, it can still operate even when a DoS attack renders information about the vehicle ahead unavailable.

[0110] S22. Define observation error The recursive relationship of observation error can be obtained as follows:

[0111]

[0112]

[0113] The above recursive relationship of observation error indicates that the disturbance observation error of both the current vehicle and the preceding vehicle is determined by the observation error at the previous sampling time and the total disturbance change at adjacent sampling times. By adjusting the observer gain and combining it with the sampling period, the convergence speed of the observation error subsystem can be constrained.

[0114] in, , These two values ​​represent the changes in the total disturbance of the current vehicle and the preceding vehicle between adjacent sampling times, respectively. To constrain the convergence rate of the observation error subsystem, the following pole constraints are set:

[0115]

[0116] The lower bound and upper bound of the pole constraint are both preset scalars, which satisfy the condition that the lower bound is greater than 0 and the upper bound is less than 1, and the lower bound is less than the upper bound.

[0117] The technical advantage of S2 lies in: constructing a system that relies solely on the vehicle's own acceleration. And the local perturbation observer of the nominal dynamics term, for the total perturbation Real-time estimation is performed, and observation errors are controlled through pole constraints. The convergence speed is limited to a preset range; thus, when a DoS attack makes the information of the preceding vehicle unavailable, the information of the current vehicle can still be used to complete the disturbance compensation, reduce the impact of parameter mismatch, drag change and unmodeled input on the car-following error, and provide a stable local state basis for the subsequent mode-dependent control law.

[0118] S3. A two-modal Markov chain is used to describe the random switching state of the communication link under a DoS attack.

[0119] S31. A two-modal Markov chain is used to describe the communication link state. (Note: The original text contains some inconsistencies and unclear formatting. A more accurate translation would require the full context.) For the first The communication link mode in which a following vehicle receives information from the vehicle in front is then... ,in This indicates that communication is normal. This indicates a DoS attack.

[0120] S32, the communication mode transition probability satisfies:

[0121]

[0122] The above transition probability relationship means that when the communication link is currently in a certain mode, the probability of switching to any mode at the next sampling time is determined by the corresponding transition probability; where mode 1 corresponds to normal communication and mode 0 corresponds to a DoS attack.

[0123] The corresponding transition probability matrix is:

[0124]

[0125] This Markov model is used to describe the stochastic bursts and state-dependent recovery characteristics of DoS attacks, where Indicates the current sampling time The communication link mode in which it is located, Indicates the next sampling time The communication link mode in which it is located, and ; Indicates the communication mode by Transferred to The probability, This represents the probability of maintaining normal communication. This indicates the probability of a normal communication session turning into a DoS attack. This represents the probability of recovering normal communication after a DoS attack. Indicates the probability of a DoS attack persisting; A larger value indicates that normal communication is more likely to continue. The larger the value, the longer the DoS attack lasts.

[0126] The technical advantage of S3 lies in transforming the random switching of communication links between normal communication and DoS attacks into a system where... The described state-related transition process not only indicates whether the previous vehicle's information has been lost, but also the probability of attack persistence and recovery; this processing enables subsequent stability criteria to be based on... and It distinguishes between short-term, occasional packet loss and sustained DoS attacks, thereby reducing the conservatism of controllers designed based on worst-case scenarios and improving adaptability to random, sudden communication failures.

[0127] S4. Construct an augmented state vector from the following error state of the vehicle, the local coordination state of the preceding vehicle, the disturbance observation error of the vehicle and the disturbance observation error of the preceding vehicle, and combine it with the Markov mode transfer characteristics to establish a mode-dependent augmented closed-loop system.

[0128] S41. For both normal communication and DoS attack modes, the following mode-related control law is adopted:

[0129]

[0130] The above-mentioned mode-related control law states that the control input consists of the vehicle's following error feedback term and the preceding vehicle's cooperative feedback term. When communication is normal, both types of feedback participate in the control. During a DoS attack, the preceding vehicle's cooperative feedback term automatically exits, and only the vehicle's error feedback is retained, thereby avoiding the use of unavailable preceding vehicle information.

