In this paper, an artificial reference-based terminal-free nonlinear model predictive control (NMPC) strategy is proposed for autonomous parking in constrained scenarios. Artificial references are introduced as additional decision variables in terminal-free NMPC to effectively integrate local planning and motion control. Both a terminal constraint and a terminal cost are removed in terminal-free NMPC to improve practical feasibility. Smooth and differentiable collision avoidance constraints are employed to ensure safety in irregularly confined environments. Stability and recursive feasibility are analyzed through a sufficiently large prediction horizon and forward invariant set theory. Experiment results demonstrate effectiveness and superiority of the proposed artificial reference-based terminal-free NMPC strategy for autonomous parking among irregularly placed vehicles.

In this article, cycle-time configuration is realized using max-plus algebra for a parallel processing system via a synchronous feedback controller. As a key efficiency metric of parallel processing systems, throughput is determined by cycle time, which is threatened by clock asynchrony and the curse of dimensionality. Using instruction dependency and weak linear independence, the parallel processing system is equivalent to a max-plus nonautonomous system to mitigate the curse of dimensionality caused by numerous processing tasks. Based on the max-plus nonautonomous system, the cycle-time configuration is achieved via a synchronous feedback controller while adhering to time restrictions of the parallel processing system. Numerical simulations validate the effectiveness of the proposed cycle-time configuration in parallel processing systems.

In this article, a heterogeneous opinion dynamics model is proposed by multiple interdependent topics in a time-varying interactive network with competing relationships. A reducible topic matrix is used to describe logical interdependent relationships within different topics. Based on a topic partition method for the multitopics, consensus and convergence are analyzed for the heterogeneous opinion dynamics model with the presence of multiple stubborn individuals. Simulation results demonstrate effects of the number of stubborn individuals on the opinion evolution processes with the reducible topic matrix.

In this paper, trajectory planning is realized for an autonomous vehicle in urban road environments based on a digital twin (DT) system. A feedforward-feedback control framework is also proposed to complete virtual-physical synchronous in the DT system. An A${}^{\ast }$algorithm is improved to obtain a global path based on a high-precision map in OpenDRIVE format. The global path is utilized by a virtual vehicle with a model predictive controller to produce a reference trajectory and feedforward inputs for a physical vehicle. A backstepping controller with the feedforward inputs is designed for the physical vehicle to track the reference trajectory. Experimental results demonstrate effectiveness of the trajectory planning and feedforward-feedback control method based on the DT system.

The uncertainty of wireless communication seriously affects the control performance of the platoon. In this paper, a model predictive control (MPC) method based on dynamic event-triggering is proposed to address the impact of non-ideal communications on multi-vehicle systems. Firstly, a hierarchical platoon architecture combining backbone layer and sub-platoon layers is proposed to achieve efficient coordination among multiple platoons, and a communication-aware control mechanism is designed for each vehicle to effectively mitigate the adverse effects of non-ideal communication scenarios. Secondly, a dynamic event-triggering mechanism is established for each vehicle, which is related to time-varying delay and random packet loss parameters, so as to effectively reduce the frequency of MPC solutions and data transmission. Additionally, based on different communication topologies, distributed model predictive controllers are suggested for backbone layer and sub-platoon layer to achieve precise and comfortable tracking. Then, sufficient conditions are provided to ensure the recursive feasibility of the MPC algorithm and the stability of the platoon system. Finally, extensive simulations are conducted, and the results demonstrate the effectiveness of the proposed algorithm in terms of control performance and low computational complexity under non-ideal communication conditions.

In this paper, event-triggered secure fusion estimation is investigated for a multirate multisensor system under linear man-in-the-middle (MITM) attacks and correlated heavy-tailed noises. A dynamic event-triggered mechanism is proposed to reduce measurement information transmission over communication networks with linear MITM attacks. A watermarking strategy is designed to address impact of linear MITM attacks by fully recovering measurement information. An event-triggered local estimator is designed to obtain local estimates under correlated heavy-tailed noises and event-triggered measurements. A distributed fusion estimator is presented to improve estimation accuracy based on sequential fast covariance intersection fusion technique. Sufficient conditions are given to ensure boundedness on estimation error scale matrices of the event-triggered local estimator and the distributed fusion estimator. Simulation and experimental results are given to illustrate validity of the event-triggered secure fusion estimation.

