Denial of Service Attack of QoS-Based Control of Multi-Agent Systems

Abstract

This paper presents a secure formation control design of multi-agent systems under denial of service (DoS) attacks. Multiple unmanned aerial vehicle systems (UAVs) are considered in this paper. The proposed technique takes into account communication time delay, as well as formation and cyberattack, and provides a robust guidance method as well as a reliable middleware for information transfer and sharing. To ensure optimal guidance and coordination, a combined approach of L1 adaptive control and graph theory is used. The packet transmission between all UAVs is handled by the data distribution services (DDS) middleware, which overcomes the interoperability problem when dealing with multiple UAVs of different platforms and can be considered as an extra security level based on its quality of service (QoS). The graph theory is utilized to coordinate multiple UAVs in a hexagon formation, while the L1 controller is utilized as a local controller to stabilize the UAV’s dynamic model. A robust control security level is built to handle the effect of cyberattacks based on linear matrix inequalities (LMIs) control. Simulations are used to verify and show the performances of the proposed technique under the conditions indicated earlier.

1. Introduction

In recent years, multi-agent systems (MASs) have been used in wide areas [1]. Distributed systems containing two or more autonomous agents are known as MASs [2], which are the important applications of distributed systems found in real-time systems; one of these systems is multi-UAV systems which can work together to solve complex problems with high efficiency, reliability, and robustness. Formation control of multi-UAV systems is one of the most interesting study issues in the MASs field, and it has a broad range of uses. Agents must communicate to maintain the shape of the formation by exchanging (e.g., velocity, displacement, and/or direction information). The formation control can be classified into different categories: leader-following [3,4,5], virtual-based [6,7], and behavior-based [8,9,10]. These days, formation control of multiple UAV systems can be built for military use, personal use, recreation, etc. As technology develops faster than ever before, cyber security has never been more crucial. Multi-UAVs can take care of their cyber security to keep their formation. Most of the previous research considers that attackers insert misleading data (misleading data injection attacks) or attempt to make the system unstable by intercepting transmission (DoS attacks). Then, resilient control or fault-tolerant control can be used to defeat the attacks. The attacks aim to influence robot velocities and displacements in order to produce a physical influence on the formation control of the robot. Robots may vary from desired locations because of displacement attacks. The objectives of velocity attacks are to increase energy consumption and reduce work performance by lowering robot velocity. Secure coordinate control of multiple linear agent systems with linked and unconnected topologies due to connectivity broken/maintained attacks was achieved by Feng et al. [11]. Consequently, an arbitrary Markov model is used to describe a secure coordinate control of multiple linear agent systems under strategic attacks in [12]; however, the secure coordinate control has been designed based on hybrid stochastic control. A secure multi-agent systems synchronization for the case of sensor/controller communication under misleading data injection attacks was addressed in [13]. Accordingly, Ref. [14] investigated a secure consensus control of multi-agent systems for the case of sensor/controller communication under misleading data injection attacks that can result in random packet losses. In addition, Ref. [15] studied the secure consensus control of multi-agent systems based on event-triggered conditions for two cases of controller/actuators and sensor/controller communications under misleading data injection attacks. A secure distributed control of multi-agent systems based on event-triggered control to withstand a certain amount of packet loss caused by denial of service (DoS) attacks was studied in [16]. Yang et al. [17] achieved a secure formation control of multiple nonlinear systems based on hybrid event-triggered control under denial of service (DoS) attacks. Secure model-based formation control of multiple ground vehicles under denial of service (DoS) attacks was proposed in [18]. Secure adaptive formation control of a multi-agent system under actuator attack was developed in [19]. A secure event-triggered control of T-S fuzzy-model-based nonlinear networked systems and T-S fuzzy-model-based five-DOF active semi-vehicle subject to denial of service (DoS) attacks was proposed in [20,21]. An event-triggered control of stochastic nonlinear systems with unpredictable backlash-like hysteresis and unmeasured states based on adaptive fuzzy was proposed in [22]. The data-driven fuzzy control of tower crane systems was developed in [23]. An adaptive state observer was designed to minimize the impact of cyberattacks on communication. Moreover, the Nussbaum function and back-stepping controller were utilized to stabilize the agent’s dynamic model. Formation control of multiple UAVs based on DDS middleware was introduced in [24,25,26]. DDS middleware was developed to solve data loss issues between multiple UAVs as well as the interoperability issues that occur with different UAV platforms. As a result, using the DDS middleware approach improved portability, flexibility, and reliability significantly. Researchers are becoming more interested in the secure consensus of multi-agent systems, as evidenced by the preceding literature review. However, most of the multi-agent systems’ secure consensus literature available has focused solely on attack resilient control or detecting attacks. There is a scarcity of studies on the secure formation of multi-agent systems. The following are the major contributions of this study:

• A robust navigation framework for multiple UAVs’ secure formation control has been designed.
• A robust control security level is built to handle the effect of cyberattacks.
• Reliable QoS middleware for extra cyber security and sharing information has been built.

The rest of the paper is arranged as follows. The preliminaries of DDS middleware, graph theory techniques, DoS attacks, and quadrotor dynamics are addressed in Section 2. The secure formation control of multiple UAVs utilizing linear matrix inequalities (LMIs) and L1 approach are discussed in Section 3. Section 4 presents and discusses the simulation results. Finally, the conclusions, as well as the final recommendations, have been noted.

2. Preliminaries

This section contains some preliminary quadrotor dynamics, DoS attacks, graph theory techniques, and DDS middleware.

2.1. Quadrotor’s Dynamics

The translational equation model of a quadrotor built on the Euler–Lagrangian equations is provided by [26,27]:

$$\begin{array}{c}\hfill \ddot{{\rm Y}}=-g\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]+\left[\begin{array}{ccc}c\theta c\psi & -s\psi c\varphi +c\psi s\varphi s\theta & s\varphi s\psi +c\varphi c\psi s\theta \\ c\theta s\psi & c\varphi c\psi +s\psi s\varphi s\theta & -s\varphi c\psi +c\varphi s\psi s\theta \\ -s\theta & s\varphi c\theta & c\theta c\varphi \end{array}\right]\left[\begin{array}{c}0\\ 0\\ \frac{{\sum }_{i=1}^4{\Omega }_i^2\ast k_i}{m}\end{array}\right]-\frac{k_t}{m}\dot{{\rm Y}}\end{array}$$

(1)

where the (x,y,z) position is represented by ${\rm Y}$, ($\theta$,$\varphi$,$\psi$) motion denotes the pitch(), roll(), and yaw(), respectively, g and m represent the gravity and mass, respectively, the drag coefficient is represented by $k_t$, the angular speeds of the motors are represented by ${\Omega }_i$, $k_i$ denotes positive constants, and $c(.)=cos,s(.)=sin,t(.)=tan$ with the assumption of $\theta \ne {90}^{\circ }$ and $\varphi \ne {90}^{\circ }$.

The rotational equation for a quadrotor is given below:

$$\begin{array}{c}\hfill {\dot{\nu }}_2=diag{(I_x,I_y,I_z)}^{-1}(-({\nu }_2\times I{\nu }_2)-I_R({\nu }_2\times {[0,0,1]}^T)({\Omega }_1-{\Omega }_2+{\Omega }_3-{\Omega }_4)-k_r{\nu }_2+\tau )\end{array}$$

(2)

where the angular velocity is represented by ${\nu }_2$, the inertia of a quadrotor is represented as $(I_x,I_y,I_z)$, the inertia of a propeller is indicated by the symbol $I_R$, the cross product is indicated by ×, the rotational drag is represented by $k_r$, and $\tau ={[{\tau }_p,{\tau }_q,{\tau }_r]}^{\top }$ represents the torques on the body frame. Rotational and translational motions of the quadrotor are as follows:

$$\begin{array}{c}\hfill \left[\begin{array}{c}{\tau }_p\\ {\tau }_q\\ {\tau }_r\\ u\end{array}\right]=\left[\begin{array}{cccc}0& l& 0& -l\\ l& 0& -l& 0\\ d& -d& d& -d\\ 1& 1& 1& 1\end{array}\right]\left[\begin{array}{c}{f}_1\\ f_2\\ f_3\\ f_4\end{array}\right]\end{array}$$