[0131] in, hour , hour ; This represents the control gain for the vehicle's following error state under normal communication mode. This represents the control gain for the vehicle's following error state under the DoS attack mode. This represents the gain of the preceding vehicle's cooperative state. In normal communication mode, the control input utilizes both the vehicle's error state and the preceding vehicle's cooperative state; in DoS attack mode, the preceding vehicle's cooperative term is removed from the control law.

[0132] S42. Define the augmented state and external input as follows:

[0133]

[0134]

[0135] The above-mentioned augmented state and external input definitions mean that the vehicle following error, the preceding vehicle's coordination state, and the disturbance observation errors of the vehicle and the preceding vehicle are uniformly regarded as the closed-loop analysis state. At the same time, the preceding vehicle's auxiliary control input and the total disturbance change are regarded as external inputs, so as to uniformly characterize the impact of communication failure and disturbance change on the closed-loop system.

[0136] in, This represents the augmented state vector composed of the following error state of the current vehicle, the local coordination state of the preceding vehicle, the disturbance observation error of the current vehicle, and the disturbance observation error of the preceding vehicle. Represents the external input vector. Indicates the auxiliary control input for the front vehicle. and These represent the total disturbance changes for the vehicle in question and the vehicle in front of it, respectively.

[0137] S43. The following augmented closed-loop system is obtained from the discrete model of the i-th following vehicle, the local state satisfaction relation of the preceding vehicle, and the recursive relation of the observation error:

[0138]

[0139] The above-mentioned augmented closed-loop system indicates that the augmented state at the next sampling moment is evolved from the current augmented state through the closed-loop system matrix corresponding to the communication mode, and is superimposed with the changes in the preceding vehicle input and disturbance under the action of the external input matrix; therefore, this model can simultaneously describe the coupling effect of DoS mode switching, vehicle following dynamics and disturbance observation error.

[0140] Among them, for ,definition:

[0141]

[0142]

[0143] in, Indicates the communication mode index. Representing modes The following vehicle's following error state control gain, , and These are all intermediate matrices used to construct the closed-loop system matrix.

[0144] Closed-loop system matrix and They are respectively:

[0145]

[0146]

[0147] in, Representing modes The closed-loop system matrix below, This represents the external input matrix.

[0148] The technical advantage of S4 lies in: mode-dependent control laws in When introducing the preceding vehicle coordination state ,exist The system automatically filters out unavailable preceding vehicle coordination terms while maintaining closed-loop control using the vehicle's own error state and disturbance observation compensation. The augmented closed-loop system unifies following error, preceding vehicle coordination state, observation error, and disturbance changes into a unified whole. and This allows for the joint analysis of DoS random switching, disturbance estimation error, and vehicle following dynamics within the same matrix model, providing a structured model for subsequent LMI solutions.

[0149] S5. Select Lyapunov weight matrices for different communication modes and construct mode-dependent Lyapunov functions; combine with the strict dissipative supply rate derivation to obtain sufficient conditions for the stochastic exponential stability of the augmented closed-loop system and satisfy dissipative performance, and further give sufficient conditions for the chordal stability of the finite vehicle queue.

[0150] Furthermore, the stability, dissipation, and string stability analysis in S5 includes the following specific steps:

[0151] S51. Regarding the above-mentioned closed-loop augmentation system, the control objective of the present invention is:

[0152]

[0153] The aforementioned stochastic exponential stability objective states that, in the absence of external input, the mathematical expectation of the closed-loop augmented state energy decays exponentially with increasing sampling time, thus demonstrating that the vehicle queue can remain stable under stochastic DoS mode switching.

[0154] when When the value is not zero, the closed-loop system satisfies the following strict dissipation performance:

[0155]

[0156] The above strict dissipative performance condition means that, within a given finite time range, the expected cumulative energy of the car-following error output should be less than the upper bound of the expected cumulative energy of the external input after being weighted by the dissipative performance index, thereby constraining the influence of external disturbances and the input from the preceding vehicle on the car-following error.

[0157] in, Represents the mathematical expectation. Represents positive numbers. Represents the exponential decay coefficient. Indicates a finite-time terminal. This indicates the dissipation performance index.