In this paper, a fusion estimator is investigated for positioning systems with location constraint of a camera and an ultra-wideband (UWB). Local camera and UWB estimators are designed independently for positioning with missed detections and local UWB estimates are aligned to local camera estimates for fusion estimation. Next the location constraint of the camera and UWB is transformed to a state constraint by state extension, and a constrained estimation projection method is applied to construct a fusion estimator. To measure the accuracy of the designed constrained fusion estimator, it is demonstrated that the estimation error covariance of the proposed method is equal to that of the matrix-weighted fusion method. Moreover, it is found that the proposed method has significant advantages over the matrix-weighted fusion method in computational cost, which is crucial for the real-time requirements of perception systems. Finally, the effectiveness of the proposed fusion estimator is displayed by simulation results and experimental results on the positioning system for an Ackerman vehicle.

In this paper, a framework integrating planning and control is designed to deal with the parallel parking problem of autonomous vehicle. In the planning section, efficient planning is achieved by directly setting target points. In the control part, it is mainly based on nonlinear model predictive control (NMPC) scheme for implementation. Firstly, the parking task is divided into four stages by setting different target points to solve the non-convex state constraint problem in parallel parking. Then, a state-dependent switching law is designed to describe the switching process in different stages based on the different constraints present. In addition, the terminal constraints and terminal cost functions of NMPC scheme are removed to increase the solvability of optimization problems and improve the smoothness of parallel parking for autonomous vehicle. Asymptotic stability and recursive feasibility of autonomous vehicle are ensured. The experimental results show that the NMPC scheme is effective in parallel parking of autonomous vehicle. Note to Practitioners—The motivation of this paper is to solve the problem of parallel parking for autonomous vehicles, with a focus on the design of planning and control framework. In recent years, automatic parallel parking technology has received widespread attention. However, there are still two issues that need further consideration: 1. Most existing planning and control schemes rely on nonlinear optimization processes, but multi-layer nonlinear optimization processes inevitably affect the efficiency and real-time performance of automatic parallel parking schemes. 2. The special construction of parallel parking lots makes it difficult to solve nonlinear optimization problems because the constraint domain is non-convex. To overcome these issues, we first divide the parallel parking process into several stages and directly plan the target points for each stage based on the characteristics of the parallel parking lots, rather than planning the complete parallel parking path. Then, with the help of the prediction and rolling optimization characteristics of the NMPC scheme, the optimal approach to each target point is achieved. In addition, the classic NMPC scheme has been improved (by removing terminal constraints and terminal cost functions) to further enhance its solvability and real-time performance. It is worth noting that the framework of this paper is applicable to most automatic parallel parking needs, as the characteristics of standard parallel parking slots (including size, exit and entrance requirements, safety distance requirements, etc.) are consistent with the planning requirements of the target points in this paper. Moreover, most vehicle models are known, which enables the NMPC scheme in this paper to adapt to different types of autonomous vehicles. In future work, we will further explore the possibility of extending our algorithm to more complex and chaotic environments (including but not limited to the presence of obstacles and external interference) for automatic parking systems.

In this article, switched model predictive control (MPC) is proposed for nonholonomic mobile robots with adaptive dwell time and a dual-terminal set. The dual-terminal set is used to reduce on-line complexity of the switched MPC for the nonholonomic mobile robots with multiple constraints. By a switched signal with the adaptive dwell time, cost functions are switched to improve control performance under multiple constraints. The switched MPC with feasibility and stability can adjust a tradeoff between control performance and computational complexity for the closed-loop system. Simulation results are given to illustrate superiority of the switched MPC for nonholonomic mobile robots.

In this article, the leader-following consensus problem is investigated for a class of nonlinear multiagent systems with transmission outliers. First, through the relative output information and observer states of neighbor agents, a distributed stubborn reduced-order observer is proposed to estimate the leader-following consensus error which is affected by abnormal and isolated transmission outliers. Moreover, considering that the leader agent in practice is a controllable plant, another distributed stubborn reduced-order observer is designed by using the relative information and inputs of neighbor agents. Sufficient conditions are established in terms of the Laplacian matrix such that two stubborn reduced-order observers are convergent and the studied nonlinear multiagent system could achieve leader-following consensus with directed topology. Finally, an example of the multispacecraft system is provided to illustrate the effectiveness of the proposed methodology.