(3)

where u represents the force on the body frame, $(f_1,f_2,f_3,f_4)$ represents the upward-lifting forces, and the distance from the center to the motors is denoted by l, while the drag factor is given by d. The system utilized in the above formula is an underactuated system model since the degrees of freedom number is greater than the actuation. The following is the underactuated model that is presented in this study:

$$\ddot{\eta }=G(\eta ,\dot{\eta })+Q\left(\eta \right)u$$

(4)

where $\eta$ represents the coordinates vector, G denotes the dynamic vector, and u and Q represent the control inputs and the input matrix. More details can be found in [26,27].

2.2. Denial of Service (DoS) Attacks

Denial of service (DoS) attacks are a type of cyberattack that attempts to make a machine or network resource unavailable to its intended users. While DoS attacks have been around since the 1970s, they have grown in prevalence and severity in recent years. In 2013, internet security experts estimated that $15\%$ of all websites were suffering from a DoS attack on any given day. The FBI reported that there were more than 3 million active denial of service attacks per month in 2016. The most common DoS attack vector targets web servers by flooding them with unwanted requests, making them unable to deliver the intended content. Such attacks are typically difficult to detect and prevent since they can be orchestrated remotely by an attacker over the Internet. The attacker often has no need to identify the server he or she is attacking; all that is needed is a high level of bandwidth or computing power, which may be acquired over the Internet anonymously. The impacts and effectiveness of DoS attacks vary. Some DoS attacks can be merely inconvenient, while others can prevent affected systems from performing useful work for hours or even days. Advanced persistent DoS (APDoS) attacks can be intended to permanently destroy data or computer resources. The DoS attack can affect multi-agent systems by producing some packet dropout during their communication. In this article, the packet dropout produced by DoS attacks and the communication’s time-varying delays are considered for the formation control of multiple UAVs systems. The packet drops produced by DoS attacks are modeled by parameter $m_i\left(k\right)$, This parameter specifies whether a packet is lost or not.

$$m_i\left(k\right)=\left\{\begin{array}{ccc}\hfill 0& \mathrm{if}& p_i\left(k\right)and{v}_i\left(k\right)arereceived\hfill \\ \hfill 1& \mathrm{if}& p_i\left(k\right)and{v}_i\left(k\right)arelost\hfill \end{array}\right.$$

(5)

where $p_i\left(k\right)$ and $v_i\left(k\right)$ indicate the sampled position and the sampled velocity of agent i, respectively. We assume the time-varying delays are bounded by ${\tau }_{d_{max}}$ and ${\tau }_{d_{min}}$ with bounded sampling by $h_{max}$ and $h_{min}$ and the number of subsequent packet dropouts are bounded by $\overline{\delta }$, which means

$$\sum _{v=k-\overline{\delta }}^k{m}_i\left(v\right)\le \overline{\delta }$$

(6)

Then, the admissible sequences can be described as follows:

$$\begin{array}{c}\hfill {\wp }_i=\left\{\begin{array}{c}\hfill {(s_i\left(k\right),{\tau }_{d_i}\left(k\right),m_i\left(k\right))}_{k\in N}|h_{min}\le s_i(k+1)\\ \hfill -s_i\left(k\right)\le h_{max},\\ \hfill s_i\left(0\right)=0,{\tau }_{d_{min}}\le {\tau }_{d_i}\left(k\right)\le {\tau }_{d_{max}},\sum _{v=k-\overline{\delta }}^k{m}_i\left(v\right)\\ \hfill \le \overline{\delta }\end{array}\right.\end{array}$$

(7)

where $s_i\left(k\right)$ represents the sampling instants:

$$s_i\left(k\right)=\sum _{k=0}^m{h}_i\left(k\right)m\ge 1s_0=0$$

(8)

which are having the same distance in time made by $h_i\left(k\right)>0$, and this is denoted to sampling intervals.

