Remote Fault-Tolerant Control for Industrial Smart Surveillance System

We design a remote fault-tolerant control for an industrial surveillance system. (e designed controller simultaneously tolerates the effects of local faults of a node, the propagated undesired effects of neighboring connected nodes, and the effects of networkinduced uncertainties from a remote location. (e uncertain network-induced time delays of communication links from the sensor to the controller and from the controller to the actuator are modeled using two separate Markov chains and packet dropouts using the Bernoulli process. Based on linear matrix inequalities, we derive sufficient conditions for output feedbackbased control law, such that the controller does not directly depend on output, for stochastic stability of the system.(e simulation study shows the effectiveness of the proposed approach.


Introduction
Surveillance of processes is generally defined as monitoring of activities and behavior to collect information to influence, manage, or direct. In industries, the surveillance is done via industrial drones that have applications in defense, newsgathering, telecommunication, humanitarian needs, public and private safety, traffic monitoring, security, and process industry [1]. ese drones are equipped with a gimbal camera sensor that collects information and sends it to a remote control room through a communication network. A smart surveillance system makes use of a remote control mechanism that can handle the surveillance operation. e remote control of geographically distributed networked systems is widely used [2][3][4] for cost reduction, simple installation, and maintenance and for increasing efficiency and reliability in the recent industrial revolution. Recent advances in industrial control mechanisms call for more sophisticated schemes for remote surveillance. Such surveillance schemes are desired to take care of detecting and diagnosing faults and tolerating them if needed.
In controlling plants from a remote location over communication networks, controllers face two main issues that are network-induced uncertainties and faults. e network lines induce random time delays and data packet dropouts during plant-controller communication over a network. ese communication imperfections degrade the system performance. To achieve a prescribed performance, control engineers are trying to tolerate its effects. For this purpose, the researchers modeled the time delays as constant, time-varying, or random variable [5,6]. Markov chain is suitable to model for these network-induced effects as it depends on the current state only. However, in practice, especially in NCSs, the exact values of Transition Probabilities (TPs) are either hard to determine or costly. Consequently, for a practical design, it is necessary to consider more complex TPs, such as uncertain TPs or partly unknown TPs [7][8][9]. Similarly, packet dropouts are modeled with probability-based switches for networked systems [10][11][12][13].
Parallel with network uncertainties faults in the sensor, the actuator, or in the process itself may occur in networked systems. A lot of work has been done in the fault diagnosis and tolerance of such industrial processes [14] as maintenance and repair cannot always be achieved immediately in automated systems. For remotely distributed connected systems, these faults become more uncertain due to the propagation of fault over network links to neighboring connected nodes [15]. e propagated faulty effects may be nonlinear that may add to the already existing faults of other connected nodes [16][17][18].
e objective is to tolerate the effects of local simultaneous faults, propagated effects of faults that occur at other connected nodes, and networkinduced uncertainties.
Researchers have put their efforts into the diagnosis of faults in such geographically distributed connected systems [19,20]. Most of the researchers addressed either the actuator faults or sensor faults with network-induced effects especially with time delays [14]. In real-time applications, both the sensor and actuator faults may occur simultaneously. at is why it is important to address both types of faults at a time. For this purpose, the authors of [21] addressed both sensor and actuator simultaneous faults but with relatively conservative fault models. e authors' designed a state feedback-based controller that has limitations in practical applications due to the rare accessibility of fully known state vectors. One other source of motivation is that the existing literature addressed the components' faults only without the propagated effects [15][16][17] of faults of other nodes. e authors of [18] presented a new fault model for actuators and tolerated its effects using a state feedback controller. e model addressed the nonlinear effects too that may occur due to faults or other technical limitations. In this approach, the following things are important to note. Firstly, we need tolerance of simultaneous sensors and actuators faults in practical applications while the authors addressed only actuator faults. Secondly, the designed state feedback controller has limitations from a practical point of view due to the rare accessibility to all states. e third one is that only time delays are considered in the sensor-to-controller link that means the controller receives packets over a link and command the actuator directly without network link. Furthermore, packet dropout, which may occur in links due to network traffic, is not taken into account in the same link.
To address the aforementioned issues, we have designed a remote fault-tolerant control for an industrial smart surveillance system with the following contributions.
(1) e random time delay and the data packet dropouts are modeled in sensor-to-controller (S/C) links and controller-to-actuator (C/A) links separately. e time delays are modeled using two separate Markov chains with partly unknown transition probabilities and packet dropouts with two separate Bernoulli processes. e formulation helps us to establish a new framework to analyze a remote fault-tolerant control problem for industrial systems over a network.
(2) e mode-dependent output feedback-based remote controller is designed such that the controller does not directly depend on the sensor's output. Such dynamic remote fault-tolerant controllers are significant for industrial processes where the system's states are unknown. (3) Sufficient conditions are derived in terms of linear matrix inequality (LMI) for a closed-loop Markovian Jump nonlinear system. e derived control law ensures the stochastic stability of the system and tolerates the sensors and actuator simultaneous faults to maintain the prescribed performance in a networked environment.
We organized the subsequent sections of the paper in the following way. We dedicate Section 2 for system description and problem formulation, where uncertain network-induced imperfections are modeled as a Markov chain, and then present a new fault model for networked systems. e symbols used throughout the paper are given in Table 1. In Section 3, remote fault-tolerant control is designed for the industrial surveillance system using a new LMI. In Section 4, simulation results are presented and compared with a conventional remote control for the effectiveness of our proposed control design, and then, the paper is concluded.