In this article, tube-based model predictive control (MPC) is investigated for a linear parameter-varying (LPV) system with external disturbances. The LPV system comes from an autonomous vehicle with external disturbances and scheduling parameters in trajectory tracking. An interval predictor is designed for state constraints under external disturbances and scheduling parameters. With a robust controller based on the nominal state obtained by solving MPC, antidisturbance ability and dynamic performance are improved for the LPV system with external disturbances. Both recursive feasibility and input-to-state stability are analyzed for the closed-loop system using the tube-based MPC with the interval predictor. The effectiveness of the tube-based MPC is shown by numerical simulation on trajectory tracking for the autonomous vehicle.

In this study, a cooperative control methodology is developed for an air-ground system under a complicated environment. The air-ground system consists of a car-like mobile robot (CLMR) with road bumps and a quadrotor with gust winds. For the quadrotor, a cooperative integral sliding-mode controller is suggested to achieve bidirectional signal connection. A fixed-time extended state observer (ESO) is used to assess the external disruptions brought on by gust winds. For the CLMR, a double closed-loop tracking control approach is utilized to track the trajectory. An outer loop kinematics controller generates desired velocities. An inner loop nonlinear ESO estimates velocities and compensates for road bumps. Based on the Lyapunov method, stability analyses are given for the air-ground systems. Experimental results verify that the proposed approach for the air-ground system is effective.

In this paper, a composite longitudinal controller for velocity regulation of unmanned ground vehicles (UGVs) is proposed. First, both the empirical model and mixed logical dynamic model are developed in terms of the experimental data processing method. Second, a composite longitudinal control strategy incorporating steady-state controller and active disturbance rejection state feedback controller is designed for velocity regulation control during acceleration and deceleration. Finally, the stability analysis of velocity error is given with the global sector condition, and the comparative experimental tests show the effectiveness and robustness of the proposed composite longitudinal regulation control strategy.

This article focuses on hybrid dynamic event-triggered security tracking control of wheeled mobile robots (WMRs) against round-trip stochastic denial of service (DoS) attacks. To characterize the random properties, DoS attacks are modulated as Markov switched processes. A hybrid dynamic model is characterized and a hybrid dynamic event-triggering mechanism (ETM) is proposed for the WMR, which achieve larger triggering intervals than the static one. To actively defend against the DoS attacks and achieve the trajectory tracking control, a hybrid dynamic controller is designed with a dynamic parameter that reflects the DoS attacks in real time. The uniformly globally asymptotically stability (UGAS) condition of the addressed hybrid dynamic WMR system is obtained. Practical experiments are provided for illustration of the provided theoretical results.

This article develops an event-triggered model-predictive control (EMPC) strategy to realize trajectory tracking and obstacle avoidance for a wheeled mobile robot (WMR) subject to input constraints and external disturbances. In the EMPC strategy, a potential field is introduced in the cost function to guarantee a smooth path for the WMR. An event-triggered mechanism is designed to reduce the computational load of solving an optimal control problem (OCP). Moreover, an adaptive prediction horizon is utilized to further achieve computation reduction. Both recursive feasibility of the OCP and practical stability of the resulting closed-loop system are analyzed for the WMR with the input constraints and the external disturbances. Simulation results are provided to demonstrate the effectiveness and superiority of the proposed EMPC strategy.

In this article, an event-driven output feedback control approach is proposed for discrete-time systems with unknown mismatched disturbances. To estimate the unavailable states and disturbances, a reduced-order extended state functional observer is proposed, and by introducing an event-driven scheduler, the ZOH-based event-driven output feedback disturbance rejection controller is designed, and the stability and disturbance rejection analyses are performed. To further save the network resources, the predictive event-driven output feedback disturbance rejection control approach is proposed, and the stability and disturbance rejection analyses of the systems with predictive control are also conducted. It can be shown that the disturbances are compensated completely in output channels of the systems, and compared with the time-driven control schemes. And event-triggering frequency is greatly reduced with the proposed event-driven control methods. Finally, the effectiveness of the provided control approaches is demonstrated by numerical simulations.