2.3. Algebraic Graph Theory

A multi-agent system’s communication network can be modeled using a directed graph. A directed graph is a non-empty finite set with N nodes, arcs, or edges, and the $A_{dir}=\left[a_{ij}\right]\in {\mathcal{R}}^{N\times N}$ correlated adjacency matrix. The nodes of the communication-directed graph in a quadrotor are agents. The communication linkages are denoted by the edges of the communication network’s matching directed graph. The $(x_j,x_i)$ represents an edge between j node and i nodes, indicating that j node sends the data to i node, and the weight of the edge $(x_j,x_i)$ is denoted by $a_{ij}$. Node i is regarded as a neighbor of node j. $N_j$ refers to the neighbor set of j node. If j node and i node are neighbors in a directed graph, then the j node and i node can obtain information from each other. The in-degree matrix is configured to $D_{dir}=diag(d_i\in {\mathcal{R}}^{N\times N})$. The Laplacian matrix is defined as $L_g=D_{dir}-A_{dir}$. An edge series is a straight link from the i node to the j node. The spanning tree of a directed graph happens when a root node has a direct path connecting to every other node in the graph.

2.4. Data Distribution Service Middleware

A data distributed service is commonly regarded as the ideal middleware for unmanned aerial formation control due to its ability to handle data as a result of real-time mission-critical and publication–subscription systems. It also has a pliable established policy setting for quality of service (QoS) that may be used for a variety of applications. DDS middleware is deemed in our investigation for UAV formation control because it gives almost all performance measures. The DDS middleware is built on the concept of a subscription-publishing, by postulating some of these UAVs acting as publishers and others as subscribers collaborating with each other. A publish–subscribe structure encourages flexible and dynamic loose coupling between the data architecture. DDS-based systems can easily be adapted and applied to different conditions and criteria. In addition, a publish–subscribe structure is where multiple subscribers and publishers share highly typed information across a common topic. A reliable quality of service model manages the communication. These QoS regulations might be used separately or as a set, in order to influence different aspects of communications, such as reliability, durability, and data persistence. These QoS regulations sets are a feature of the DDS not available in all other middleware approaches for communication. They guarantee high reliability, performance, and low-latency integration of DDS data transmission. On the other hand, The DDS middleware has some drawbacks, such as that QoS policies are only enforced in a tight DDS framework. In addition, DDS requires double bandwidth compared to MQTT middleware. Furthermore, Web applications are not supported by DDS. To solve this, the OMG designed a web-enabled DDS standard. A web application can be constructed utilizing this interface that interacts directly with the DDS system via a gateway. The following are a customizable set of quality of service settings criteria that must be completed prior to the interaction between both the UAV subscriber and the UAV publisher:

• Durability: Indicates whether or not the publisher formerly transferred information to a new subscriber.
• Reliability: Can decide whether the DDS should retransmit information that has been lost over the middleware. Reliability can be configured in two ways: RELIABLE (retransmit missing information) or BEST EFFORT (do not retransmit missing information). With this QoS, the DDS middleware can prevent the formation system from losing the information caused by the DoS attacks.
• History: Indicates whether or not data receipted or transmitted by a publisher would be kept for a subscriber. History can be configured in two ways: KEEP ALL and KEEP LAST. The first option does not store an infinite amount of data.
• Deadline: Sets the maximum period for specimens to arrive for subscribers.
• Ownership: Can decide whether or not a subscriber would receive new samples that were collected from different publishers at the same time. There are two types of ownership: EXCLUSIVE and SHARED.
• Presentation: Manages how the middleware presents the information received by the subscriber.
• Time-based Filter: Confirms the minimum time duration between the current information and the future information received by the subscriber.
• Latency budget: Indicates the time allowed by the middleware to deliver the information.
• Lifespan: Determines for how long the middleware will accept the validity of the information sent by the publisher.
• Resource Limits: Sets the memory space that a publisher or subscriber could assign for storing information in cache memory.

