Contents Introduction
During the past decades, Autonomous Vehicles(Autonomous Vehicles, AVs) have become more and more popular in our daily life because its advantages of flexility and intelligence [1], [2]. With the development of advanced control and communication technologies, AVs, equipped with sensors, controllers and actuators, are typically characterized by networked worked control systems because its share vehicle status information real-time information through controller area network (CAN). Due to the introduction of CAN bus, the communication efficiency are greatly improved. However, the network risk is also significantly increasing [3], [4].
In recent years, several cyber-attack incidents on AVs have generated the most enthusiasm on security control of AVs from both academia and industry communities [5]. Generally, Denial of Service (DoS) attacks [6], [7] and False Data Injection (FDI) attacks [8], [9] are the two main types of attacks which can jeopardize the control action of AVs [10]. DoS attacks can prevent the control actions in vehicle from their desired time instants by transmitting a large volume of useless data. This therefore leads to the degradation of the control performance of AVs because its open loop operations [11]. For example, a resilient control of network control systems under denial-of-service attacks based on Markov processes is investigated in [12]. To address the behaviour of vulnerabilities in the Autonomous electric vehicle ecosystem that can launch DoS attacks on the grid during Autonomous electric vehicle charging, two detection schemes for the presence of DoS attacks on Autonomous electric vehicle are designed in [13].
Different from DoS attacks, FDI attacks can hijack and tamper with the real measurement and control data which in turn lead to wrong operations of AVs [14]. Compared with DoS attacks, FDI attacks are generally known as a more server attacks which directly tamper with sensor or actuator data and give more challenging issues on the security of AVs. In [15], the collaborative control problem of a group of connected vehicles loaded with adaptive cruise control systems under FDI attacks is investigated, and based on the above problem, an observer-based diagnostic algorithm is designed, and the ability of the algorithm to detect and isolate the FDI attacks is demonstrated through simulation verification. For secure cruise control system of automatic vehicles under false data injection attack, [3] proposed a sigmoid-like event-triggering scheme, and verified the effectiveness of the proposed control strategy through experimental simulation. In recent years, the cyber security of Robotic vehicles has attracted much attention [16]. For example, AVs anti-lock braking systems (ABS) were attacked to tamper with wheel speed sensor readings by injecting magnetic fields [17]. A shortest path and non-interference attack algorithm is designed for obstacle avoidance mobile robots subjected to smart physical attacks [18].
As a main function of AVs, path following [19], [20] describe the scenario that the vehicle collect target path information through sensors, transmit it to the Electronic Control Unit (Electronic Control Unit, ECU) for processing and then track the desired path through the control actions of actuator. Up to now, there are some control method such as coordinated control strategy [24], model predictive control [22], fuzzy PID method [23], are prosed to improve the control performance of path following of AVs. However, cyber-security issues of path following are not fully taken into consideration. In [24], a learning-based event triggering mechanism is proposed, which not only reduces the communication network burden of autonomous vehicles, but also improves the path following performance under deception attacks. A novel distributed data-driven control approach for a homogeneous connected autonomous vehicle platoon under false data injection attacks is investigated to ensure the driving performance of connected autonomous vehicles [25]. A robust sliding mode security control strategy combined with an event-triggered control method is designed to solve the path following problem of AVs under both sensor and actuator attacks [26]. It is well known that Sliding Mode Control (SMC) has been widely used in AVs control systems because of its simple structure, fast response speed, and strong robustness to parameter variations and external disturbances [27], [28], [29].
Motivated by the fact that SMC is of inherent stability property to internal or external uncertainties or disturbance, this work attempts to stabilize the path following of AVs under actuator attacks using fuzzy terminal sliding mode control approach. Compared with the previous results, the main contributions of the paper can be summarized as follows
The global fast terminal sliding mode control approach is designed for mitigating the malicious actuator attacks imposed on the steering gear. Comparing with most existing results [30], [31], the global fast terminal sliding control method can stabilize the AVs path following control system under actuator attack for a finite time, which provides a more practical and effective control method for many engineering scenarios.
The attack-aware-based fuzzy rules is well designed for regulating the switching gain of sliding model controller, adaptively. Traditional switching gain of sliding controller is often designed based on the worst case of attacks while leading to a serious chattering under sliding control scheme. However, the fuzzy rule designed in this paper can adaptively adjust the switching gain according to the change of actuator signal. Then the chattering phenomenon is significantly alleviated.