For wireless cyber–physical systems (CPSs) suffering jamming attacks, an optimal resilient control method is proposed through a novel cross-layer dynamic game structure in this article. To confirm to practical conditions of the cyber-layer, incomplete communication information is taken into consideration, and a Bayesian Stackelberg game approach is utilized to model interactions between a smart jammer and a cyber-user. Then, an$H_{\infty }$optimal resilient controller is studied for the closed-loop system with jam-induced packet losses and external disturbance in the sense of physical layer. With assumptions that the smart jammer has abilities of decoding system inputs and states, the changes of the jamming strategy are studied, and a coupled design between cyber and physical layers is presented with an algorithm to depict the dynamic variations of the CPSs. Moreover, the convergence of the proposed algorithm is also discussed. To validate the advantages of the proposed methods, a numerical simulation is performed in the end.

In this article, a composite nonlinear feedback (CNF) controller with anti-windup extended state observer (ESO) is proposed for path-following control of unmanned ground vehicles (UGVs). To describe steering dynamics accurately, a saturation model with bounded disturbances is developed subject to path-following, lateral dynamic, and steering capability. The anti-windup ESO is investigated for real-time disturbance estimation under saturated input. The CNF controller is designed for path-following. In terms of asymptotically null controllability, a practical semiglobal stabilization result is derived for the closed-loop system with saturated input and bounded disturbances. Experimental results show that the proposed strategy is effective for UGVs.

In this article, a distributed stochastic model predictive control (MPC) algorithm with a multirate sampling mechanism is proposed for a networked linear system with multiple dynamic subsystems. A delta operator approach is used for the multiple dynamic subsystems with different sampling periods in the multirate sampling mechanism. Both stochastic disturbances and probabilistic constraints of the multiple dynamic subsystems are satisfied by the distributed stochastic MPC algorithm. Packets dropout are considered by the stochastic MPC algorithm and state predicted errors are compensated. Recursive feasibility and quadratic stability are obtained for the networked linear system under the distributed stochastic MPC algorithm. A numerical example is given to illustrate effectiveness of the proposed algorithm.

In this article, event-triggered distributed fusion is investigated for a multirate multisensor system subject to heavy-tailed noises under packet dropout. The heavy-tailed noises are modeled by a multivariate$t$-distribution for the multirate multisensor system. An event-triggered local estimator is designed to gain local estimates with packet dropout in communication networks. An event-triggered distributed fusion algorithm is proposed by sequential fast covariance intersection (SFCI) fusion technology. Sufficient conditions on the boundedness of the estimation error scale matrices are given for the event-triggered local estimator and distributed fusion. Finally, numerical simulation is put forward to indicate validity of the presented event-triggered local estimator and distributed fusion.

This article is concerned with a distributed state estimation problem over sensor networks. The communication links of the sensor networks are subject to bounded time-varying transmission delays. A distributed Kalman filtering algorithm is designed to estimate the state based on a Kalman consensus filtering algorithm. Moreover, sufficient conditions are derived for convergence on estimation errors and the boundedness of error covariances, respectively. Finally, the effectiveness of the designed algorithm is validated by a simulation example.

This paper investigates an H∞static output feedback for a low-frequency (LF) networked control system (NCS). A decentralized event-triggered scheme (DETS) is proposed to reduce the network communication loads. The LF NCS with the DETS is modeled as a time-delay system with an LF constraint. With this model, H∞performance analysis is developed via an LF integral quadratic constraint method and a generalized Kalman-Yakubovich-Popov lemma. Furthermore, a detailed controller design algorithm is presented to obtain an H∞static output feedback controller for the LF NCS with the DETS via a two-stage approach. The numerical results are provided to demonstrate the effectiveness and superiority of the proposed techniques.

In this paper, event-triggered active model predictive control is investigated for a nonlinear multiagent system (MAS) with packet losses. By designing event-triggered mechanisms which reduce sensing cost, event-triggered conditions are detected at certain sampling instants. The prediction horizons of all agents are selected actively through the event-triggered mechanisms. Selecting a maximal predictive horizon, a common predictive horizon of the nonlinear MAS is obtained to ensure synchronous updating. The Bernoulli distributions are applied to describe the packet losses which are dealt with by model predictive control. Finally, the effectiveness of the proposed algorithm design is verified by a numerical simulation.