[0158] The Lyapunov function is constructed as follows:

[0159]

[0160] The Lyapunov function described above indicates that weight matrices are selected for different communication modes to measure the energy of the augmented state; different weights are used for the normal communication and DoS attack states to reflect the impact of communication state changes on closed-loop stability.

[0161] The modal correlation weight matrix is ​​selected in the following block format:

[0162]

[0163]

[0164] in, and These represent the Lyapunov weight matrices corresponding to the normal communication mode and the DoS attack mode, respectively. , , , and The positive definite matrix to be found

[0165] S52. Define the following for the following cat-following error output and weighted performance output:

[0166]

[0167]

[0168] The above output definition means that: first, the spacing error and velocity error are extracted from the augmented state as the following error output, and then a weighted output for dissipation performance evaluation is formed through the output weight.

[0169] in, This represents the car-following error output vector. This represents the weighted performance output vector. Indicates the output matrix. This indicates the output weighting coefficient.

[0170] S53, Define the supply ratio matrix The supply rate is as follows:

[0171]

[0172]

[0173] The aforementioned supply rate means that the weighted performance output energy is used as the term to be suppressed, and the external input energy is used as the allowable input term. The difference between the two is used to evaluate the closed-loop system's ability to attenuate external disturbances.

[0174] in, It is a dissipation performance index used to adjust the weight of external input energy in the supply rate.

[0175] S54. Based on the above closed-loop augmented system and supply rate, the sufficient condition for the closed-loop augmented system to be stable and satisfy strict dissipation performance is:

[0176] Given scalar >0 and scalar ,1> >0, if a positive definite matrix exists >0、 >0、 >0、 >0、 >0, and the matrix , , And L makes for any All of the following are available:

[0177]

[0178] in:

[0179]

[0180]

[0181] in, Represents the closed-loop system matrix and external input matrix The augmented matrix formed by splicing This represents the Lyapunov weight matrix of the next mode obtained by weighting according to the Markov transition probabilities. and Representing the current mode The probability of transitioning to mode 1 and mode 0.

[0182] Where I represents the dimension-matched identity matrix, and the symbol * denotes the transpose of the elements at symmetric positions along the diagonal of the matrix. Simultaneously, if the observer poles satisfy the above pole constraints, then the closed-loop augmented system is stochastically exponentially stable and satisfies strict dissipative performance, with the performance index being: The above sufficient stability condition is proved as follows:

[0183] The above sufficient condition means that as long as the weight matrix, control gain and observer gain that satisfy the positive definiteness requirement can be obtained, and the matrix inequalities under each communication mode are valid, the closed-loop system can be guaranteed to be stable under random DoS switching and meet the preset disturbance attenuation performance.

[0184] The technical advantage of S5 lies in: utilizing the modality-related Lyapunov weight matrix. With a strict dissipative supply rate, the DoS attack persistence / recovery probability in S3 and the closed-loop matrix obtained in S4 are jointly incorporated into the stability criterion. In the vehicle platoon control scenario, this processing not only characterizes general random switching, but also transforms the impact of the availability of the preceding vehicle's information on the cooperative control term into a solvable stability constraint. This simultaneously constrains the stochastic exponential stability, the attenuation performance of external disturbance energy to the car-following error output, and the chord stability of the finite vehicle platoon, avoiding the problem of only verifying the stability of a single vehicle while ignoring the problem of error amplification along the platoon.

[0185] Define a vector:

[0186]

[0187] When there is no external input, that is Then, from the above closed-loop augmented system, we can obtain:

[0188]

[0189] From the Markov transition probability, we can obtain:

[0190]

[0191] Therefore, we can conclude that:

[0192]

[0193] Furthermore, it can be deduced that:

[0194]

[0195] make , We can obtain:

[0196]

[0197] Combining the above inequalities, we can obtain the aforementioned stochastic exponential stability control objective. Therefore, the closed-loop augmented system is stochastic exponentially stable when there is no external input.