Smart Surveillance
System. e smart surveillance system consists of multiple drones connected via a shared communication network. Each drone is equipped with a gimbal camera sensor and is controlled from a remote location, as shown in Figure 1. e drone is used to carry the gimbal-based camera sensor to different locations for monitoring and surveillance. e collected information via a camera sensor or from other connected drones is then sent to a remote control room. e camera sensor is pivoted in the inner channel of the gimbal system that decouples it from the drone body. e decoupling helps the camera sensor to collect information with minimum viewpoint changes [22]. e camera sensor inside the gimbal system is actuated using BLDC motors according to the commands of the controller. is gimbal-based smart surveillance system for industries has to be controlled from remote locations for safe and easy use.
To make the smart monitoring and surveillance system, we consider two things. Firstly, the controller can stabilize and control the camera system from a remote location for safe and easy use. Secondly, the designed controller can tolerate the effects of local faults, propagated or external faults that may be nonlinear, and network-induced uncertainties simultaneously. e local faults are sensors and actuators faults in our case. is smart surveillance system has applications in industries where we need information from remote locations with safety and ease.

Problem Formulation.
Consider the remote control scenario of a smart surveillance system in Figure 2 where a remote controller controls the gimbal camera sensor through a shared communication network. e system modeling with related detail can be seen in [23,24]. e state dynamics of the system are given as where x(k) ∈ R n is the state vector, u * (k) ∈ R m is the input signal, and y(k) ∈ R p is the output. A, B, and C are system constant matrices of compatible dimensions. Besides, the matrix C has a full-row rank.

Sensor-to-Controller Communication.
From the sensor to the controller, the output signals propagate via network links and then are available to the controller. Output of the camera sensor available to the controller may be with faulty effects in the camera sensor and with communication uncertainties. To model the output y(k) with faults, we introduce e sensors faults are modeled as where Ω denotes the faults' matrix and the functions ω l ∈ [0, 1], for l � 1, . . . , p, indicate the status of each individual actuator as the sensor is working normally, 0, the sensor is failed completely, otherwise, the sensor is partially working.
For the gimbal-based surveillance system, p � 1 because of only one camera sensor that is in the inner channel of the gimbal system. f(·) is a nonlinear term that may add due to occurrence of fault or other technical limitation [18]. e aforementioned faulty output data may or may not reach to the controller due to network traffic. e scenario can be modeled with random events as Event 1: Succesful transmission and output is available, Event 2: Link fail and output is not available. (5) To model the random events, we introduce a(k) which is a binary random vector. A value "1" of a i (k) indicates that the packet was delivered successfully in the i th channel and "0" indicates that the packet was dropped. Here, We assume the following probabilities for a i (k): where Pr a i (k) � 1 is the probability of packet transmission in S/C links and E is the mathematical expectation. When the probability of a i (k) � 1, it means maximum probability or successful transmission of data packet through S/C links, else the packet is lost.