3. Multiple UAVs Control Design

3.1. L1 Adaptive Control

The fundamental advantage of using the L1 adaptive controller is its capability of adjusting quickly and robustly, as well as the decoupling of robustness and adaptability. It also provides a guaranteed time-delay margin and eliminates hardware performance constraints. The proper design of the bandwidth-limited filter is a challenging issue when using the L1 adaptive controller [28]. The state-space form required for applying an L1 controller on the dynamics’ rotational in Equation (2) is described as follows:

$$\begin{array}{cc}\hfill \dot{x}=& A_{m}x+b(f(t,x\left(t\right))+\omega u_{ad}),x\left(0\right)=x_0\hfill \\ \hfill y=& c^{\top }x\left(t\right)\hfill \end{array}$$

(9)

where

$$\begin{array}{c}x\triangleq {\nu }_2,\mathrm{a}\mathrm{known}\mathrm{Hurwitz}\mathrm{matrix}\triangleq A_m\in {\mathbb{R}}^{n\times n}\hfill \\ \omega \triangleq I_{\mathrm{M}}^{-1},b=1,u_{ad}\triangleq {\mathcal{L}}_1\mathrm{Adaptive}\mathrm{control}\triangleq \tau \hfill \\ I_{\mathrm{M}}^{-1}(-({\nu }_2\times I_{\mathrm{M}}{\nu }_2)-I_R({\nu }_2\times z_e)\Omega -k_r{\nu }_2)\triangleq f(t,x\left(t\right))\hfill \\ c^{\top }=I_{3\times 3}\hfill \end{array}$$

(10)

Equation (9) can be rewritten as follows:

$$\begin{array}{cc}\dot{x}=& A_{m}x+{b(\theta \parallel x\parallel }_{\infty }+\sigma +\omega u_{ad}),x\left(0\right)=x_0\hfill \\ \hfill y=& c^{\top }x\left(t\right)\hfill \end{array}$$

(11)

Equation (11) has a predictor state of

$$\begin{array}{cc}\hfill \dot{\widehat{x}}=& A_m\widehat{x}+b(\widehat{\theta }{\parallel x\parallel }_{\infty }+\widehat{\sigma }+\widehat{\omega }{u}_{ad}),\widehat{x}\left(0\right)=x_0\hfill \\ \hfill \widehat{y}=& c^{\top }\widehat{x}\hfill \end{array}$$

(12)

where $\widehat{x}\in {\mathbb{R}}^n$ represents the estimated state, $\widehat{y}\in {\mathbb{R}}^n$ represents the estimated output, and $\widehat{\theta }\mathrm{and}\widehat{\sigma }$ represent the estimated parameters. $\tilde{\theta }=\widehat{\theta }-\theta$, $\tilde{x}=\widehat{x}-x$, and $\tilde{\sigma }=\widehat{\sigma }-\sigma$ are the error definitions. The following is the dynamic error:

$$\begin{array}{c}\hfill \dot{\tilde{x}}=A_m\tilde{x}+b(\tilde{\theta }{\parallel x\parallel }_{\infty }+\tilde{\sigma }),\tilde{x}\left(0\right)=0\end{array}$$

(13)

The adaption law is derived as follows:

$$\begin{array}{cc}\hfill \dot{\widehat{\sigma }}=& \dot{\tilde{\sigma }}=\Gamma \mathrm{Proj}(\tilde{\sigma },-bP\tilde{x})\hfill \\ \hfill \dot{\widehat{\theta }}=& \dot{\tilde{\theta }}=\Gamma \mathrm{Proj}(\tilde{\theta },-{\parallel x\parallel }_{\infty }bP\tilde{x})\hfill \end{array}$$