In this paper, both a trajectory tracking controller and a position controller are investigated for leader-follower trajectory control of quadrotors. A tracking differentiator is designed to generate speed signals for the quadrotors which are composed of a leader and some followers. Based on state errors between the leader and followers, a nonlinear disturbance observer is used in the trajectory tracking controller. A saturation law with anti-trigonometric functions is adopted in the position controller for the leader and followers. Experiment results are given to show the applicability of the proposed method for quadrotors.

In this paper, a predictive cloud control scheme is investigated for a networked multiagent system (NMAS) with quantized signals under denial-of-service (DoS) attacks. An arbitrary region quantizer is applied to take effective values of control signals. A Stackelberg game is adopted to model the DoS attacks which result in attack-induced packet dropouts. Based on cloud computing and predictive control, the predictive cloud control scheme is designed to compensate for network-induced delays and the attack-induced packet dropouts actively. By a “zoom” strategy, sufficient conditions are given to achieve consensus for the NMAS. Effectiveness and computing superiority of the proposed scheme are demonstrated by simulation results.

This article considers a cyber-physical system with multiple remote state estimation subsystems under denial-of-service (DoS) attack. Suppose that there are multiple distributed estimation systems, in each of which, a sensor monitors the system and sends its local estimation to a remote estimator over one of multiple wireless channels. A DoS attacker emits noise power to jam the wireless channels. A scheduler is installed to dispatch each sensor to transmit information through the specific channel to minimize the total estimation error covariance on account of energy-saving. Whereas, the DoS attacker attempts to jam a channel to realize an opposite objective. With considering interference from other individuals, a multisensor multichannel remote state estimation model is constructed. A myopic policy and a long-term online interaction strategy under varying network environment are investigated and compared by solving a two-player zero-sum game and a Markov game, respectively. Simulations are provided to demonstrate our results.

In this paper, an adaptive fuzzy tracking controller is developed for a class of strict-feedback Markovian jumping systems subjected to multisource uncertainties. The unpredictable actuator failures, the unknown nonlinearities, and the unmodeled dynamics are simultaneously taken into consideration, which evolve according to the Markov chain. It is noted that the elements in the transition rate matrix of the Markov chain are not fully available. In virtue of the norm estimation approach, the challenges caused by the complex multiple uncertainties and actuator failures are effectively handled. Furthermore, to compensate for the unavailable switching nonlinearities, the fuzzy logic systems are employed as online approximators. As a result, a novel adaptive fuzzy fault-tolerant tracking control structure is constructed. The sufficient condition is provided to guarantee that the studied system is stochastically stable. Finally, a number of illustrative examples are employed to demonstrate the effectiveness of the proposed methodology.

In this paper, the security problem for a cloud control system (CCS) is studied. In the CCS, so-called advanced persistent threats (APTs) can be launched by a malicious attacker to reduce the quality of service of cloud and deteriorate the system performance further. To defend against APTs and create a security as a service scheme, a defender needs to allocate defense resource to different units serving to different plants for improving the overall system performance when the CCS accommodates multiple physical plants simultaneously. After observing the defender's action, the attacker decides which serve units to comprise. Considering that both defender and attacker are subject to resource constraints, the interaction of two sides is modeled by a Stackelberg game. The optimal solutions for two players under different types of budget constraints are investigated. Simulation examples and comparison results are provided to verify the main results of this paper.

In this article, resilient strategy design is investigated for a cloud control system (CCS) subject to jamming attack. In the presence of jammer, signals, including measurements and control inputs between cloud server and physical plant may be interfered, which degrades the signal-to-interferencelus-noise ratio and further leads to packet dropout of signals. A Stackelberg game is applied to depict the interaction of transmitter and jammer. On account of game equilibria of two players, controller is devised for CCS with time-varying delay. A novel cross-layer dynamic pricing mechanism is devised to drive the disturbance attention performance of CCS to a desired region under constrained information and time-varying networks. The simulation results are provided to verify the effectiveness of the proposed methodology.

In this paper, a generalized nonlinear extended state observer is applied to an integral sliding mode (ISM) tracking control method for a pneumatic cylinder servo system with varying loads. The observer is established to estimate the total disturbance and its derivative for the system. An ISM controller is designed to ensure control performances of the system. Both finite-time convergence of the observer and finite-time stabilization of the closed-loop system are realized using Lyapunov's stability theory. Lastly, experimental results demonstrate that control precision and response rapidity are improved using the proposed method.

This paper concentrates on the remote state estimation problem for nonlinear systems over a communication-limited wireless sensor network. Because of the non-Gaussian property caused by nonlinear transformation, the unscented transformation technique is exploited to obtain approximate Gaussian probability distributions of state and measurement. To reduce excessive data transmission, uncontrollable and controllable stochastic event-triggered scheduling schemes are developed to decide whether the current measurement should be transmitted. Compared with some existing deterministic event-triggered scheduling schemes, the newly developed ones possess a potential superiority in maintaining Gaussian property of innovation process. Under the proposed schemes, two nonlinear state estimators are designed based on the unscented Kalman filter. Stability and convergence conditions of these two estimators are established by analyzing behaviors of estimation error and error covariance. It is shown that an expected compromise between communication rate and estimation quality can be achieved by properly tuning event-triggered parameter matrix. Numerical examples are provided to testify the validity of the proposed results.

This paper generalizes stability for a high frequency networked control system (NCS) subject to actuator saturation via integral quadratic constraints. A delta operator system with a high frequency constraint is used to model the high frequency NCS. Double-loop stability is treated via outer-loop and interloop feedback configurations for the high frequency NCS. Stability criteria are derived with the high frequency constraint and actuator saturation by a generalized Kalman-Yakubovich-Popov lemma. Numerical results are provided to demonstrate the effectiveness of the proposed techniques in this paper.

In this paper, a countermeasure for wireless networked control systems suffering from jamming attacks is studied by a variable sampling approach. A Stackelberg game framework is utilized to analyze interactions between a smart jammer and a legitimate user. The variable sampling approach is exploited to deal with data packets dropout between a sensor and a controller. Moreover, a resilient variable sampling controller is designed by a delta operator method. Besides, stability conditions are provided for systems with proposed controller. Finally, a numerical simulation is provided to validate the effectiveness of the proposed method.

In this paper, the near-Nash equilibrium (NE) control strategies are investigated for a class of discrete-time nonlinear systems subjected to the round-robin protocol (RRP). In the studied systems, three types of complexities, namely, the additive nonlinearities, the RRP, and the output feedback form of controllers, are simultaneously taken into consideration. To tackle these complexities, an approximate dynamic programing (ADP) algorithm is first developed for NE control strategies by solving the coupled Bellman's equation. Then, a Luenberger-type observer is designed under the RRP scheduling to estimate the system states. The near-NE control strategies are implemented via the actor-critic neural networks. More importantly, the stability analysis of the closed-loop system is conducted to guarantee that the studied system with the proposed control strategies is bounded stable. Finally, simulation results are provided to demonstrate the validity of the proposed method.

In this study, a power allocation scheme for two‐tier femtocell networks is proposed to maximise the user utilities constrained with satisfactory quality of service, where femtocell users share the same frequency with macrocell users (MUEs). Since the environment changes and the channel gains cannot be assumed to be constants, a worst‐case method is used to address the uncertainty of the power allocation problem. A non‐cooperative game model is developed to maximise the utilities of femtocell users by letting the users competing the utilities with others. As the robustness can be affected by the changing gains of communication links, the robust Stackelberg game is proposed to model this hierarchical competition where the MUEs and femtocell users act as leaders and followers, respectively. Two effective pricing schemes are applied to maximise the utilities, when different user demands are required, where the uniqueness of Nash equilibrium is proved in the two schemes. Numerical results show the convergence of the Stackelberg game with uncertainty and also the results demonstrate the effectiveness of the power allocation algorithm.

In this paper, networked predictive control is investigated for planar nonlinear systems with quantization by an extended state observer (ESO). The ESO is used not only to deal with nonlinear terms but also to generate predictive states for dealing with network-induced delays. Two arbitrary region quantizers are applied to take effective values of signals in forward channel and feedback channel, respectively. Based on a "zoom" strategy, sufficient conditions are given to guarantee stabilization of the closed-loop networked control system with quantization. A simulation example is proposed to exhibit advantages and availability of the results.

In this paper, event-driven is used in a networked control system (NCS) which is subjected to the effect of quantization and packet losses. A discrete event-detector is used to monitor specific events in the NCS. Both an arbitrary region quantizer and Markov jump packet losses are also considered for the NCS. Based on zoom strategy and Lyapunov theory, a complete proof is given to guarantee mean square stability of the closed-loop system. Stabilization of the NCS is ensured by designing a feedback controller. Lastly, an inverted pendulum model is given to show the advantages and effectiveness of the proposed results.