[0198] When there is external input, that is When the integer is not 0, combining the above linear matrix inequality conditions, we can obtain:

[0199]

[0200]

[0201] Translate the above equation from Accumulate to And consider zero initial conditions and The formula can be obtained. Then the closed-loop augmented system satisfies strict dissipation performance.

[0202] S55. Furthermore, for a finite vehicle queue, if the initial augmented state satisfies And the external input energy satisfies:

[0203]

[0204] The above finite vehicle queue condition means that when the external input energy meets a given upper bound, the following error energy of the next vehicle does not exceed the error output energy of the previous vehicle; therefore, the error will not be amplified when it propagates backward along the vehicle queue, thus satisfying the string stability requirement of the finite vehicle queue.

[0205] S6. Based on the LMI synthesis conditions of stochastic exponential stability and strict dissipation, and combined with the observer pole constraint, jointly solve the control gain of normal communication mode, control gain of DoS attack mode, cooperative gain of the preceding vehicle, and gain of the disturbance observer.

[0206] In S6, the above sufficient conditions are linearized to decouple the mutually coupled terms to be solved, and the controller gain matrix and disturbance observer gain are derived.

[0207] S61. Applying Schul's complement lemma to the above sufficient conditions, we can obtain the following equivalent matrix inequalities:

[0208]

[0209] in:

[0210]

[0211] S62. Multiply both sides of the above equivalent matrix inequality by the following block diagonal matrix. and its transpose:

[0212]

[0213] And define:

[0214]

[0215]

[0216] in, , , , and A positive definite matrix , , , and The corresponding inverse matrix variable, , , and This is the variable substitution matrix used to linearize the controller gain and observer gain.

[0217] S63, Note , , and order Defined in the following block format:

[0218]

[0219] Then we can obtain the following linear matrix inequality:

[0220]

[0221] in Depend on , , , and output matrix The composition is as follows:

[0222]

[0223] in for:

[0224]

[0225] According to state components , , , and external input The complete block structure is as follows:

[0226]

[0227] S64. Meanwhile, the observer pole constraint, after variable substitution, can be written as the following linear constraint:

[0228]

[0229] S65. Solve the matrix using the above linear matrix inequalities and linear constraints. , , , , , , , and Then the gains of the controller and the disturbance observer are:

[0230]

[0231]

[0232] S66. At each sampling time k, obtain the spacing error, speed error, acceleration, and auxiliary commands of the i-th following vehicle, and based on the current communication mode... Determine whether the preceding vehicle's coordination status is available; simultaneously update the total disturbance estimate using the local disturbance observer, and then calculate the auxiliary control input based on the mode-dependent control law in the formula. Update filter command And the vehicle execution input is generated by the nominal reverse compensation relationship. This enables robust car-following control of the i-th following vehicle.

[0233] Example 2:

[0234] This embodiment considers a heterogeneous vehicle platoon consisting of one lead vehicle and four follower vehicles. The total simulation duration is 120 seconds, and the sampling period is... Time interval constant stationary safe distance Vehicle length Expected time constant The four following vehicles are subjected to different parameters in terms of mass, damping, transmission parameters, and actuator time constant, and the perturbations are superimposed.

[0235] The baseline DoS condition adopts , , , Strong DoS conditions adopt , , , LMI solution parameters are taken , , The observer pole constraint interval is (0.10, 0.50).

[0236] like Figure 2 As shown, taking the first following vehicle as an example, the communication link randomly switches between normal communication state and DoS attack state, and the attack segment is distributed in short time and intermittently, indicating that the established two-modal Markov chain can characterize the random burst and state recovery characteristics of DoS attack.

[0237] The normal mode gain is obtained by solving the linear matrix inequalities. Attack mode gain Forward vehicle cooperative gain Observer gain Corresponding observer poles .

[0238] Navigation vehicle auxiliary input A smooth pulse signal with a half-cosine transition segment is used to make the navigator undergo multiple acceleration, constant speed and deceleration switching, and the transition is continuous at the start and end of each maneuver window.

[0239] like Figure 3As shown, within a typical maneuvering window, after the input and acceleration of the lead vehicle change smoothly, the spacing error, speed error, and acceleration response of each following vehicle remain bounded and gradually decrease, indicating that the mode-dependent control law can maintain stable platoon following during vehicle maneuvers.

