Robust event‐triggered model predictive control for cyber‐physical systems under denial‐of‐service attacks

This paper investigates the resilient control problem for constrained continuous‐time cyber‐physical systems subject to bounded disturbances and denial‐of‐service (DoS) attacks. A sampled‐data robust model predictive control law with a packet‐based transmission scheduling is taken advantage to compensate for the loss of the control data during the intermittent DoS intervals, and an event‐triggered control strategy is designed to save communication and computation resources. The robust constraint satisfaction and the stability of the closed‐loop system under DoS attacks are proved. In contrast to the existing studies that guarantee the system under DoS attacks is input‐to‐state stable, the predicted input error caused by the system constraints can be dealt with by the input‐to‐state practical stability framework. Finally, a simulation example is performed to verify the feasibility and efficiency of the proposed strategy.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

Feedback control with signal transmission after‐effects

In many practical systems, the physical plant, controller, sensor, and actuator are difficult to be located at the same place, and thus signals are required to be transmitted from one place to another. One immediate problem arising from such situations is that signals may exhibit after‐effect phenomena during their transmission. In this paper, we present a new model to characterize the state‐feedback control systems with signal transmission after‐effects, which deals with the transmission after‐effects from sensor to controller and from controller to actuator separately. Analysis and synthesis results based on this new model are established by using a Lyapunov–Krasovskii approach. Numerical simulations are provided to illustrate the usefulness of the theoretical results. Copyright © 2007 John Wiley & Sons, Ltd.     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Self‐triggered state‐feedback control of linear plants under bounded disturbances

This paper addresses the problem of self‐triggered state‐feedback control for linear plants under bounded disturbances. In a self‐triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on the current sampled state and on a priori knowledge about the plant. Besides comparing some existing approaches to self‐triggered control available in the literature, we propose a new self‐triggered control strategy that allows for the consideration of model‐based controllers, a class of controllers that includes as a special case static controllers with a zero‐order hold of the last state measurement. We show that our proposed control strategy renders the solutions of the closed‐loop system globally uniformly ultimately bounded. We further show that there exists a minimum time interval between sampling times and provide a method for computing a lower bound for it. An illustrative example with numerical results is included in order to compare the existing strategies and the proposed one. Copyright © 2014 John Wiley & Sons, Ltd.     

Observer‐based synthesis of linear parameter‐varying mixed sensitivity controllers

This article presents a computationally efficient way of synthesizing linear parameter‐varying (LPV) controllers. It reviews the possibility of a separate observer and state feedback synthesis with guaranteed performance and shows that a standard mixed sensitivity problem can be solved in this way. The resultant output feedback controller consists of an LPV observer, augmented with dynamic filters to incorporate integral control and roll‐off properties, and an LPV state feedback gain. It is thus highly structured, which is beneficial for implementation. Moreover, it does not depend on scheduling parameter rates regardless of whether parameter‐dependent Lyapunov matrices are used during synthesis. A representative control design for active flutter suppression on an aeroelastic unmanned aircraft demonstrates the benefits of the proposed method in comparison with state‐of‐the‐art LPV output feedback synthesis.     

Development Of Cvt Control System And Its Use For Fuel‐Efficient Operation Of Engine

Continuously variable transmission (CVT) provides an automobile with the ability to change the gear ratio continuously, which can then improve not only ride quality such as acceleration performance but also fuel‐efficiency. However, to take advantage of the ability, a control system that can precisely control the gear ratio is required. This paper proposes such a control system for a belt‐driven CVT system. For controller design, first the CVT system is modeled by analytical and experimental approaches. The resultant static and dynamic characteristics provide a nonlinear first‐order model with an uncertain time constant and time delay. The nonlinear steady‐state gain is adjusted to one by a gain‐scheduled pre‐compensator. Thereby the plant model becomes a linear first‐order lag system with a dead time. The next step is controller design using the plant model. To guarantee stability and control performance against the parameter variation and time delay, the μ‐synthesis, a robust control method, is employed for feedback control. In addition, a feedforward controller is incorporated into the feedback control system to obtain better output response. The feedforward controller is given by a combination of the inverse system of the plant and a reference model that gives desired output response. As a result, the control system becomes a two‐degree‐of‐freedom control system. To evaluate the performance of the control system and its effectiveness on the fuel‐efficiency, computer simulation and driving tests were conducted. The simulation and experiment results prove that the proposed control system can make the gear ratio track a reference output quickly and precisely in the presence of the uncertainties. The results also show that the control system improves fuel‐efficiency by changing the gear ratio so that the engine torque and its revolution speed can satisfy optimum‐efficiency operating condition.     