In this study, the authors study the power control for a two‐tier network system which is comprised of a central macrocell and several femtocells. In practice, the communication environment is fairly complex and dynamic which leads to the imperfect channel state information (CSI). To enhance the robustness of the two‐tier network system, the imperfect CSI in both signal links and interference links are considered and the uncertainties of the CSI are uniformly distributed in an ellipsoid uncertainty set. Then, a probability‐constrained optimisation problem is formulated to deal with the uncertainties and protect the quality‐of‐service of all users. A novel method is provided to convert probability constraints into deterministic ones. Based on them, they propose an iterative algorithm and an admission control algorithm to enhance the network efficiency. They also investigate the case when the distributions of the uncertainties of the CSI are unknown. Finally, numerical results are given to illustrate the effectiveness of the authors’ power control scheme.

We consider the problem of resilient control of networked control system (NCS) under denial-of-service (DoS) attack via a unified game approach. The DoS attacks lead to extra constraints in the NCS, where the packets may be jammed by a malicious adversary. Considering the attack-induced packet dropout, optimal control strategies with multitasking and central-tasking structures are developed using game theory in the delta domain, respectively. Based on the optimal control structures, we propose optimality criteria and algorithms for both cyber defenders and DoS attackers. Both simulation and experimental results are provided to illustrate the effectiveness of the proposed design procedure.

In this study, the minimum transmission power of each femtocell user in a two‐tier network, in which femtocells and macrocell use the spectrum simultaneously, is investigated. That is, the authors are aiming at finding the power that characterises robustness and energy‐efficient when taking the uncertain gains into consideration. To solve the optimisation problem with uncertainty, an opportunistic power control strategy for the femtocells is introduced. Since the channel gain from a femtocell user to the femtocell base station is changeable with the environment, it is difficult to track channel gains instantaneously. For the reason that the mean channel gains, from the femtocell users to the femtocell base stations are usually achievable, the information of mean and probability density function are used to model the optimisation problem. Moreover, outage probability for each femtocell user's throughput is originated instead of considering the total throughput of the system, because high total throughput may not ensure that of each femtocell user. The signal‐to‐interference‐plus‐noise ratio of the macrocell is ensured by setting appreciate interference temperature. A distributed algorithm is designed to calculate the powers of femtocell users. Numerical results show the effectiveness of the proposed outage probabilistic method and the distributed algorithm.

In “Comments on Constrained Infinite-Horizon Model Predictive Control for Fuzzy-Discrete-Time Systems” (IEEE Trans. Fuzzy Syst.), Ding criticized that the application of Lyapunov method, the handling of the output constraint, and the resultant linear-matrix-inequality-optimization problem are incorrect in IEEE Trans. Fuzzy Syst. , vol. 18, no. 2, pp. 429-436, Apr. 2010. This rebuttal answers some key points raised in the comments.

This paper investigates the problem of fault detection for Takagi-Sugeno (T-S) fuzzy discrete systems in finite-frequency domain. By means of the T-S fuzzy model, both a fuzzy fault detection filter system and the dynamics of filtering error generator are constructed. Two finite-frequency performance indices are introduced to measure fault sensitivity and disturbance robustness. Faults are considered in a middle frequency domain, while disturbances are considered in another certain finite-frequency domain interval. By using the generalized Kalman-Yakubovic-Popov Lemma in a local linear system model, the design methods are presented in terms of solutions to a set of linear matrix inequalities, which can be readily solved via standard numerical software. The design problem is formulated as a two-objective optimization algorithm. A numerical example is given to illustrate the effectiveness and potential of the developed techniques.

The problem of constrained infinite-horizon model-predictive control for fuzzy-discrete systems is considered in this paper. New sufficient conditions are proposed in terms of linear-matrix inequalities. Based on the optimal solutions of these sufficient conditions at each sampling instant, we design both parallel-distributed compensation and nonparallel-distributed compensation state-feedback controllers, which can guarantee that the resulting closed-loop fuzzy-discrete system is asymptotically stable. In addition, the fuzzy-feedback controllers meet the specifications for the fuzzy-discrete systems with both input and output constraints. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.