[0240] Under the baseline DoS condition, the average DoS percentage of the communication link is approximately 1.15%. Taking the first following vehicle as an example, its attack segment consists of 113 segments, with an average duration of approximately 0.0108 seconds and a maximum duration of approximately 0.03 seconds. Simulation results show that under this short-term random communication failure condition, the closed-loop error response still maintains a decaying trend.

[0241] In the final recovery interval Within the simulation, the spacing and speed errors of each following vehicle converged to near zero, with the maximum spacing error at the end of the simulation being 5.85 × The peak velocity error in the final stage is 1.20× .

[0242] like Figure 4 As shown, the final error response and its local amplification results indicate that the distance and speed errors of each following vehicle converge to near zero within the recovery interval, and there is no phenomenon of continuous amplification along the queue direction.

[0243] In the simulation of string stability trend, under the condition of zero initial formation error, the spacing error ℓ between adjacent vehicles at 2 / 1, 3 / 2, and 4 / 3 is... The ratios were 0.9599, 0.9537, and 0.9780, respectively, with a speed error of ℓ. The ratios were 0.9526, 0.9600 and 0.9633, respectively, all less than 1, indicating that the error does not amplify when propagating backward along the queue in the limited vehicle queue.

[0244] like Figure 5 As shown, the error energy ratios of the finite vehicle queues are all less than 1, indicating that the energy of the spacing error and speed error between adjacent vehicles does not amplify when propagating backward along the queue. From a numerical perspective, this demonstrates that the error in the finite vehicle queue exhibits non-amplified string stability when propagating backward along the queue.

[0245] To verify the compensation effect of the local disturbance observer, two scenarios were compared under the same random DoS sequence: one with a disturbance observer and one without. The results show that the local disturbance observer, relying only on the vehicle's own acceleration information and nominal dynamics term, can still maintain tracking of the total disturbance during DoS switching. The maximum root mean square error of disturbance tracking for the four following vehicles in the last 10 seconds is approximately 1.10 × 10⁻⁶. .

[0246] like Figure 6As shown, under the same random DoS sequence, the local disturbance observer can continuously track the integrated disturbance during the communication mode switching process, indicating that the observer does not rely on the communication information of the preceding vehicle and can maintain the disturbance compensation function during the DoS attack.

[0247] Performance comparison results show that, under the proposed method, the DoS rate is approximately 1.15%, and the maximum spacing error at the end segment is 5.85× The RMS spacing is 0.2813 m, and the RMS velocity is 0.8891 m / s; with an undisturbed observer, the maximum spacing error in the final segment is 1.02 × The RMS distance was 0.4378m, and the RMS velocity was 0.9386m / s. Under strong DoS conditions, the DoS percentage was approximately 39.41%, and the maximum distance error at the end was 5.66× The RMS distance is 0.2945m and the RMS speed is 0.9010m / s.

[0248] The results above show that after introducing the perturbation observer, the maximum spacing error in the final segment is reduced from 1.02× Reduced to 5.85× The root mean square value of the spacing error decreased by approximately 35.75%, and the peak value of the velocity error across the entire time domain decreased from 6.38 m / s to 4.81 m / s.

[0249] Under strong DoS conditions, the average DoS percentage was approximately 39.41%, and the longest continuous attack time for the first following vehicle was 0.22 seconds. Although the local envelope of the formation error increased when the attacks were more concentrated, the maximum spacing error at the end remained within the acceptable range. The magnitude of the closed-loop error remains bounded and eventually converges.

[0250] like Figure 7 As shown, the comparison results of the full formation error envelope under different operating conditions demonstrate that the proposed method can maintain the bounded closed-loop error and eventually converge under both the baseline DoS condition and the strong DoS condition, reflecting the vehicle platoon's tolerance to random DoS attacks and comprehensive disturbances.

[0251] In summary, this embodiment demonstrates that the present invention can maintain stable vehicle platooning and effectively reduce the propagation of combined disturbances in the vehicle platoon when random DoS switching, heterogeneous vehicle parameter perturbations, and external disturbances coexist.

[0252] Example 3:

[0253] A robust control system for heterogeneous vehicle queuing under DoS attacks, comprising:

[0254] The vehicle dynamics modeling module is used to establish discrete-time models of heterogeneous vehicle platoons.

[0255] The local disturbance observer module is used to construct a discrete local disturbance observer that relies only on the vehicle's own acceleration measurement and nominal dynamics term for the total disturbance of each following vehicle, and to estimate the total disturbance in real time.

[0256] The DoS attack modeling module is used to describe the random switching state of communication links under a DoS attack using a two-modal Markov chain.

[0257] The augmented closed-loop system module is used to construct an augmented state vector by unifying the following error state of the vehicle, the local coordination state of the preceding vehicle, the disturbance observation error of the vehicle and the disturbance observation error of the preceding vehicle, and to establish a mode-dependent augmented closed-loop system by combining the Markov mode transfer characteristics.

[0258] The stability analysis module is used to select Lyapunov weight matrices for different communication modes and construct mode-dependent Lyapunov functions; combined with the rigorous dissipative supply rate derivation, sufficient conditions for the stochastic exponential stability of the augmented closed-loop system and satisfaction of dissipative performance are obtained, and sufficient conditions for the chordal stability of the finite vehicle queue are further given.

[0259] The LMI solver module is used to solve the communication normal mode control gain, DoS attack mode control gain, front vehicle cooperative gain, and disturbance observer gain based on the LMI synthesis conditions of stochastic exponential stability and strict dissipation, combined with the observer pole constraint.

Claims

1. A robust control method for heterogeneous vehicle queues under DoS attacks, characterized in that, Includes the following steps: S1. Establish a discrete-time model for heterogeneous vehicle queues; S2. For the total disturbance of each following vehicle, construct a discrete local disturbance observer that relies only on the vehicle's own acceleration measurement and nominal dynamics term to estimate the total disturbance in real time. S3. A two-modal Markov chain is used to describe the random switching state of the communication link under a DoS attack. S4. Construct an augmented state vector from the following error state of the vehicle, the local coordination state of the preceding vehicle, the disturbance observation error of the vehicle and the disturbance observation error of the preceding vehicle, and combine it with the Markov mode transfer characteristics to establish a mode-dependent augmented closed-loop system. S5. Select Lyapunov weight matrices for different communication modes and construct mode-dependent Lyapunov functions; combine with the strict dissipative supply rate derivation to obtain sufficient conditions for the stochastic exponential stability of the augmented closed-loop system and satisfy dissipative performance, and further give sufficient conditions for the chordal stability of the finite vehicle queue. S6. Based on the LMI synthesis conditions of stochastic exponential stability and strict dissipation, and combined with the observer pole constraint, jointly solve the control gain of normal communication mode, control gain of DoS attack mode, cooperative gain of the preceding vehicle, and gain of the disturbance observer.

2. The robust control method for heterogeneous vehicle queues under DoS attacks according to claim 1, characterized in that, In S2, the updates to the internal state and perturbation estimates of the local perturbation observer include: The total disturbance estimate is obtained by combining the observer's internal state and the vehicle's acceleration after observer gain correction. The observer's internal state is recursively updated based on the internal state at the previous sampling time, as well as the difference between the nominal acceleration dynamics term, the vehicle's execution input, and the total disturbance estimate.

3. The robust control method for heterogeneous vehicle queues under DoS attacks according to claim 2, characterized in that, In S2, the disturbance observation error of both the vehicle and the preceding vehicle is determined by the observation error at the previous sampling time and the total disturbance change at adjacent sampling times. By adjusting the observer gain and combining it with the sampling period, the convergence speed of the observation error subsystem is constrained.

4. A robust control method for heterogeneous vehicle queues under DoS attacks according to claim 3, characterized in that, S2 include: The following pole constraints are set to constrain the convergence rate of the observation error subsystem: in, Indicates the sampling period. This represents the observer gain; both the lower and upper bounds of the pole constraints are preset scalars, satisfying that the lower bound is greater than 0, the upper bound is less than 1, and the lower bound is less than the upper bound.

5. A robust control method for heterogeneous vehicle queues under DoS attacks according to claim 1, characterized in that, S4 includes control laws related to the design mode based on communication modes: The control input consists of the vehicle's following error feedback item and the preceding vehicle's coordination feedback item. When communication is normal, both types of feedback participate in the control. During a DoS attack, the preceding vehicle's coordination feedback item automatically exits, and only the vehicle's error feedback is retained to avoid using unavailable preceding vehicle information.

6. A robust control method for heterogeneous vehicle queues under DoS attacks according to claim 5, characterized in that, In S4, constructing the augmented closed-loop system includes: defining the augmented state as consisting of the vehicle's following error state, the preceding vehicle's local coordination state, the vehicle's disturbance observation error, and the preceding vehicle's disturbance observation error, while taking the preceding vehicle's auxiliary control input and the total disturbance change as external inputs; the augmented state at the next sampling time is evolved from the current augmented state through the closed-loop system matrix corresponding to the communication mode, and the external input under the action of the external input matrix is ​​superimposed.

7. A robust control method for heterogeneous vehicle queues under DoS attacks according to claim 1, characterized in that, S5 include: S51. Define the stochastic exponential stability objective as follows: when there is no external input, the mathematical expectation of the energy of the closed-loop augmented state decays exponentially with increasing sampling time. The strict dissipation performance is defined to satisfy the following condition: within a given finite time range, the expected cumulative energy of the carousel error output should be less than the upper bound of the expected cumulative energy of the external input after weighting by the dissipation performance index; where Lyapunov weight matrices are selected for different communication modes to measure the augmented state energy. S52. Extract the spacing error and velocity error from the augmented state as the following error output; form a weighted performance output for dissipation performance evaluation by weighting the output; S53. Define the supply rate: The weighted performance output energy is used as the term to be suppressed, and the external input energy is used as the allowable input term. The difference between the two is used to evaluate the augmented closed-loop system's ability to attenuate external disturbances. S54. Based on the closed-loop augmented system and the supply rate, obtain sufficient conditions for the closed-loop augmented system to be stable and to satisfy dissipation performance.

8. A robust control method for heterogeneous vehicle queues under DoS attacks according to claim 7, characterized in that, S5 also includes: S55. Supplementary finite vehicle queue chord stability constraint: When the initial augmented state is zero and the external input energy satisfies a given upper bound, the following error energy of the next vehicle shall not exceed the error output energy of the previous vehicle.

9. A robust control system for heterogeneous vehicle queuing under DoS attacks, characterized in that, include: The vehicle dynamics modeling module is used to establish discrete-time models of heterogeneous vehicle platoons. The local disturbance observer module is used to construct a discrete local disturbance observer that relies only on the vehicle's own acceleration measurement and nominal dynamics term for the total disturbance of each following vehicle, and to estimate the total disturbance in real time. The DoS attack modeling module is used to describe the random switching state of communication links under a DoS attack using a two-modal Markov chain. The augmented closed-loop system module is used to construct an augmented state vector by unifying the following error state of the vehicle, the local coordination state of the preceding vehicle, the disturbance observation error of the vehicle and the disturbance observation error of the preceding vehicle, and to establish a mode-dependent augmented closed-loop system by combining the Markov mode transfer characteristics. The stability analysis module is used to select Lyapunov weight matrices for different communication modes and construct mode-dependent Lyapunov functions; combined with the rigorous dissipative supply rate derivation, sufficient conditions for the stochastic exponential stability of the augmented closed-loop system and satisfaction of dissipative performance are obtained, and sufficient conditions for the chordal stability of the finite vehicle queue are further given. The LMI solver module is used to solve the LMI synthesis conditions for stochastic exponential stability and strict dissipation, and, in conjunction with the observer pole constraint, jointly solves the control gain of normal communication mode, the control gain of DoS attack mode, the cooperative gain of the preceding vehicle, and the gain of the disturbance observer. The aforementioned robust control system for heterogeneous vehicle queues under DoS attacks is used to implement the robust control method and steps for heterogeneous vehicle queues under DoS attacks as described in claim 1.

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