(14)

where the adaption law’s rate is expressed by $\Gamma >0$. As seen in [29], Proj indicates the operator’s projection. $Q=Q^{\top }>0$ and $P=P^{\top }>0$ satisfy the expression

$$\begin{array}{c}\hfill -Q=P{A}_m+A_m^{\top }P\end{array}$$

(15)

Finally, the adaptive control law can be expressed as follows:

$$\begin{array}{c}\hfill u_{ad}\left(s\right)=-\frac{k}{s}(\widehat{\mu }\left(s\right)-k_{g}r\left(s\right)+\omega u_{ad}\left(s\right))\end{array}$$

(16)

where $\widehat{\mu }\left(t\right)\triangleq \widehat{\theta }\left(t\right){\parallel x\parallel }_{\infty }+\widehat{\sigma }\left(t\right)$ expresses the inverse Laplace transform of $\widehat{\mu }\left(s\right)$, $r\left(t\right)$ represents the inverse Laplace transform of the reference $r\left(s\right)$, and the feed-forward gain is expressed by $k_g\triangleq -\frac{1}{c^{\top }{A}_m^{-1}b}$. L1 adaptive control details are found in [26,27,28].

3.2. Formation Control

3.2.1. Formation Objective

Consider a multi-agent system consisting of N agents, described as follows:

$$\begin{array}{c}\hfill x_i(k+1)=A_i{x}_i\left(k\right)+B_i{u}_i\left(k\right)\\ \hfill y_i\left(k\right)=C_i{x}_i\left(k\right)i=1,2\dots N\end{array}$$

(17)

where

$$\begin{array}{c}\hfill A_i=diagonal(\left[\begin{array}{c}01\\ a_{21}^1{a}_{22}^1\end{array}\right]....\left[\begin{array}{c}01\\ a_{21}^n{a}_{22}^n\end{array}\right]),\\ \hfill B_i=I_n\otimes \left[\begin{array}{c}0\\ 1\end{array}\right],x_i\left(k\right)=\left[\begin{array}{c}{x}_{p_i}\\ x_{v_i}\end{array}\right]and{x}_i(k+1)=\left[\begin{array}{c}{x}_{v_i}\\ x_{a_i}\end{array}\right]\end{array}$$

Definition 1

([30]). A formation is a vector $h=h_p\otimes \left[\begin{array}{c}1\\ 0\end{array}\right]\in R^{2N}$. The N agents are in formation h if there are vectors $q,w\in R^N$ such that ${\left(x_p\right)}_i-{\left(h_p\right)}_i=q,{\left(x_v\right)}_i=w,i=1,\dots ,N$ where subscript p (position) and subscript v (velocity) are components of $x_i$.

Therefore, the error between vehicles is calculated as follows:

$$\begin{array}{c}\hfill e_i=-\frac{1}{|{\mathrm{J}}_i|}\sum _{j\in {\mathrm{J}}_i}(x_j-h_j)+(x_i-h_i)i=1,\dots ,N.\end{array}$$

(18)

We seek a feedback control $K_i$ that guides the agent i into a formation h using the Kronecker product of graph Laplacian matrix $L=L_g\otimes I_N$, where the graph Laplacian matrix $L_g=D_{dir}-A_{dir}$, where $D_{dir}$ and $A_{dir}$ indicate the degree matrix and the adjacency matrix, respectively, such that the following objective is achieved:

$$\begin{array}{c}\hfill \underset{t\to \infty }{lim}\left|\right|x_i-h_i\left|\right|=q,\forall i\in N\end{array}$$

(19)

Then, by substituting $u_i$ into Equation (17), we obtain

$$\begin{array}{c}\hfill x_i(k+1)=A_{1_i}{x}_i\left(k\right)+B_{1_i}{K}_{i}L(x_i-h_i)\\ \hfill y_i\left(k\right)=C_{1_i}{x}_i\left(k\right)i=1,2...N\end{array}$$

(20)

with $A_{1_i}=I_N\otimes A_i,B_{1_i}=I_N\otimes B_i,and{C}_{1_i}=I_N\otimes C_i$.

3.2.2. Formation Design

In this section, we discuss the design of the control gains $K_i$ for each agent i based on LMI techniques.

The proposed LMI approach used in this research is a modification of the method in [31]. If there exist symmetric positive definite matrices $Y_i\left(j\right)$∈$R^{n+(\overline{d}+\overline{\delta })mxn+(\overline{d}+\overline{\delta })m}$, a matrix $\overline{Z_i}$∈$R^{mxn}$, matrices

$$X_i\left(j\right)=\left[\begin{array}{c}{\overline{X}}_i(1,j)0\\ {\overline{X}}_i(2,j){\overline{X}}_i(3,j)\end{array}\right]$$

(21)

with ${\overline{X}}_i(1,j)$∈$R^{nxn},$${\overline{X}}_i(2,j)$∈$R^{(\overline{d}+\overline{\delta })mxn}$${\overline{X}}_i(3,j)$∈$R^{(\overline{d}+\overline{\delta })mx(\overline{d}+\overline{\delta })m}$, j = 1, 2, … and a scalar $\gamma <1$ satisfying the following LMI matrix:

$$\left[\begin{array}{c}{X}_i\left(j\right)-Y_i\left(j\right)X_i{\left(j\right)}^T{H}_{F,i}^T-{\left({\overline{Z}}_{i}0\right)}^T{H}_{G,i}^T\\ H_{F,i}^T{X}_i^T\left(j\right)-H_{G,i}^T{\left({\overline{Z}}_{i}0\right)}^T(-\gamma )X_i\left(j\right)\end{array}\right]>0$$

(22)

where

$$H_{F,i}=\left[\begin{array}{c}{e}^{A_i{h}_i}{\int }_{h_{min}}^{h_{max}}{e}^{A_{i}s}ds{B}_i\hfill \\ 00\end{array}\right],\mathrm{and}{H}_{F,i}=\left[\begin{array}{c}{\int }_{h_{min}}^{h_{max}}{e}^{A_{i}s}ds{B}_i\\ 1\end{array}\right]$$

then the formation for all agents $i\in 1,2,\dots$ with ${\overline{K}}_i={\overline{Z}}_i{\overline{X}}_i^{-1}$ is globally asymptotically stable.

Proof. 

See Appendix A. □

4. Simulation Results

Simulation studies were conducted in MATLAB considering a the formation of six UAVs. The DDS middleware, graph theory, LMI, and L1 adaptive controller are used.

Table 1. The quadrotor parameters.

Symbol	Value/Unit	Properties
g	9.8 m/s${}^2$	Gravity Acceleration
m	0.52 kg	Mass
$k_r$	$0.105$	Drag’s Rotational
L	0.205 m	Arm Length
$k_t$	$0.95$	Drag’s Translational
d	7.5 × 10${}^{-7}$	Ratio of Drag and Thrust
$I_z$	0.0129 kg·m${}^2$	Inertia of z-axis
$I_y$	0.0069 kg·m${}^2$	Inertia of y-axis
$I_x$	0.0069 kg·m${}^2$	Inertia of x-axis
$I_R$	3.36 × 10${}^{-5}$ kg·m${}^2$	Propeller Inertia

shows the quadrotor parameters that were used [27].

Furthermore, the controller parameters are set to $k_d$ = 10, $k_p$ = 10 and $\gamma$ = ${10}^6$. Figure 1 shows the flowchart of multiple UAVs’ formation control utilizing graph theory and LMI controllers. Figure 2 depicts the network topology between multiple UAVs, which is based on a set of QoS criteria (

Table 2. Quality of service (QoS) policies.

QoS Policies	QoS Value
	Subscriber	Publisher
Deadline	Infinite	Infinite
Durability	Volatile	Volatile
History	Keep Last	Keep All
Reliability	Reliable	Reliable
Ownership	Shared	Shared

) that must be met before interaction between the subscribers and publishers may begin. The degree matrix $D_{dir}$ and the adjacency matrix $A_{dir}$ of the graph in Figure 2 are

$$\begin{array}{c}\hfill D_{dir}=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]\mathrm{and}{A}_{dir}=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ 1& 0& 0& 0& 0& 0\end{array}\right]\end{array}$$

(23)

The following cases were taken into account in the formation control’s simulation:

• UAVs formation without DoS attacks: In the first case, we considered six UAV models with communication delay only. The proposed LMI condition was used to find the formation feedback gain, which means without dropout packet produced by DoS attacks or $\overline{\delta }$ = 0, $h_{min}$ = 0.01, $h_{max}$ = 0.014, ${\tau }_{max}$ = 100$h_{max}$, and ${\tau }_{min}$ = 10$h_{min}$ in the delay, as shown in Figure 3, with ${\gamma }_0$ = 0 and h = 1, and the same initial values of the UAVs, shown in Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8. This demonstrates how a swarm of six unmanned aerial vehicles (UAVs) may establish a certain topology in 2D space without the effect of the DoS attacks.
• UAVs formation under DoS attacks: In the second case, we considered six UAVs model with communication delay and dropout packet produced by DoS attacks for when we applied the effect of the DoS attacks, as in Figure 9 on the system, with the same parameters and same controller as in the first case and the same initial values of the UAVs. This is shown in Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14. The figures illustrate how a swarm of six unmanned aerial vehicles (UAVs) may establish a certain topology in 2D space under the effect of the DoS attacks.

Figure 4, Figure 5, Figure 6 and Figure 7 show the formation control of six UAVs without the effect of DoS attacks. It can be seen that all of the UAVs were built in a hexagon shape. Figure 8 shows the full-view map of UAVs’ formation without the effect of DoS attacks. It is clear that at each time, the six UAVs are constructed in a hexagon shape. The DDS middleware was used to share data between the six UAVs.

Figure 10, Figure 11, Figure 12 and Figure 13 illustrate the formation control of six UAVs under the effect of DoS attacks. It can be seen that all of the UAVs were recognized in a hexagon shape. This huge variance caused by DoS attacks had no effect on the system’s performance. Figure 14 illustrates the full-view path of UAVs’ formation under the effect of DoS attacks. It is clear that the six UAVs are structured in a hexagon shape at each time. Information was transmitted across the six UAVs using the DDS middleware.

5. Discussion Summary

The DDS formation between multiple UAVs systems is shown in Figure 2. To make this communication, all of the UAVs consider publishers’ UAVs and subscribers’ UAVs at the same time. A set of QoS criteria must be followed when publishers’ UAVs and subscribers’ UAVs communicate. The formation control of six UAVs in the absence of DoS attacks is illustrated in Figure 4, Figure 5, Figure 6 and Figure 7. Six of the UAVs were positioned in a hexagon formation. The whole path of UAV formation without the influence of DoS attacks is depicted in Figure 8. The DDS middleware is used to facilitate information transmission between the UAVs. The formation control of multiple UAVs under the effect of DoS attacks is shown in Figure 10, Figure 11, Figure 12 and Figure 13. All of the UAVs are identified as being in the shape of a hexagon. The whole map of UAV formation with the effect of DoS attacks is shown in Figure 14. The DDS middleware is used to make data communication between the UAVs easier.

6. Conclusions

This paper presents a novel architecture for secure formation control of several UAVs. The LMI controller, DDS middleware, L1 controller, and graph theory approach are used to construct multiple UAV formation control under DoS attacks. The LMI controller is utilized to overcome the communication time delay and packet drops produced by DoS attacks. As a result, data were exchanged between the UAVs using the DDS middleware, In addition, it can be considered as an extra security level based on its reliable QoS. Furthermore, the L1 controller is utilized as a local controller to stabilize the UAV’s dynamic model. Moreover, the graph theory approach is utilized to maintain the UAVs in hexagon formation. The L1 adaptive and LMI controller perform effectively in the face of DoS attacks. According to the simulation results, the L1 adaptive controller, LMI controller, and DDS middleware significantly improved overall performance.