C2A-induced delays Network
Controller S2C-induced delays Sensor Figure 2: Control over network. Controller's output u * (k) Actuator's output with faults and network effects y(k) Sensor's output y * (k) Controller's input with faults and network effects Θ Actuator fault matrix Mathematical Problems in Engineering e data packets that reach from the sensor to the controller face random time delays τ ksc . We assume that τ ksc varies randomly between 0 and τ 1 , where τ 1 is the maximum time delay of a packet. We model the time delays τ ksc with a Markov chain Θ 1 with N number of stats, i.e., Θ 1 ∈ 1, 2, . . . , N 1 . Let ρ 1 be the transition probability matrix of the Markov chain that is given as where where ? in the matrix are unknown state transition probabilities of time delays and the rest of entries are known transition probabilities. e stochastic faulty output that is available to the controller is Due to the network-induced probabilistic packet dropouts and time delays in the network links, the controller mode may not synchronize with the system modes. For this networked system, we introduce a dynamic output feedbackbased remote control F(τ ksc ) as follows: Remark 1. e direct output of the camera sensor is not available to the controller due to network impurities. e network uncertainties are stochastic, that is why the output may or may not be available. e available output is the delayed version with a time delay of τ ksc and maybe with the effects of faults.

Controller-to-Actuator Communication.
e controller output u(k) propagates via network links from the controller to the actuator, as shown in (2). e data face packet dropout and random time delay in the controller-to-actuator links. It means the data packets of the controller may reach the actuator or may drop due to network traffic. is communication is modeled with random events as Event 1: Succesful transmission and u(k) is available, Event 2: Link fail and u(k) is not available.
For the random events that occur in the controller-toactuator links, we introduce b(k) that is a binary random vector. b i (k) � 1 indicates that the packet delivered successfully in the ith channel while b i (k) � 0 indicates that the packet dropped. Here, i ∈ 1, 2, . . . , m { }. We assume the following probabilities for b i (k): where Pr b i (k) � 1 is the probability of packet transmission in C/A links and E is the mathematical expectation. When the probability of b i (k) � 1, it means maximum probability or successful transmission of data packet through C/A links, else the packet is lost. e data packets that successfully transmit via C/A link face random time delays τ kca . We assume that τ kca varies randomly between 0 and τ 2 , where τ 2 is the maximum time delay. We model the time delays τ kca with a Markov chain Θ 2 with N 2 number of stats, i.e., Θ 2 ∈ 1, 2, . . . , N 2 . Let ρ 2 be the transition probability matrix of the Markov chain that is given as where e transition probability matrix is similar to the sensor-tocontroller link. We assume that ρ � ρ 1 + ρ 2 . e industrial surveillance system may experience local faults in the actuators. e effects of actuators' faults can be modeled as where Θ denotes the faults matrix and functions θ l ∈ [0, 1], for l � 1, . . . , m 2 , indicate the status of each individual actuator, that is, the actuator is working normally, 0, the actuator is failed completely, otherwise, the actuator is partially working.
e plant's input u * (k) with the communication link impurities can be written as where g(·) is the nonlinear term that may add due to technical limitations [18].
Remark 2. Equation (16) demonstrates that the control signal may or may not reach the actuator. If b i (k) � 1, then the delayed version of u(k) with time delay of τ kca will be available to the actuator. e packet dropouts and time delays in C/A links and S/C links are considered independent random events. We consider time delays for those packets which are successfully transmitted via network links. e lump delay is τ k � τ ksc + τ kca . Consequently, considering the augmented state vector as (10) and (16) in (1) leads us to the closed-loop dynamics of the networked system as follows: Remark 3.
e output feedback-based closed-loop networked system derived in (17) is a nonlinear stochastic system with two data packet dropout modes a i (k) and b i (k) and two time-delay modes τ ksc and τ kca .
e system in (17) can be written in a compact form as follows: where

Fault-Tolerant Control Design
Assumption 1. We assume that there is no packet dropouts and time delays in the bounded nonlinear functions that we add to the sensor and actuator faults f(y(k)) and g(u(k)), respectively, which satisfy the following local Lipschitz conditions: f T (y(k))f(y(k)) ≤ ] 2 y T (k)y(k), where ] > 0 and c > 0 are the bounding parameters for nonlinear functions f(y(k)) and g(u(k)).
Here, we present our LMI for the proposed remotely located output feedback controller design to ensure stochastic stability. Theorem 1. Consider the closed-loop system for the industrial surveillance systems as in (18), and let ] > 0, c > 0, ϵ 1 > 0, and ϵ 2 > 0 be the given scalars. A desired output feedback controller gain of form (10) exists if there exist matrices X i > 0, where ξ 11