Bounded consensus for multiagent systems by event‐triggered data transmission,time delay,and predictor‐based control

This paper investigates the consensus issue of multiagent systems with data transmission time delay. The state measurement of each local agent is directly sent to a private event‐trigger and further authorized to be broadcasted to its neighbors via communication network only when the threshold of the event‐trigger is violated. Since the controller always receives discrete‐time neighbor information with data transmission time delay, a predictor is employed to estimate the continuous‐time neighbor state. Based on the estimated state, a novel consensus protocol is mainly proposed for achieving the bounded consensus of the multiagent systems. By the proposed method, the asynchronous neighbor information is allowed and the margin of data transmission time delay is also given. Furthermore, it has been proved that the unwanted Zeno phenomena can be naturally excluded. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Guaranteed cost control of cyber‐physical systems with packet dropouts under dos jamming attacks

Cyber‐Physical Systems (CPSs) are vulnerable to malicious network attacks due to tight combination of cyber‐system and physical system through a more open network communication. In this paper, a guaranteed cost control problem for a CPS under DoS jamming attacks is solved via both state feedback and output feedback methods. Specifically, an energy constraint DoS jammer with clear periodic attack strategy is proposed to attack wireless channel and to degrade the system performance. Without knowing the DoS jammer's attack strategy, a passive attack‐tolerant mechanism is established, and the corresponding state feedback and output feedback controllers are designed to achieve guaranteed cost control for the CPS with inherent packet dropouts under DoS jamming attacks. Finally, numerical examples are presented to demonstrate the effectiveness of the guaranteed cost controllers.     

Robust state estimation for wireless sensor networks with data‐driven communication

Robust state estimation problem for wireless sensor networks composed of multiple remote sensor nodes and a fusion node is investigated subject to a limitation on the communication rate. An analytical robust fusion estimator based on a data‐driven transmission strategy is derived to save the sensor energy consumption and reduce the network traffic congestion. The conditions guaranteeing the uniform boundedness of estimation errors of the robust fusion estimator are investigated. Numerical simulations are provided to show the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Simultaneous Design of Parallel Distributed Output Feedback and Anti‐windup Compensators for Constrained Takagi‐Sugeno Fuzzy Systems

This paper is devoted to developing a novel approach to deal with constrained continuous‐time nonlinear systems in the form of Takagi‐Sugeno fuzzy models. Here, the disturbed systems are subject to both input and state constraints. The one‐step design method is used to simultaneously synthesize the dynamic output feedback controller and its anti‐windup strategy. A parameter‐dependent version of the generalized sector condition is used together with Lyapunov stability theory to derive linear matrix inequality design conditions. Based on this result and for different design specifications, the synthesis of an anti‐windup based dynamic output feedback controller is expressed on the form of convex optimization problems. A physically motivated example is given to illustrate the effectiveness of the proposed method.     

Hybrid threshold strategy‐based adaptive tracking control for nonlinear stochastic systems with full‐state constraints

This article focuses on the adaptive tracking control problem for a class of interconnected nonlinear stochastic systems under full‐state constraints based on the hybrid threshold strategy. Different from the existing works, we propose a novel pre‐constrained tracking control algorithm to deal with the full‐state constraint problem. First, a novel nonlinear transformation function and a new coordinate transformation are developed to constrain state variables, which can directly cope with asymmetric state constraints. Second, the hybrid threshold strategy is constructed to provide a reasonable way in balancing system performance and communication constraints. By the use of dynamic surface control technique and neural network approximate technique, a smooth pre‐constrained tracking controller with adaptive laws is designed for the interconnected nonlinear stochastic systems. Moreover, based on the Lyapunov stability theory, it is proved that all state variables are successfully pre‐constrained within asymmetric boundaries. Finally, a simulation example is presented to verify the effectiveness of proposed control algorithm.     

Observer‐based attack‐resilient control for linear systems against FDI attacks on communication links from controller to actuators

For the adversarial attacks on the communication links from the controller to the actuators, most of the existing attack‐resilient control results focus on denial‐of‐service attacks. Unlike the existing results, this paper studies the observer‐based attack‐resilient control problem for linear systems with false data injection attacks and process disturbances. Due to limited resources, the malicious attacker is assumed to only manipulate a certain number of communication links from the controller to the actuators. A novel control architecture is proposed, which consists of an attack‐resilient state observer, a controller gain scheme, and a supervisory switching strategy. The observer is developed based on the maximin strategy, and state estimation will be used to construct the controller. The switching strategy is designed to pick an appropriate controller gain and prevent the attack signals from entering the plant automatically. It is shown that the closed‐loop system is stable with an attack‐resilient performance. Finally, to verify the effectiveness of the proposed controller, simulation results on a linearized reduced‐order aircraft system and an IEEE six‐bus power system are provided.     

Robust model predictive control for polytopic uncertain systems with state saturation nonlinearities under Round‐Robin protocol

This paper is concerned with the robust model predictive control (RMPC) problem for polytopic uncertain systems with state saturation nonlinearities under the Round‐Robin (RR) protocol. With respect to the practical application, one of the most commonly encountered obstacles that stem from the physical limitation of system components, ie, state saturation, is adequately taken into consideration. In order to reduce the network transmission burden and improve the utilization of the network from the controller nodes to the actuator node, a so‐called RR protocol is employed to orchestrate the data transmission order. At each transmission instant, only one controller node that obtains the priority is accessible to the shared communication network. Our aim of the underlying problem is to design a set of controllers in the framework of RMPC such that the closed‐loop system is asymptotically stable. By taking the influence of the RR protocol and the state saturation precisely into account, some sufficient criteria are established in terms of the token‐dependent Lyapunov‐like approach. Then, an online optimization problem subjected to some matrix inequality constraints is provided, and the desired controllers can be obtained by solving the certain upper bound of the objective addressed. Finally, a distillation process example is provided to illustrate the effectiveness of the proposed RMPC approach.     

Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

The fuzzy model predictive control (FMPC) problem is studied for a class of discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems with hard constraints. In order to improve the network utilization as well as reduce the transmission burden and avoid data collisions, a novel event‐triggering–based try‐once‐discard (TOD) protocol is developed for networks between sensors and the controller. Moreover, due to practical difficulties in obtaining measurements, the dynamic output‐feedback method is introduced to replace the traditional state feedback method for addressing the FMPC problem. Our aim is to design a series of controllers in the framework of dynamic output‐feedback FMPC for T‐S fuzzy systems so as to find a good balance between the system performance and the time efficiency. Considering nonlinearities in the context of the T‐S fuzzy model, a “min‐max” strategy is put forward to formulate an online optimization problem over the infinite‐time horizon. Then, in light of the Lyapunov‐like function approach that fully involves the properties of the T‐S fuzzy model and the proposed protocol, sufficient conditions are derived to guarantee the input‐to‐state stability of the underlying system. In order to handle the side effects of the proposed event‐triggering–based TOD protocol, its impacts are fully taken into consideration by virtue of the S‐procedure technique and the quadratic boundedness methodology. Furthermore, a certain upper bound of the objective is provided to construct an auxiliary online problem for the solvability, and the corresponding algorithm is given to find the desired controllers. Finally, two numerical examples are used to demonstrate the validity of proposed methods.     

State and mode feedback control strategy for discrete‐time Markovian jump linear systems with time‐varying controllable mode transition probability matrix

In this article, the state and mode feedback control strategy is investigated for the discrete‐time Markovian jump linear system (MJLS) with time‐varying controllable mode transition probability matrix (MTPM). This strategy, consisting of a state feedback controller and a mode feedback controller, is proposed to ensure MJLS's stability and meanwhile improve system performance. First, a mode‐dependent state feedback controller is designed to stabilize the MJLS based on the time‐invariant part of the MTPM such that it can still keep valid even if the MTPM is adjusted by the mode feedback control. Second, a generalized quadratic stabilization cost is put forward for evaluating MJLS's performance, which contains system state, state feedback controller, and mode feedback controller. To reduce the stabilization cost, a mode feedback controller is introduced to adjust each mode's occurrence probability by changing the time‐varying controllable part of MTPM. The calculation of such mode feedback controller is given based on a value‐iteration algorithm with its convergence proof. Compared with traditional state feedback control strategy, this state and mode feedback control strategy offers a new perspective for the control problem of general nonhomogeneous MJLSs. Numerical examples are provided to illustrate the validity of the proposed strategy.     

Event‐triggered distributed constrained consensus

We consider a distributed consensus problem for continuous‐time multi‐agent systems with set constraints on the final states. To save communication costs, an event‐triggered communication‐based protocol is proposed. By comparing its own instantaneous state with the one previously broadcasted to neighbours, each agent determines the next communication time. Based on this event‐triggered communication, each agent is not required to continuously monitor its neighbours' state and the communication only happens at discrete time instants. We show that, under some mild conditions, the constrained consensus of the multi‐agent system with the proposed protocol can be achieved with an exponential convergence rate. A lower bound of the transmission time intervals is provided that can be adjusted by choosing different values of parameters. Numerical examples illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed event‐triggered consensus control with fully continuous communication free for general linear multi‐agent systems under directed graph

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under a directed graph. We propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus. In this strategy, continuous communication in both controller update and triggering condition monitoring is not required, which means the proposed strategy is fully continuous communication free. Each agent only needs to monitor its own state continuously to determine if the event is triggered. Additionally, the approach shown here provides consensus with guaranteed positive inter‐event time intervals. Therefore, there is no Zeno behavior under the proposed consensus control algorithm. Finally, numerical simulations are given to illustrate the theoretical results.     

Modeling and Control Approach to Coupled Tanks Liquid Level System Based on Function‐Type Weight RBF‐ARX Model

A multi‐input multi‐output (MIMO) FWRBF‐ARX model, which adopts radial basis function (RBF) neural networks with function‐type weights (FWRBF) to approximate the coefficients of the state‐dependent AutoRegressive model with eXogenous input variables (SD‐ARX), is utilized for describing the dynamics of a coupled tanks liquid system. Based on local linearization information of the MIMO FWRBF‐ARX model, a predictive control strategy is proposed. In the algorithm, the control actions of the model predictive control (MPC) are calculated based on the local linearization of the MIMO FWRBF‐ARX model at current working point. Real‐time control experiments are carried out on the coupled tanks liquid system. The detailed comparative experiments demonstrate the feasibility and effectiveness of the proposed modeling and model‐based control strategy for the coupled tanks plant.