The simulation results and numerical analyses under three scenarios are carried out by the CarSim-Simulink co-simulation experimental platform, and the results show that the method improves the robustness of the AVs control system under actuator attack in multiple scenarios.
At the end of this section, Table. 1 summarises the most commonly used symbols in AVs path-following control systems.
Problem Formulation
A. Path Following Control of AVs Under Actuator Attacks
The path following control of AVs is to achieve precise following of the target path by controlling the front wheels angle of the vehicle, which belongs to the lateral control of the vehicle. The 
\begin{align*} \begin{cases} \displaystyle \dot {Y}=v_{x}sin\varphi +v_{y}cos\varphi \\ \displaystyle \dot {X}=v_{x}cos\varphi -v_{y}sin\varphi \\ \displaystyle \,\dot {\varphi }=\omega _{r} \\ \displaystyle \dot {v_{y}}=-v_{x}\omega _{r}+m^{-1}[C_{f}(\beta +l_{f}\omega _{r}v_{x}^{-1}-\delta _{f}) \\ \displaystyle \quad \,+C_{r}(\beta -l_{r}\omega _{r}v_{x}^{-1})] \\ \displaystyle \dot {\omega _{r}}=I_{z}^{-1}[l_{f}C_{f}(\beta +l_{f}\omega _{r}v_{x}^{-1}-\delta _{f}) \\ \displaystyle \quad \,-l_{r}C_{r}(\beta -l_{r}\omega _{r}v_{x}^{-1})]\end{cases} \tag {1}\end{align*}
We observe that (1) is a classical underdriven system. The reduced dimension of the system can significantly decrease the complexity of the control. In [32], the complex path following control is simplified to yaw angle following control by dimension reduction of the system (1). The tracking control of the reference path is achieved by tracking the desired yaw angle.
Denote by \begin{align*} \begin{cases} \displaystyle \dot {e}_{1}=e_{2}=\dot {\varphi }-\dot {\varphi _{d}} \\ \displaystyle \dot {e}_{2}=f(\beta,\omega _{r})+bu(t)-\ddot {\varphi }_{d} \\ \displaystyle y=e_{1} \end{cases} \tag {2}\end{align*}
The interested path following control of AV is shown in Fig. 2, where an actuator attacker can disrupt the steering actions by tampering with steering angle signal. Suppose that there are actuator attacks \begin{equation*} \widetilde {u}(t)=u(t)+\sigma _{a}(t,x(t)) \tag {3}\end{equation*}
Assumption 1:
Due to the energy constraint of attacker, it is assumed that
By considering steering control with actuator attacks (3), the closed-loop of path following control of AV is characterized by\begin{align*} \begin{cases} \displaystyle \dot {e}_{1}=e_{2}=\dot {\varphi }-\dot {\varphi _{d}} \\ \displaystyle \dot {e}_{2}=f(\beta,\omega _{r})+b\widetilde {u}(t)-\ddot {\varphi }_{d} \\ \displaystyle \widetilde {u}(t)=u(t)+\sigma _{a}(t,x(t)) \\ \displaystyle y=e_{1} \end{cases} \tag {4}\end{align*}
Remark 1:
From (4),
B. Design Goals
Based on the established path following control model (4) of AV, the objectives of the security control approach are presented as follows
The finite time stability of path following control of AV can be achieved by using the proposed control approach when there are no actuator attacks, i.e.
\sigma _{a}(t,x(t))=0 The actuator attacks on steering control actions can be well estimated and counteracted for the proposed control approach when there are actuator attacks, i.e.
\sigma _{a}(t,x(t))\neq 0
Global fast terminal sliding mode control approach is exploited to achieve finite time stability of path following control of AV, even there are actuator attacks or other disturbances.
The design of fuzzy rule is used to estimate the actuator attack signal which will be further used to regulate the switching controller gain to counteract the actuator attack signal without a server ‘chattering’.
Secure Path Following Control Design
In this section, the stability analysis and its controller design are presented as well as the finite time convergence property.
A. Sliding Mode Controller Design
Theorem 1:
For some given positive constants \begin{align*} u(t)& =1/b(-f(\beta,\omega _{r})+\ddot {\varphi }_{d} \\ & \quad -\,\,\alpha _{0}\dot {e}_{1}-\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}_{1}-Ksgn(s(t))) \tag {5}\end{align*}
Proof:
Construct the following sliding mode surface\begin{equation*} s(t)=\dot {e}_{1}+\alpha _{0}e_{1}+\beta _{0}e_{1}^{p/q} \tag {6}\end{equation*}
Differentiating (6) yields\begin{align*} \dot {s}(t)& =\ddot {e}_{1}+\alpha _{0}\dot {e}_{1}+\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}_{1} \\ & =\ddot {\varphi }-\ddot {\varphi }_{d}+\alpha _{0}\dot {e}_{1}+\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}_{1} \tag {7}\end{align*}
\begin{equation*} V=\dfrac {1}{2}s(t)^{2}. \tag {8}\end{equation*}
\begin{align*} \dot {V}& =s(t)\dot {s}(t) \\ & =s(t)(\ddot {\varphi }-\ddot {\varphi }_{d}+\alpha _{0}\dot {e}_{1}+\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}_{1}) \\ & =s(t)(f(\beta,\omega _{r})+b(u(t)+\sigma _{a}(t,x(t)))-\ddot {\varphi }_{d} \\ & \quad +\,\alpha _{0}\dot {e}_{1}+\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}_{1}) \tag {9}\end{align*}
\begin{align*} \dot {V}& =s(t)(f(\beta,\omega _{r})+b\frac {1}{b}(-f(\beta,\omega _{r})+\ddot {\varphi }_{d} \\ & -\,\alpha _{0}\dot {e}_{1}-\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}_{1}-Ksgn(s(t))) \\ & \quad +\,b\sigma _{a}(t,x(t))-\ddot {\varphi _{d}}+\alpha _{0}\dot {e}_{1}+\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}_{1}) \\ & =s(t)(b\sigma _{a}(t,x(t))-Ksgn(s(t))) \\ & =b\sigma _{a}(t,x(t))s(t)-K|s(t)| \\ & \leq -\varepsilon |s(t)| \tag {10}\end{align*}
\begin{equation*} \dot {V}=s(t)\dot {s}(t)\leq 0. \tag {11}\end{equation*}
Remark 2:
In fact, the fixed switching gain K plays a very important role in attack/diturbance attenuation due to the inherent robustness of sliding mode control approach. However, it is also clear that the fixed switching gain will aggravate the ‘chattering’ phenomenon when there are no actuator attacks. This is the main drawback when we use a fixed switching gain K to counteract the malicious effects caused by actuator attacks.
Theorem 2:
For the actuator attacked path following control (4), the yaw angle error (i.e.,\begin{equation*} t_{a}=\dfrac {q}{\alpha _{0}(q-p)}ln\left ({{\dfrac {\beta _{0}+\alpha _{0}e_{1}(0)^{\dfrac {q-p}{q}}}{\beta _{0}}}}\right) \tag {12}\end{equation*}
Proof:
Considering the fact that \begin{equation*} \dfrac {de_{1}}{dt}e_{1}^{-p/q}+\alpha _{0}e_{1}^{1-p/q}=-\beta _{0} \tag {13}\end{equation*}
\begin{equation*} \dfrac {dz}{dt}=\dfrac {q-p}{q}\cdot e_{1}^{-p/q}\cdot \dfrac {de}{dt} \tag {14}\end{equation*}
\begin{equation*} \dfrac {dz}{dt}+\dfrac {q-p}{q}\cdot \alpha _{0}\cdot z=-\dfrac {q-p}{q}\cdot \beta _{0}. \tag {15}\end{equation*}
\begin{equation*} z=e_{1}^{\int _{0}^{t}\dfrac {q-p}{q}\alpha _{0}dt}\left ({{\int _{0}^{t}-\dfrac {q-p}{q}\beta _{0}e_{1}^{\int _{0}^{t}\dfrac {q-p}{q}\alpha _{0}dt}+C}}\right) \tag {16}\end{equation*}
By letting \begin{equation*} z=-\dfrac {\beta _{0}}{\alpha _{0}}+\dfrac {\beta _{0}}{\alpha _{0}}e_{1}^{-\dfrac {q-p}{q}\alpha _{0}t}+z(0)e_{1}^{-\dfrac {q-p}{q}\alpha _{0}t} \tag {17}\end{equation*}
\begin{equation*} \dfrac {\beta _{0}}{\alpha _{0}}e_{1}^{-\dfrac {q-p}{q}\alpha _{0}t_{a}}+z(0)e_{1}^{-\dfrac {q-p}{q}\alpha _{0}t_{a}}=\dfrac {\beta _{0}}{\alpha _{0}} \tag {18}\end{equation*}
\begin{equation*} \dfrac {\beta _{0}+\alpha _{0}z(0)}{\beta _{0}}=e_{1}^{-\dfrac {q-p}{q}\alpha _{0}t_{a}} \tag {19}\end{equation*}
\begin{equation*} t_{a}=\dfrac {q}{\alpha _{0}(q-p)}ln\dfrac {\beta _{0}+\alpha _{0}e_{1}(0)^{\dfrac {q-p}{q}}}{\beta _{0}} \tag {20}\end{equation*}
Attack-Based Fuzzy Rule Design
In the design of sliding mode controller, the main purpose of the controller switching term gain is to eliminate the adverse effects of actuator attack, in order to ensure the necessary conditions for the existence of sliding mode. Since the actuator attack studied in this paper is random and varies with time, a fixed switching term gain cannot effectively compensate for the adverse effect of the actuator attack signal, which results in the phenomenon of chattering. Fuzzy control does not require precise mathematical models and has good robustness, compared with other control methods, it can make good use of expert experience in designing fuzzy rules to make the system meet the design requirements. So in this section, we will use attack-aware-based fuzzy rule design to alleviate the chattering phenomenon for the proposed secure sliding mode control approach.
A. Fuzzy Rule Design
Due to existing of the fixed switching gain K, it is clear that it will arouse ‘chattering’ even there are no actuator attack. In order to mitigate the ‘chattering’ phenomenon, the ideal case is that design a time varying switching gain such that \begin{equation*} s(t)\dot {s}(t)\lt 0 \tag {21}\end{equation*}
\begin{align*} \text {If}~~s(t)\dot {s}(t)\gt 0, \text {Then}~~K_{\sigma }(t)~~\text {should be increased} \tag {22}\\ \text {If}~~s(t)\dot {s}(t)\lt 0, \text {Then}~~K_{\sigma }(t)~~\text {should be decreased} \tag {23}\end{align*}
\begin{align*} s(t)\dot {s}(t)& =\{NB\quad NM\quad NS\quad ZO\quad PS\quad PM\quad PB\} \\ \sigma (t,x(t))& =\{NB\quad NM\quad NS\quad ZO\quad PS\quad PM\quad PB\} \\ K_{\sigma }(t)& =\{NB\quad NM\quad NS\quad ZO\quad PS\quad PM\quad PB\} \tag {24}\end{align*}
Then the membership functions of the input and output of fuzzy rules are given as following Fig. 3a, Fig. 3b and Fig. 3c respectively. In choosing the membership function, the triangular membership function is chosen due to its higher resolution and better control sensitivity.
The fuzzy rule table contains fuzzy rules that consider the correlation between the inputs and outputs of the fuzzy system, which are constructed based on extensive driver experience and taking into account factors such as vehicle path accuracy and passenger comfort.
The above fuzzy rules is shown in Table. 2.
Fig. 4 depicts the response surface between inputs and outputs under fuzzy rules. With the above fuzzy rule, when an actuator attack occurs during the vehicle path following process, the switching term gain is adaptively adjusted in order to ensure that the vehicle follows a close target path.
In what follows, the steering control actions will be designed according to the above fuzzy rules.
Remark 3:
Note that the closed-loop stability of a global fast terminal sliding mode control system based on fuzzy rules is guaranteed by the sliding mode controller.
Remark 4:
The chattering problem is inevitable in the proposed global fast terminal sliding mode control. A attack-aware-based fuzzy rules is designed to mitigate the adverse effects of chattering problem on the AV system.
B. Steering Wheel Angle Design
Firstly, in order to counteract the malicious effects caused by actuator attacks, the switching control gain is determined by\begin{equation*} \hat {K}_{\sigma }(t)=\vartheta \int _{0}^{t}K_{\sigma }(t)dt \tag {25}\end{equation*}
Thus the fuzzy-rule-based sliding mode controller can be represented as\begin{align*} u(t)& =1/b(-f(\beta,\omega _{r})+\ddot {\varphi }_{d} \\ & \quad -\,\alpha _{0}\dot {e}_{1}-\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}-\hat {K}_{\sigma }(t)sgn(s(t))) \tag {26}\end{align*}
\begin{align*} \delta _{f}& =\dfrac {I_{z}}{l_{f}C_{f}}\big[\dfrac {l_{f}C_{f}-l_{r}C_{r}}{I_{z}}\beta +\dfrac {l_{f}^{2}C_{f}+l_{r}^{2}C_{r}}{I_{z}v_{x}}\omega _{r} \\ & \quad -\,\ddot {\varphi }_{d}+\alpha _{0}\dot {e}_{1}+\beta _{0}(p/q)e_{1}^{p/q-1}\dot {e}_{1}+\sigma _{a}(t,x(t)) \\ & \quad -\,\hat {K}_{\sigma }(t)sgn(s(t))\big] \tag {27}\end{align*}
\begin{equation*} \delta _{sw}=\delta _{f}\cdot i_{sw} \tag {28}\end{equation*}
For the implementation of the switching controller, a saturation function is replaced with the sign function which is given as follows\begin{align*} sat(s(t))= \begin{cases} \displaystyle 1,& s(t)\gt \Delta \\ \displaystyle ls(t),& |s(t)|\leq \Delta \quad l=\dfrac {1}{\Delta } \\ \displaystyle -1,& s(t)\lt -\Delta \end{cases} \tag {29}\end{align*}
Step 1: Initialize the parameters
\alpha _{0} \beta _{0} \vartheta \Delta Step 2: For the determined yaw angle and lateral distance of the AVs, calculate the sliding mode surface variable
s(t) Step 3: Design the fuzzy rules based on the sliding mode dynamics which may affected by actuator attacks. Then calculate the switching gain
K_{\sigma }(t) s(t)\dot {s(t)} Step 4: Design the fuzzy set and design the membership function based on (24).
Step 5 Calculate the steering angle according to (27) and (28).
Simulation Experiment
In this section, Simulink-CarSim-joint platform is exploited to validate the effectiveness of FR-GFTSMC approach by comparison examples.The MATLAB/Simulink and CarSim co-simulation block diagram is shown in Fig. 6 The C-class hatchback vehicle is selected in CarSim and the detailed parameters and operating condition are shown in Table. 3.
The lateral distance of the desired path as well as the desired yaw angle borrowed from [33] are given by\begin{align*} Y_{d}& =\dfrac {d_{1}[1+tanh(h_{1})]-d1[1+tanh(h_{2}) ] }{2} \tag {30}\\ \varphi _{d}& =arctan\left [{{d_{1}\left ({{\dfrac {1}{cosh(h_{1})}}}\right)^{2}\left ({{\dfrac {1.2}{d_{2}}}}\right)-d_{1}\left ({{\dfrac {1}{cosh(h_{2})}}}\right)^{2}\left ({{\dfrac {1.2}{d_{2}}}}\right)}}\right ] \tag {31}\end{align*}
A. Simulation Experiments Scenario 1
The following setups are used to conduct the simulations. The double lane change path experimental road is set up in CarSim with its initial speed of vehicle
1) Sliding Mode Control With a Fixed Switching Gain K
Based on the above settings, the simulation results of case I of path following are provided from Fig. 7 to Fig. 12.
From Fig. 7, the actual path following of the vehicle without actuator attacks show a good performance, and the actual driving path fits the target path in a high degree. Fig. 8 and Fig. 9 depict the yaw angle error and the tracking error, respectively. The results show that the actual yaw angle deviates from the target yaw angle to a small extent while the accuracy of path following can be guaranteed in the absence of actuator attack.
As can be seen in Fig. 9 to Fig. 12, the yaw angle error, the side slip angle,the yaw rate and the actual steering angle, show unexpected changes and fluctuations to some different extents when an actuator attack occurs during path following. From Fig. 7 to Fig. 9, it can be seen that when the actuator attack occurs, the max tracking deviation of path following is 19.7% and the yaw angle is 22.4%. This indicates that when there is an actuator attacks, the performance of path following of AV are significantly damaged.
As can be seen from the green dashed lines in Fig. 7 to Fig. 12. GFTSMC method to improve the impact of actuator attack behaviour on the AV path tracing process, and the phenomena of sudden changes and waveforms occurring in the yaw angle and the steering wheel angle are mitigated, and the following effect of the yaw angle is greatly improved compared to the previous one, and the yaw angle error is reduced from
2) Sliding Mode Control With Fuzzy-Rule-Based Switching Gain \hat {K}_{\sigma }(t)
To solve the chattering problems introduced by the fixed switching gain, the fixed term is replaced by a time varying one, which a better path following performance is excepted.
Based on Fig. 7–Fig. 12, it can be seen that the introduction of the GFTSMC strategy has greatly mitigated the adverse effects caused by the actuator attacks, but the chattering phenomenon leads to a reduction in path following accuracy. As can be seen from Fig 13 and Fig 15, the original switching term gain using a fixed value is replaced by a switching term gain that can be changed in real time with the arrival conditions of the sliding mode through the design of fuzzy rules. It is therefore that the ‘chattering’ phenomenon of the path following performance is improved, and the vehicle’s actual travelling path is more closely fitted to the target path with a smaller yaw angle following error, path following max deviation reduce 2.1%,yaw angle reduce 0.7%. From Fig. 16 to Fig. 18, it can be seen that the effect of the chattering phenomenon on the side slip angle, yaw rate and steering wheel angle decreases, with the most obvious effect on the steering wheel angle. These show that it is effective to improve path following performance for the proposed method. The chattering phenomenon in side slip angle, yaw rate and steering angle is eliminated, the deviation of the yaw angle is substantially reduced. The path following performance are improved, confirm the effectiveness of the proposed FR-GFTSMC method.
Table. 4 describes the changes in each state of the vehicle for the three scenarios.
B. Simulation Experiments Scenario 2
The following setups are used to conduct the simulations experiments scenario 2. The double lane change path experimental road is set up in CarSim with its initial speed of vehicle
1) Sliding Mode Control With a Fixed Switching Gain K
Based on the above settings, the simulation results of case II of path following are provided from Fig. 19 to Fig. 24.
From Fig. 19 to Fig. 24, it can be seen that in Case 2, the path following error increases due to the increase in vehicle speed and lateral displacement. As can be seen in Fig. 21 to Fig. 24, the yaw angle error, the side slip angle, the yaw rate and the actual steering angle, show unexpected changes and fluctuations to some different extents when an actuator attack occurs during path following. From Fig. 21 to Fig. 24, it can be seen that when the actuator attack occurs, the max tracking deviation of the yaw angle is 15.1% and the yaw rate is 58%, the side slip angle is 66% and the steering angle is 46.8%. This indicates that when there is an actuator attacks, the performance of path following of AV are significantly damaged.
As can be seen from the green dashed lines in Fig. 20 to Fig. 24. GFTSMC method to improve the impact of actuator attack behavior on the AV path following process, and the phenomena of sudden changes and waveforms occurring in the yaw angle and the steering wheel angle are mitigated, and the following effect of the yaw angle is greatly improved compared to the previous one, and the yaw angle is reduced from
2) Sliding Mode Control With Fuzzy-Rule-Based Switching Gain \hat {K}_{\sigma }(t)
In order to solve the chattering problems introduced by the fixed switching gain, the fixed term is replaced by a time varying one, which a better path following control performance is excepted.
Based on Fig. 19 to Fig. 24, it can be seen that the introduction of the GFTSMC strategy has greatly mitigated the adverse effects caused by the actuator attacks,but the chattering phenomenon leads to a reduction in path following accuracy. As can be seen from Fig. 25 to Fig. 27, the original switching term gain using a fixed value is replaced by a switching term gain that can be changed in real time with the arrival conditions of the sliding mode through the design of fuzzy rules. It is therefore that the chattering phenomenon of the path following performance is improved, and the vehicle’s actual travelling path is more closely fitted to the target path with a smaller yaw angle following error,path following max deviation reduce 2.4%, yaw angle reduce 0.5%.
From Fig. 28 to Fig. 30, it can be seen that the effect of the chattering phenomenon on the side slip angle, yaw rate and steering wheel angle decreases, with the most obvious effect on the steering wheel angle. These show that it is effective to improve path following performance for the proposed method. The chattering phenomenon in side slip angle,yaw rate and steering angle is eliminated, the deviation of the yaw angle is substantially reduced. The path following performance are improved,confirm the effectiveness of the proposed FR-GFTSMC method.
Table. 5 describes the changes in each state of the three vehicle states in scenario 2.
C. Simulation Experiments Scenario 3
1) Compared With Other Controllers
In order to test the path following performance of the improved controller, a conventional fuzzy sliding mode controller(F-SMC),attack-aware-based FR-GFTSMC are simulated under the same driving conditions.
As can be seen from Fig. 31, the path following performance of the FR-GFTSMC control strategy proposed in this paper is better than that of the F-SMC control strategy, and the following error is reduced by 3.1%.
Fig. 32 and Fig. 33 depict the yaw angle error and the tracking error, respectively. The results show that the FR-GFTSMC control strategy proposed in this paper has better control performance than F-SMC control strategy when tracking the reference yaw angle under actuator attack, and the tracking error is reduced by 2.1%. Fig. 34 and Fig. 36 depict the side slip angle,the yaw rate and the steer wheel angle, respectively. The results show that the FR-GFTSMC control strategy proposed in this paper outperforms the F-SMC control strategy in improving chattering. the side slip angle max deviation reduce 22%, yaw rate reduce 24.7%, steer wheel angle reduce 35%.
From the above data, it can be seen that the FR-GFTSMC control performance proposed in this paper is better than the F-SMC control strategy.
2) Comparison of the Impact of Key Parameters of Fuzzy Systems on the System
In order to test the influence of the key parameters of the fuzzy system on the overall vehicle performance, the fuzzy rules based on attack aware are modified under the same driving conditions. The modified fuzzy rule table is shown in Table. 6. It can be seen from Fig. 37 and Fig. 40 that the variation of key parameters in the fuzzy rule system affects the performance of this controller in suppressing chattering.From Fig. 37, the yaw angle following error increases after changing the fuzzy rule parameters, the max deviation increases 9%. From Fig. 38 and Fig. 40, the steer wheel angle max deviation increases 16%, the side slip angle increases 9.8%, the yaw rate increases 9.9%. It can be seen from the above data that the modification of the key parameters of the fuzzy system affects the suppression ability of the proposed control strategy for chattering, which further affects the vehicle path following performance.
Conclusion
In order to enhance the security of path following of AVs under actuator attacks, FR-GFTSMC approach has been developed to mitigate the adverse effects of actuator attacks and alleviate ‘chattering’ phenomenon. The proposed FR-GFTSMC approach is of the two advantages. On the one hand, the switching gain of sliding mode controller is developed to counteract the actuator attacks. Thus, arbitrary actuator attacks can be well coped with rather than the ones following some specific rules such as probability distribution or periodic. On the other hand, a fuzzy-rule-based switching gain is used to improve the control performance of path following of AVs. In fact, due to the concealment of actuator attacks, it is not easy to learn the actuator attacks. However, we use the fuzzy rule to regulate the switching gain in real time according to the estimation of actuator attacks. At last, the proposed FR-GFTSMC approach is verified through Simulink-CarSim-joint simulation platform.
Although there are some advantages for the proposed secure control method, the proposed control scheme in this paper suffers from the following shortcomings
Although this FR-GFTSMC scheme can handle the problem of actuator attacks during AVs path tracking, this paper does not consider the limited resource availability in the environment of AVs communication networks, which may lead to some incompatibility problems in real-world implementation scenarios.
While this FR-GFTSMC scheme is able to deal with the problem of actuators being attacked during AVs path tracking, the sensors, which are also one of the key components of AVs, are also potentially vulnerable to the problem of cyber-attacks. Questions about sensor attacks, actuator attacks, and the two occurring at the same time need to be completed in our future work.
Future improvements may extend to connected cars, where machine learning control methods are essential. As an important part of machine learning, federated learning has significant advantages in improving vehicle system performance and protecting data privacy [34], [35].
Although a large number of simulation experimental data have verified that this FR-GfTSMC scheme can deal with the problem of actuator attack in the process of AVs path following, the real vehicle verification is more convincing.
Based on the above analysis, our future research mainly includes limited resource availability, multiple attack signals, machine learning and application problems in real vehicle path following control.