Mathematical Problems in Engineering
Proof. We choose the Lyapunov function candidate as and then, we have It can be shown that ΔV ≤ 0 implies E Σ ∞ k�0 ‖η k‖ 2 |η(0), τ k0 , a (0) , b I (0)} ≤ ∞ that guaranteed stochastic stability for the augmented state vector given in (18). By defining the augmented state vectors, we can write equation (26) as 6 Mathematical Problems in Engineering Multiplication of diag(G T i , I) from left and diag(G i , I) from right to ξ 0 and defining X i � P −1 i , F(τ k )CG i � R i C, then, by using the Schur complement and the introduction of network-induced uncertainties as in [18] results the following is obtained: where □ Lemma 2. For C with rank p, there exist nonsingular matrices Q i such that Q i C � CG i for which there exist a full-rank matrices G i satisfying where

Remark 4.
e output matrix C is assumed as a full-row rank. e bilinear matrix inequalities are transformed under this assumption into a set of linear matrix inequalities. e assumption is removed in [10]. As it can be satisfied for many practical applications, that is, why it is not a major constrain. In [18], a similar problem is solved for the faulttolerant control design of networked systems with the state feedback control design. e state feedback control is not significant for real-time applications due to the rare accessibility of all states.

Simulation Study
A gimbal-based camera sensor communicates with a remote controller through a communication link and the control controls the actuator over a network link, as shown in Figure 2. State variables of the surveillance system are the angular positions ϕ and ψ of inner and outer channels and angular velocities of inner and outer channels _ ϕ and _ ψ of the gimbal system, respectively. To actuate the system, two brushless DC motors are used with torques U τ 1 , U τ 2 , respectively. Angular velocity of the inner channel, which holds the camera sensor, is taken as output of the surveillance system. e system dynamics [23,25] for the surveillance system with initial conditions are ere are two actuators and one sensor. e first actuator is working normally and the second actuator and the sensor both are working partially. e fault matrices are given as follows: Θ � 1 0 0 0.7 and Ω � 0.6 . e nonlinearities that may add to faults are g(·) � 0.6u(k)cos(u(k)) and f(·) � 0.7y(k)cos(y(k)). e complex transition probability matrices for the sensor-to-controller link and the controller-to-actuator link, respectively, are given as if τ kca � τ ksc � 3. e Bernoulli stochastic variables for sensor-to-controller and controller-to-actuator links are a i (k) � b i (k) � 0.7. e data packet dropouts and random time delay for the sensor-to-controller link and controller-to-actuator links are given in Figures 3 and 4, respectively. Similarly, the Markov evaluation of the controller modes and the system modes are given in Figure 5.
e simulation results of a smart surveillance system for the tolerance of simultaneous local sensors and actuator faults propagated effects of faults of other nodes, and network-induced uncertainties are shown in Figures 6 to 8. In Figure 6, we plot the tolerance of faults with and without the nonlinear effects. e blue solid line is for tracking without nonlinear effects and the red dotted line is for tracking with nonlinearities. Similarly, Figure 7 demonstrates the tracking performance with and without network-induced uncertainties. For comparison in tracking response and fault tolerance, we plot the output of a conventional controller and the proposed controller in presence of network-induced uncertainties without faults in Figure 8. Oscillation in the tracking response of the conventional controller will further increase if we add faults, especially, if we add simultaneous faults. is proves the superiority of the proposed controller in fault tolerance and in tracking targets. In Figure 9, we plot the tracking response with states to show that the states are stable even in the presence of the sensor fault. Starting with different initial conditions, all the states are stable and converge to zero with output tracking the reference input. e output feedback controller gain of the remote controller for the industrial smart surveillance system are calculated using MATLAB LMI toolbox and is given as

Conclusion
We presented two new fault models for sensors and actuators that are more general than the existing fault models. Random time delays and uncertain data packet dropouts of the network links are modeled in S/C links and C/A network lines separately by using Markov chains and Bernoulli processes, respectively. e remote fault-tolerant controller successfully tracks the reference input and tolerates the effects of simultaneous faults in the presence of networkinduced uncertainties. Simulation results for the surveillance system verify the stochastic stability of the systems and the applicability of the controller design.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest.