This article investigates the sliding mode control (SMC) problem for a class of Markov jump systems (MJSs), in which the system states are sampled randomly and nonuniformly according to Markov chain. Besides, the transmission of sampled states through the shared network channel is inevitably subject to deception attacks obeying Markov model. In order to facilitate the subsequent design and analysis, the encountered three Markov chains are first mapped into one, meanwhile, a suitable mode detection scheme is put forward to simultaneously detect the partially inaccessible modes including the controlled system modes and attack modes. And then, a detected-mode-dependent sliding mode controller is designed to effectively cope with the stochastic features of sampling processes and attack occurrences. Furthermore, the reachability of the specified sliding surface and the mean-square exponential ultimate boundedness of the closed-loop system are analyzed and the corresponding conditions are derived. Finally, two simulation examples are provided to illustrate the designed control method.

A security control problem is addressed for a kind of networked Markov jump system subject to two-side stochastic denial-of-service (DoS) attacks, in which the attack occurrence situation obeys the Markov chain. To resist the attack effects, a redundant channel protocol is adopted, wherein measurement/control signals are sent to the controller/actuator via the redundant channel when the primary channel suffers from cyber-attacks. According to the above redundant channel protocol, both measurement and input models are established to represent the received signals by the controller and actuator, respectively. Then, a novel two-layer mapping strategy via logical operations is proposed to describe attack occurrences and system jumping. These facilitate the design of a security sliding mode controller, under which the exponential mean-square stability of the networked Markov jump systems subject to DoS attacks and the corresponding sufficient conditions are derived. Eventually, the simulation results via the DC chopper circuit system are provided to illustrate the proposed redundant-channel-based security control method.Note to Practitioners—This paper is motivated by the attack resistance problem in networked control systems. With the revolutionary evolution of wireless communication technology, in many practical systems, such as smart power grids, unmanned aerial vehicles (UAVs), and unmanned surface vehicles (USVs), the physical devices including sensors, actuators, controllers, and other intelligent devices are interconnected and transmitted the data through a network infrastructure. The inevitable DoS attacks may cause reliability degradation of data transmission, which in practice results in shaky grid frequency, failed UAV formation, and inaccurate USV detection. Distinguished from the previous investigation results from a passive perspective, this paper proposes a redundant-channel-based method to solve the reliability degradation problem caused by DoS attacks from a proactive perspective. The developed redundant channel method against Markov-chain-based DoS attacks can improve the reliability of data transmission, and the proposed novel two-layer mapping strategy via logical operations can increase the freedom of security controller design. A DC chopper circuit is used to verify the effectiveness of the proposed novel control method and comparison simulation results show the advantages of the redundant channel method. How to improve the reliability of vulnerable channels is a knotty problem in communication. With the groundbreaking research of this paper, against other attacks, such as deception attacks, reply attacks, and frequency-and duration-constrained DoS attacks, the attack resistance problems via proactively strengthening the reliability of data transmission should be further explored in the future.

Focusing on the sliding mode control of interval type-2 fuzzy systems with restricted communication capability, this study designs an event-triggered mechanism and a dynamic quantizer. Firstly, a membership-function-based dynamic event-triggered scheme is elaborately designed to reduce the transmission of the system state. As a result, only the triggered state is available for the fuzzy sliding mode controller and its membership functions (MFs). Since the event-triggered fuzzy controller contains different MFs from the system and the controller’s MFs are only updated at triggering instants, the above two factors result in the mismatching phenomenon between the system’s and the controller’s MFs. Under the event-triggered scheme, the MFs’localinformation of both controller and system is extracted to derive sufficient conditions for ensuring the control performance of the closed-loop dynamic system and the sliding mode dynamics. Furthermore, a dynamic quantizer’s parameter is adjusted online to improve the quantization procedure of the control signal, and an optimization problem is introduced to balance the system’s dynamic performance with communication resource utilization by reducing the convergence domain and increasing the triggering threshold. Finally, the practicability of the proposed control scheme is illustrated via a numerical example and the single-link manipulator.Note to Practitioners—In many practical engineering applications, the equipment units in the control system are generally implemented on the network platform, and measurement and control signals are transmitted through wired/wireless network channels. The usage of communication resources is important to prevent packet loss and communication congestion. The event-triggered scheme and quantization are two effective ways to reduce the communication burden. In this work, an event-triggered control scheme and a quantization transmission mechanism are proposed for a networked control system under IT2 fuzzy modeling. In order to improve the limited quantizer’s levels due to the hardware cost, a dynamic variable is introduced, and the adjustment scheme is proposed to ensure that the dynamic quantizer can be implemented on the practical digital platform. The co-design scheme of event-triggered, quantization, and controller is proposed for ensuring the dynamic performance of networked control systems.

This work investigates the problem of direct data-driven control (DDC) for linear systems under stochastic sensor/actuator faults. A fault model obeying Markov chain is firstly constructed to capture the random characteristic of various possible sensor faults. By introducing novel parameterization relations to deal with the unknown fault matrix and stochastic detected modes, data-based representations of the closed-loop system are established via input/state data without/with noise, respectively. Thus, the model-based controller and stability conditions can be converted into data-based forms such that they can be implemented by only utilizing the pre-collected input/state data without requiring explicit knowledge of system matrices. Besides, the case of simultaneous sensor and actuator faults is also investigated. It is shown that the actuator fault will not affect the structure of the data-based representation, except for the collected data sequence involved in stability conditions and the computation of controller gains. Finally, simulation results are provided to verify the proposed control strategy.

This paper develops an event-triggered sliding mode control (ETSMC) strategy for partially unknown disturbed systems via adaptive dynamic programming, where the system matrix is considered to be unknown to the designer. Both the sliding function and ETSMC scheme are constructed without using system matrix. An input-based event-triggered mechanism is introduced between the plant and the sliding mode controller to reduce the communication frequency. Compared with existing results on ETSMC, the proposed event-triggered mechanism can guarantee the reachability to the ideal sliding surface$s(t)=0$and thus the external disturbances can be eliminated completely. An online policy iteration algorithm is formulated to implement the partial-model-free ETSMC strategy. It is proven that in all policy iteration steps, the reachability of the prescribed sliding surface and the optimal control performance of the sliding mode dynamics are ensured simultaneously by the proposed online updated ETSMC scheme as well as the Zeno phenomenon of the proposed event generator can be excluded. Finally, the effectiveness and the applicability of the proposed ETSMC scheme are illustrated by a numerical example and a real experiment on the permanent magnet synchronous motor speed regulation system.Note to Practitioners—ETSMC is an effective robust control strategy for the practical networked control systems that can compensate the matched disturbances in the plant as well as reduce the information transmission frequency between the plant and controller. However, the design of the existing ETSMC strategies depends on the completely known system dynamics, which is difficult or expensive to be obtained in many engineering applications. Meanwhile, the ideal sliding motion cannot be attained by the existing ETSMC approaches so that the disturbance rejection performance is degraded unsatisfactorily. To address these concerns, this paper develops a novel partial-model-free ETSMC strategy based on adaptive dynamic programming for disturbed systems to achieve the optimal control performance without using the system matrix. The reachability of the ideal sliding surface and the exclusion of the Zeno behavior as well as the convergence of the online policy iteration algorithm are analyzed theoretically. The engineering applicability of the novel ETSMC scheme is verified in the speed regulation problem of the permanent magnet synchronous motor.

This work proposes a design scheme of the desired controller under the lossy digital network by introducing a dynamic coding and packet-length optimization strategy. First, the weighted try once-discard (WTOD) protocol is introduced to schedule the transmission of sensor nodes. The state-dependent dynamic quantizer and the encoding function with time-varying coding length are designed to improve coding accuracy significantly. Then, a feasible state-feedback controller is designed to attain that the controlled system subject to possible packet dropout is exponentially ultimately bounded in the mean-square sense. Moreover, it is shown that the coding error directly affects the convergent upper bound, which is further minimized by optimizing the coding lengths. Finally, the simulation results are provided via the double-sided linear switched reluctance machine systems.

In this article, the sliding mode control (SMC) problem is addressed for two-dimensional (2-D) systems depicted by the second Fornasini-Marchesini (FMII) model. The communication from the controller to actuators is scheduled via a stochastic protocol modeled as Markov chain, by which only one controller node is permitted to transmit its data at each instant. A compensator for other unavailable controller nodes is introduced by means of previous transmitted signals at two most adjacent points. To characterize the features of 2-D FMII systems state recursion and stochastic scheduling protocol, a sliding function associated with the states at both the present and previous positions is constructed, and a scheduling signal-dependent SMC law is designed. By constructing token- and parameter-dependent Lyapunov functionals, both the reachability of the specified sliding surface and the uniform ultimate boundedness in the mean-square sense of the closed-loop system are analyzed and the corresponding sufficient conditions are derived. Furthermore, an optimization problem is formulated to minimize the convergent bound via searching desirable sliding matrices, meanwhile, a feasible solving procedure is provided by using the differential evolution algorithm. Finally, the proposed control scheme is further demonstrated via simulation results.

This article investigates the sliding mode control (SMC) problem for a class of uncertain 2-D systems described by the Roesser models with a bounded disturbance. In order to reduce the communication usage between the controller and the actuators, it is supposed that only one actuator node can gain the access to the network at each sampling time along horizontal or vertical direction, where a proper 2-D round-robin protocol is designed to periodically regulate the access token and a set of zero-order holders (ZOHs) is employed to keep the other actuator nodes unchanged until the next renewed signal arrives. Based on a novel 2-D common sliding function, a token-dependent 2-D SMC scheme with first-order sliding mode is appropriately constructed to cope with the impacts from the periodic scheduling signal and the ZOHs. Furthermore, a novel super-twisting-like 2-D SMC scheme with second-order sliding mode is designed to improve the robustness against the bounded disturbance. By resorting to token-dependent Lyapunov-like function, sufficient conditions are obtained to guarantee the ultimate boundedness of the horizontal and vertical states as well as the 2-D common sliding function. For acquiring the optimized gain matrices, two searching algorithms are formulated to solve two optimization problems arising from finding optimized control performance. Finally, two comparative examples are exploited to demonstrate the effectiveness and the advantageous of the proposed first- and second-order 2-D SMC design schemes under round-robin scheduling mechanism.

The path-tracking control of an intelligent vehicle always suffers from the high-frequency measurement noises. To confront this issue, this work puts forward a novel delayed output-feedback implementation of proportional-integral-derivation (PID) control, which is called multidelay proportional-integral-retarded (PIR) control. The mathematical model of the vehicle system is represented in the form of a linear parameter-varying (LPV) system, which uses the car position as the scheduling variable for regulation. On this basis, the multidelay PIR controller is designed such that the tracking errors gradually converge to zero with the aid of the proportional and integral actions, and the harmful high-frequency measurement noises are attenuated by the retarded term consisting of a few delayed proportional actions. To tune the PIR controller parameters, linear matrix inequalities (LMIs), derived by applying Taylor's expansion to the retarded term, are used to compute the convex subcontroller gains. Then, the self-scheduled tracking controller is formulated as the weighted sum of convex subcontrollers, and the weight functions scheduled by the current position are adaptive to the different operational conditions. Experiments in real time using a laboratory car-like vehicle are employed to assess the performance of the proposed controller.

This article deals with the load frequency control problem of multiarea power systems subject to multiple intermittent denial-of-service (DoS) attacks that can interrupt the data transmission of each area independently. A decentralized event-triggering (ET) scheme under periodic sampling is proposed to reduce the transmission burden. Then, a decentralized ET-based controller is designed by tuning several parameters. Such control scheme can reduce the computational complexity while achieving privacy preserving. Moreover, sufficient conditions are derived for ensuring the input-to-state stability of multiarea power systems and an optimization solution method via particle swarm algorithm is provided. Finally, a three-area power system is employed to verify the effectiveness of the proposed scheme.

This work investigates the control design and reachable set estimation problem for T-S fuzzy systems under bounded external disturbances. By designing a fuzzy controller, the reachable set of the closed-loop fuzzy system can be bounded by an ellipsoid that is minimized via two optimization algorithms. When the fuzzy control scheme is implemented under an event-triggered framework, the limited information availability may degrade desired control performance due to only the triggered state being available for the fuzzy controller. To alleviate this problem, a novel reachable-set-dependent event-triggering condition is proposed such that satisfactory control performance can still be ensured by the above fuzzy controller. Meanwhile, the bounding ellipsoid of the reachable set is explicitly given, and a relationship is established between control performance and communication cost under the event-triggered scheme. In addition, under the condition that the reachable set remains within a specified safe area, the communication rate can be reduced while still achieving optimal control performance. The proposed strategies are verified via a simulation example.

This article is concerned with the sliding mode control (SMC) problem for a class of Markov jump systems subject to packet dropouts, in which the dropped or received status of packet is described by a Markov chain. To enhance the reliability of data transmission, multiple redundant channels are employed between sensors and the controller. Different from the existing measurement model under redundant channels with Bernoulli-process-based packet dropouts, a novel measurement model under Markov-chain-based packet dropouts is proposed under the redundant channel transmission. It is assumed that the modes of the controlled system and packet-dropout model are unavailable, and then a mode detection mechanism is proposed to detect the partially unavailable modes. By utilizing the detected modes, a dynamic observer is constructed to estimate the unmeasurable system state, based on which a detected-mode-dependent sliding mode controller is designed to achieve the mean-square exponential ultimate boundedness of the closed-loop system. Meanwhile, incremental search technique and particle swarm optimization algorithm are, respectively, utilized to solve two optimization problems for enhancing the closed-loop performances. Finally, two simulation examples are provided to verify the effectiveness of the proposed schemes.

This work proposes an economic model-free super twisting control (STWC) algorithm for the FCT of a singularly perturbed MAS. Specifically, the intelligent model-free control framework is designed to be the sum of a MISTWC and an iterative learning control (ILC). First, time scales are artificially introduced into the STWC for the multiagent formation construction, without overestimating the control gains. Then, the input-output data collected from the iterative experiments are used to learn the model of unknown repeated uncertainties, and drive the whole system toward satisfactory consensus tracking performance. By utilizing the$\epsilon$-dependent Lyapunov method, the convergence properties of the STWC-type ILC are rigorously analyzed in both the iteration domain and the time domain. The selection method of the design parameters is also provided. Simulation results validate the effectiveness of the proposed controller in terms of formation construction, trajectory tracking, and robustness to system uncertainties.

This article proposes a cloud-based load frequency control (LFC) scheme with privacy preserving for multiarea power systems. To prevent sensitive information of power systems from disclosure in the cloud service, Paillier cryptosystem is adopted to encrypt the sampling data. An encrypted LFC scheme is constructed by means of the homomorphism of Paillier cryptosystem, that is, the encrypted output does not need to be decrypted in cloud service. Considering that a bigger key size provides better privacy level, but will result in longer time delay, the tradeoff between privacy preserving level and control performance is analyzed by utilizing deterministic network calculus to evaluate the delay bound. Meanwhile, the decentralized characteristic of designed LFC scheme can avoid possible privacy leakage during the controller design procedure. Moreover, an optimization method is proposed for searching the suboptimal control gains. Finally, a simulation on a three-area power system is presented, in which 4 different key sizes from 256 to 2048 bits are tested to verify the effectiveness of the proposed scheme.

In this article, the sliding mode control problem is addressed for a class of sampled-data systems subject to deception attacks. The sampling periods undergo component-wise random perturbations that are governed by a Markovian chain. The component of the sampled output is transmitted via an individual communication channel that is vulnerable to deception attacks, and Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the deception attacks initiated by the adversaries. A sliding mode controller is designed to drive the state into the sliding domain around the specified sliding surface, and sufficient conditions are derived to guarantee the exponentially ultimate boundedness of the resultant closed-loop system in the mean-square sense. Furthermore, an optimization problem is established to pursue locally optimal control performance. Finally, a simulation example is given to verify the effectiveness and advantages of the developed controller design approach.

This article concerns with the asynchronous boundary control for a class of Markov jump reaction-diffusion neural networks (MJRDNNs). In consideration of nonsynchronous behavior between the system modes and controller modes, a novel asynchronous boundary control design is proposed for MJRDNNs. Based on the designed asynchronous boundary controller, a sufficient criterion is established to ensure the stochastic finite-time boundedness for the considered MJRDNNs by constructing a Lyapunov–Krasovskii functional and utilizing Wirtinger-type inequality. Then, a sufficient condition is acquired to guarantee that MJRDNNs are stochastic finite-time bounded with$H_{\infty }$performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design method.

This article investigates the sliding-mode control issue for interval type-2 (IT2) T-S fuzzy systems under limited communication resources. An event-triggering weight try-once-discard (ET-WTOD) protocol is formulated via two thresholds to determine the transmission of the state signal. The proposed ET-WTOD protocol can dynamically adjust the transmitted nodes and permits only partial components with larger error to be sent at each triggering instant, which is just the key distinction from the existing protocols. Under the imperfect premise matching framework, the controller's membership functions are reconstructed via the received state and the known upper and lower bounds, and then, a new scheduling signal set is established to design the scheduling-signal-dependent fuzzy sliding-mode controller. With the aid of the membership-function-dependent approach, the mismatching premise variables of the fuzzy model and the controller are effectively handled by introducing some slack matrices, while the relaxed stability conditions are derived to ensure the stability of the closed-loop system and the reachability of the specified sliding surface. Moreover, an optimized sliding domain is further obtained via the genetic algorithm (GA). Finally, the proposed control strategy is verified via the mass-spring-damper system.

Choosing adequate sampling frequencies in sensors has a considerably positive impact on the two time scale fuzzy logic controller design. Motivated by this concept, this article addresses the fuzzy-parallel distribution compensation (PDC)-based control synthesis for a singularly perturbed nonlinear systems (SPNS) under a nonperiodic multirate sampling mechanism, which also provides guidance on the reasonable choice of maximum allowable sampling time intervals (MASTIs) for multirate sensors. First, the sampled SPNS is converted into a continuous-time Takagi-Sugeno fuzzy singularly perturbed model (TSFSPM) with slow and fast time-varying delays. Then, an$\epsilon$-dependent Lyapunov-Krasovskii functional of order$n$is proposed to derive the sufficient conditions for stabilizing a multirate sampled TSFSPM under a two time scale PDC control. Given the slow MASTI, an efficient linear-matrix-inequality-based design is proposed to recast the$\epsilon$-dependent stabilization conditions as a set of$\epsilon$-independent linear matrix inequalities that are easily solved. On this basis, the upper bound of singular perturbation parameter$\epsilon$, i.e.,$\epsilon ^*$, should be determined to compute the fast MASTI for the possibly slow sampling of fast states. The optimal match of$(\epsilon ^*,n)$is detected for a tradeoff among the closed-loop stability, the controller performance, and the sensor cost. The superiority of the obtained results is shown in an example of a flexible joint inverted pendulum system.

In this work, the security sliding mode control problem is considered for interval type-2 (IT2) fuzzy systems, where the sensor-controller channel may be subject to the false data injection attack with multi-strategy attack model. The different attack patterns at each instant is described via a random categorical distribution. It is noted that the injected false data may result in the system state to exceed the modeling domain. In order to cope with the above phenomenon, a reconstruction method of the controller's membership functions is proposed via analyzing the variation range of the attacked state, and then, an IT2 fuzzy sliding mode controller is designed. The explicit relation between the raw state signal and attacked state is established, based on which stability conditions dependent on the regional boundaries of membership functions are obtained for the input-to-state stability in probability of the closed-loop system. Meanwhile, a framework of security performance optimization is established via searching a desirable sliding matrix, which may be solved via the particle swarm optimization algorithm. Furthermore, the proposed security control scheme is extended to the case of imperfectly matched premises, where the controller may have different fuzzy rules from the fuzzy system. Finally, the proposed security control scheme is verified by two simulations examples.

The$L$th order Rice model can effectively describe imperfect transmission, including amplitude attenuation, time delays, and stochastic disturbance, and is a popular channel fading model in one-dimensional (1-D) systems. However, due to the state evolution feature of two-dimensional (2-D) systems, the previous state signals of 2-D systems are not as directly determinable as those of 1-D systems such that the construction of the conventional and obvious$L$th order Rice model become difficulty for 2-D systems. Motivated by these, this work will investigate the sliding mode control (SMC) problem of the 2-D Fornasini–Marchesini (FMII) system under Rice fading channels. First, the previous$p$-step state signals are defined according to the evolution feature of the FMII model. Afterwards, a new applicable$L$th-order Rice fading model for 2-D FMII systems is constructed, which not only has 2-D structural characteristics but also has similar properties to 1-D cases. A 2-D-type sliding function involving the predefined previous$L$-step state signals and channel attenuation coefficients is designed, which exhibits a similar structural feature to the FMII model. A feasible SMC law is designed via the available fading states to achieve the ultimately uniformly boundedness in the mean square of the closed-loop system and the reachability of the sliding domain around the specified sliding surface. Furthermore, an optimization-solving algorithm is introduced to minimize the convergent bound. Finally, an example is applied to demonstrated the proposed results.

This article is concerned with the dissipative deconvolution filtering issue for networked two-dimensional (2-D) digital systems. By orchestrating the sensor outputs with a prescribed dynamic transmission order, a new multinode Round-Robin protocol (RRP) under the 2-D setting is developed on the sensor-to-filter channel to ease the communication overheads, and a novel compensation strategy is proposed for enhancing the deconvolution filter performance. A sufficient condition is established for ensuring the dissipativity of the deconvolution filter in terms of coupled matrix inequalities. Furthermore, a particle swarm optimization (PSO) algorithm is formulated to design the filter gain with certain optimized performance. Finally, by transforming the color image into three gray images, the proposed algorithms are applied to the remote color image restoration problem under RRP. It is shown that the use of RRP saves 33.3% communication burden, and the saving of communication resources reduces the signal-to-noise ratio (SNR) by 18.5%. In comparison to the RRP using zero-input compensation strategy in available literature, the introduction of the novel multinode RRP with compensation strategy can indeed improve the reconstruction SNR.

This article focuses on the event-triggered sliding mode control for interval type-2 (IT2) fuzzy systems subject to the randomly occurring denial-of-service (DoS) attacks. Under the resource-limited and unreliable network, a probability-dependent adaptive event-triggered scheme (AETS) is proposed, whose triggering parameter can be adaptively adjusted in accordance with the convergence trend of the system state and the attack probability. By constructing a sliding function with one-step-memorized state information, a fuzzy sliding mode resilient controller is designed, whose membership functions (MFs) dependent on the compromised triggered state do not require the same fuzzy rules as the fuzzy system. Furthermore, by employing the global bounds of mismatched MFs, the co-design conditions for the AETS and the fuzzy controller are derived for attaining both the reachability and the stability. Finally, a simulation example and the comparison results are provided.

This paper designs a novel nonsingular terminal sliding mode control (TSMC) scheme for a class of nonlinear systems under binary encoding transmission. To further ease the communication overheads between the plant and the controller, a dynamic event-triggered mechanism is also introduced to the TSMC design. Sufficient conditions are proposed, respectively, for guaranteeing the reachability to a practical sliding mode and the ultimate boundedness of the closed-loop system, in which the effects from the binary encoding and the dynamic event-triggered protocol are quantified clearly. The Zeno phenomena for the developed dynamic event-triggered mechanism is excluded via an explicit analysis. Finally, the feasibility and effectiveness of the proposed scheme are demonstrated by a numerical example and a real experiment on permanent magnet synchronous motor speed regulation system.

This work investigates the stabilization problem of uncertain stochastic Markovian jump systems (MJSs) under communication constraints. To reduce the bandwidth usage, a discrete-time Markovian chain is employed to implement the stochastic communication protocol (SCP) scheduling of the sensor nodes, by which only one sensor node is chosen to access the network at each transmission instant. Moreover, due to the effect of amplitude attenuation, time delay, and random interference/noise, the transmission may be inevitably subject to the Rice fading phenomenon. All of these constraints make the controller only receive the fading signal from one activated sensor node at each instant. A merge approach is first used to deal with two Markovian chains; meanwhile, a compensator is designed to provide available information for the controller. By a compensator and mode-based sliding-mode controller, the resulting closed-loop system is ensured to be input-to-state stable in probability (ISSiP), and the quasisliding mode is attained. Moreover, an iteration optimizing algorithm is provided to reduce the convergence domain around the sliding surface via searching a desirable sliding gain, which constitutes an effective GA-based sliding-mode control strategy. Finally, the proposed control scheme is verified via the simulation results.

This article is concerned with the model-based event-triggered sliding-mode control (SMC) issue for multi-input systems, which is motivated by some existing results in a single-input case. A model-based event-triggered SMC scheme is first designed. In particular, a triggered condition is co-designed with SMC to achieve the reachability condition of a specified sliding surface. Thus, it can effectively mitigate the burden of data communication, and also eliminate the effect of the matched external disturbance and the model uncertainties in both system and input. For ensuring the stability of the model dynamics and the resulting sliding-mode dynamics simultaneously, an auxiliary disturbance input is introduced to the nominal model by compensating the switching term of the designed SMC law. Furthermore, the positive lower bound for the minimum interevent time is analyzed to ensure the feasibility of the proposed approach. To illustrate the proposed model-based event-triggered SMC approach from a practical viewpoint, two design problems to maximize the system robustness and performance are proposed, respectively. The nontrivial optimization problems are then solved by a genetic algorithm (GA). Finally, jet transport aircraft is utilized to demonstrate the effectiveness of the proposed results and algorithm.

In some practical systems, it often remains difficult to directly measure all state variables. This article investigates the memory output sliding-mode control (SMC) for the finite-time consensus of singularly perturbed multiagent systems (SPMASs). First, the virtual state-feedback sliding surface (SFSS) is constructed to ensure the consensus of all agent states. Then, the unknown output derivatives in SFSS are approximated by a moving finite difference method with error estimation and refinement, which gives rise to a new delay-dependent sliding surface. On this basis, the memory output switching control law is designed to stabilize the consensus errors in finite time, even in the presence of estimation biases, singular perturbations, and input noises. Different from the observer-based SMC, the proposed memory output SMC is of simple static form without introducing extra dynamical structures for state estimation. The effectiveness and superiority of the design method are verified in an SPMAS with double-integrator dynamics.

In this article, we propose an improved delayed output-feedback sliding mode control of a fuzzy system with arbitrary order. A new time-delay estimator is designed for approximating the output derivatives in sliding surface, which has appealing noise attenuation capability. Then, such estimator is embedded in the feedback loops, which results in a static delayed output-feedback sliding surface. On this basis, the sliding mode control law depending on consecutive measurements is used to stabilize the fuzzy system subject to estimation biases and measurement noises. Different from the existing publications, the estimator and controller parameters are codesigned by genetic algorithm to make a tradeoff among multiple objectives: the closed-loop stability, noise attenuation, and estimation accuracy. The resulting design method is demonstrated by two examples: a mass-spring-damper system and a single-link rigid robot system.

In this article, the sliding mode control problem is considered for interval type-2 fuzzy systems under the access-constrained communication network. The sensors and actuators are selected in a random manner, under which only a part of sensor/actuator nodes can be permitted to access the communication channels. The access status of the sensor and actuator is described by two independent Markov chains. To deal with the complexity of two Markov chains on the control design, the mapping technique is used to generate a new variable obeying a Markov chain, which can simultaneously reflect the access status of the sensor and actuator. Furthermore, a scheduling signal-dependent fuzzy sliding mode controller is designed, and the MF-dependent sufficient conditions are given to ensure the stochastic stability of the controlled system and the reachability of the sliding surface. Besides, an optimization-based solving algorithm is proposed to search the sliding matrix and obtain the optimized control gains for reducing the energy consumption of control input. Finally, the simulation results of a numerical example and the 2-degree-of-freedom helicopter system are given.

Dissipativity-based asynchronous boundary stabilization problem is addressed for stochastic Markov jump reaction-diffusion systems (SMJRDSs). In practical engineering, nonsynchronous behavior between system modes and controller modes is inevitable, and the incomplete matrix information makes the problem analysis difficult, so this work considers the asynchronous stabilization. Different from the distributed control, we apply a simple boundary control strategy, which greatly reduces the cost of the control design. Note that three issues need to be addressed: 1) how to model the asynchronous behavior? 2) how to design the asynchronous boundary controller? and 3) how to process the incomplete matrix information? We deal with these problems one by one. Based on a general hidden Markov model (HMM), an asynchronous boundary feedback controller is considered. Via the Wirtinger-type inequality, Schur complement technique, and transition matrix properties, sufficient conditions ensuring exponentially mean square stability and strictly$(W, P, R)-\alpha $dissipativity are established, which covers several special cases. Finally, a numerical example is presented to illustrate the proposed control strategies.

The co-design problem of 2-D event generators and sliding mode controller (SMC) is studied in this article for the discrete-time 2-D Roesser model to reduce the communication usage between the plant and the controller. First, by resorting to the 2-D reaching law conditions, the event-based 2-D SMC schemes are proposed and a kind of horizonal/vertical independent event generator is designed. Then, the stability of the sliding-mode dynamics is analyzed and a nonlinear matrix inequality condition associated with the horizontal/vertical sliding matrices is obtained. In order to solve the derived nonlinear matrix inequality condition without introducing conservatism, a binary genetic algorithm (GA) is applied by considering a multiobjective optimization problem, which reflects the tradeoff between the convergence of the sliding-mode dynamics and the scheduling performance of the designed horizontal/vertical event generators. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed co-design approach with GA.

The sliding-mode control (SMC) problem is studied in this article for state-saturated systems over a class of time-varying fading channels. The underlying fading channels, whose channel fading amplitudes (characterized by the expectation and variance) are allowed to be different, are modeled as a finite-state Markov process. A key feature of the problem addressed is to use a hidden Markov mode detector to estimate the actual network mode. The novel model of hidden Markov fading channels (HMFCs) is shown to be more general yet practical than the existing fading channel models. Based on a linear sliding surface, a switching-type SMC law is dedicatedly constructed by just using the estimated network mode. By exploiting the concept of stochastic Lyapunov stability and the approach of hidden Markov models, sufficient conditions are obtained for the resultant SMC systems that ensure both the mean-square stability and the reachability with a sliding region. With the aid of the Hadamard product, a binary genetic algorithm (GA) is developed to solve the proposed SMC design problem subject to some nonconvex constraints induced by the state saturations and the fading channels, where the proposed GA is based on the objective function for optimal reachability. Finally, a numerical example is employed to verify the proposed GA-assisted SMC scheme over the HMFCs.

This article is to tackle the event-based state-feedback control problem for interval type-2 (IT2) fuzzy systems subject to the fading channel. For saving communication resources, a dynamic event-triggered (ET) mechanism is utilized to decide the data transmission from sensors to the controller. A time-varying random process is employed to characterize the fading phenomenon in the unpredictable communication network. By considering the effect of channel fading, a nonparallel distribution compensation (non-PDC) IT2 fuzzy controller is synthesized and its number of rules and membership functions (MFs) can be freely selected. As a consequence, the closed-loop fuzzy system possesses imperfectly matched MFs. By taking the global membership boundary information into stability analysis, the membership-function-dependent analysis method is employed to handle these imperfectly matched MFs and to obtain relaxed criteria. Besides, sufficient criteria are obtained so that the resulting closed-loop IT2 fuzzy system can achieve stochastic stability despite fading measurements. The effectiveness of the proposed method is illustrated by a mass-spring-damper system and a numerical example.

In this article, we show that a fuzzy system of relative degree two can be stabilized by proportion-integration-differentiation (PID) sliding mode control depending on the outputs and their derivatives. The main focus of this article is to formulate a novel event-based fuzzy PID sliding surface under the imperfect premise matching. First, the measured output is adequately sampled for frequently checking a delay-dependent event-triggered condition, which reduces the number of data transmissions and controller updates. Then, an artificial time-delay estimator is used to approximate the output derivative. Based on linear matrix inequalities, a heuristic algorithm is investigated to design an event-triggered sliding mode controller, which reveals how to choose the maximum sampling interval that maintains the estimation accuracy and preserves the stability under fast event triggering. In simulation, the effectiveness of the proposed design method is verified in a cart and pendulum system subject to system uncertainties.

In this article, the sliding mode control (SMC) problem is addressed for a class of Markovian jump systems via the T–S fuzzy model. First, in order to reduce the frequency of state transmission for alleviating congestion phenomenon in the bandwidth-limited communication network, a dynamic event-triggered (DET) strategy is introduced into the sensor-to-controller channel, in which an additional internal dynamical variable is employed to adjust the event-triggered condition adaptively. A fundamental issue resulting from the event-triggered strategy is that the controller cannot obtain the information about system mode during the triggering interval. Aiming at the phenomenon, this work utilizes a mode detector to estimate the unavailable system mode. Then, this article proposes a detected-mode-dependent event-triggered sliding mode controller whose membership grades are determined only via the transmitted state at the triggering instant. By constructing a relation on the membership functions (MFs) between the fuzzy model and the controllers for MF-dependent analysis, the conditions on the reachability and stability conditions are relaxed. Furthermore, an optimization algorithm is provided for the minimum control power via a high-dimensional grid searching for the coefficients of the internal dynamic variables, which, together with the designed detected-mode-dependent sliding mode controller, constitutes the novel SMC scheme under the DET strategy. Finally, the simulation results via the single-link arm system are provided to illustrate the efficiency of the proposed method.

This article addresses the security control problem of a class of interval type-2 fuzzy systems via the sliding mode control strategy. A stochastic communication scheduling protocol is utilized to govern the transmission from the sensors to the controller, by which only one sensor node has the chance to transmit its value at every instant. Meanwhile, cyber attacks from malicious adversaries might be launched in vulnerable communication channels. To quantitatively analyze the effect of the stochastic communication protocol and cyber attacks, their mathematical model is first constructed based on a compensation scheme. Since the scheduling signal may be unavailable once cyber attacks are activated, a desirable sliding mode control law is synthesized with token-independent control gains, whose membership functions are mismatched with those of the fuzzy system. To deal with these mismatched membership functions, the relations between the membership functions of the system and the control law are reconstructed. Consequently, the favorable property of perfectly matched memberships could be employed. Sufficient conditions are derived so that the resultant closed-loop interval type-2 fuzzy system is stochastically stable and, at the same time, the state trajectories can be forced into a small domain around the prescribed sliding surface. The proposed control design approach is verified by two examples.

This article investigates the hybrid sliding mode control problem for the uncertain Markovian jump systems (MJSs) via the transition rates optimal design. The stability condition for the transition rates is first established to ensure the exponential mean-square (EMS) stability of the unforced uncertain MJSs. Then the hybrid design strategy on the sliding mode controller and transition rate matrix is presented to ensure the EMS stability of the controlled system. Moreover, the iterative optimization algorithms are developed to acquire the desirable transition rates, control gain, and decay rate$\sigma $. Finally, some numerical simulation results are provided.

The adaptive sliding mode control (SMC) problem is addressed for singular semi-Markovian jump systems (S-MJSs) against actuator attacks, in which the transition rates rely on the random sojourn time and are not constant, and the system states are unavailable. Moreover, the vulnerability of control signals transmitted via communication network means that the actuators may receive the attacked control signals. For the sake of reducing the effect of actuator attacks, the neural network technique is used to approximate the false information injected by adversaries. Meanwhile, a sliding mode observer is introduced to estimate the unmeasured states. An adaptive SMC law is proposed to guarantee that the estimation states and errors can reach to the sliding surfaces, and the stochastic admissibility of the singular S-MJSs can be ensured. In the end, an example is applied to illustrate the method in this paper.

In this article, the sliding mode control (SMC) design problem is investigated for a class of discrete-time interval type-2 fuzzy systems, in which the scheduling of sensors is ruled by the round-Robin communication protocol. This means that at any time, only one sensor node can transmit its value to the controller side. To deal with this phenomenon, a compensation scheme is proposed for other sensor nodes, based on which the past measured signal stored in the corresponding buffers may be utilized by the controller. And then, a token-dependent sliding mode controller is synthesized. Sufficient conditions are derived such that the system states can reach a neighborhood of the sliding surface and the resultant closed-loop fuzzy system is input-to-state stable. Finally, simulation results verify the effectiveness of the proposed SMC method.

This article investigates the sliding-mode control (SMC) problem for a class of T-S fuzzy systems with communication constraints. The weighted try-once-discard (WTOD) protocol is utilized to arrange the transmission order of actuator nodes, under which only one node is permitted to obtain access to the communication network at any time. A key issue is how to integrate the WTOD protocol into the design of the SMC system. To this end, an update rule is proposed for the actuators to obtain the actual actuator signals. And then, a membership-function-dependent (MFD) sliding surface and a token-dependent sliding-mode controller are designed. By taking the information of membership functions into stability and reachability analysis, MFD sufficient conditions are derived such that both the asymptotic stability of the closed-loop fuzzy systems and the reachability of the specified sliding surface can be guaranteed. Moreover, the cone complementary linearization (CCL) algorithm is employed to convert nonlinear inequalities into a minimization problem with linear constraints. Finally, a numerical example is utilized to illustrate the proposed SMC design approach.

This paper focuses on the sliding mode control (SMC) problem of interval type-2 (IT2) fuzzy systems subject to the unmeasurable state and cyberattacks. A key issue is how to design a state observer under the constraint that only the bounds of membership functions are known. To this end, this paper introduces two weighting factors to construct a new membership function. Besides, the concept of input-to-state stability (ISS) is utilized to deal with the residual term resulting from the cyberattacks and external disturbances. The sufficient condition is established such that the sliding mode dynamics and the estimated error dynamics are input-to-state stable. Furthermore, by online estimating the unknown parameters in upper bounds of cyberattacks and external disturbances, an adaptive sliding mode controller is synthesized such that the reachability of the prescribed sliding surface can be guaranteed and the effect of cyberattacks on the system performance can be effectively attenuated. Finally, the validity of the proposed method is illustrated by a mass-spring-damper system.

The asynchronous sliding mode control (SMC) problem is investigated for networked Markovian jump Lur'e systems, in which the information of system modes is unavailable to the sliding mode controller but could be estimated by a mode detector via a hidden Markov model (HMM). In order to mitigate the burden of data communication, an event-triggered protocol is proposed to determine whether the system state should be released to the controller at certain time-point according to a specific triggering condition. By constructing a novel common sliding surface, this paper designs an event-triggered asynchronous SMC law, which just depends on the hidden mode information. A combination of the stochastic Lur'e-type Lyapunov functional and the HMM approach is exploited to establish the sufficient conditions of the mean square stability with a prescribed H∞ performance and the reachability of a sliding region around the specified sliding surface. Moreover, the solving algorithm for the control gain matrices is given via a convex optimization problem. Finally, an example from the dc motor device system is provided.

This paper focuses on a two-stage framework for economic optimization to maximize the profits of electric-vehicle (EV) microgrid. In the first stage, an economic optimization problem at the day-ahead time scale is solved to determine the power purchased from load serving entities (LSE), and make an optimal price decision (parking fee and charging fee) while considering with the EVs uncertainties. In the second stage, a real-time model predictive control strategy is proposed to meet the EVs requirement and minimize the operation cost. Through two-stage scheduling, EV microgrid can guarantee long-term safe and efficient operation, while ensuring maximum benefits. The simulation results show that the proposed method in this paper can provide reliable power supply to the EVs, increase the EV microgrid revenue and ensure the safe operation of the EV microgrid system.

This paper proposes a novel remote tracking control strategy for a class of discrete-time Takagi-Sugeno fuzzy systems with randomly occurring uncertainties and randomly varying local nonlinear models. The outputs of the fuzzy system are collected through an unreliable sensor subject to missing measurements. Simultaneously, the outputs of the remote models are transmitted to the controller through wireless channels, in which the fading measurements may inevitably happen. By considering the Rice fading model and the Markovian packet dropouts model, an output-feedback controller is designed such that the closed-loop fuzzy tracking system is robustly stochastically stable and a prescribed H∞remote tracking performance is achieved. Furthermore, sufficient conditions are obtained for the existence of admissible tracking controllers in terms of nonstrict linear matrix inequalities. To overcome the difficulty in computation, a modified cone-complementarity linearization algorithm is employed to cast the tracking controller design problem into a sequential minimization one, which can be readily solved by using standard numerical software. Simulation results demonstrate the effectiveness of the developed control algorithm for fuzzy remote tracking controller.

This paper studies the mean square quadratic (MSQ) detectability for multi-output networked systems over finite-state fading channels. The unreliability from the plant output to the estimator input is described by multiplicative noises. A finite-state random process is introduced to model time-varying fading channels. Necessary and sufficient conditions for MSQ detectability are given in the form of algebraic Riccati equations or linear matrix inequalities. In addition, explicit conditions on network for MSQ detectability over finite-state independent identically distributed (i.i.d.) fading channels are presented in terms of the Mahler measure of the unstable and multi-output plant. Finally, application to Gilbert-Elliott channels (GECs) is provided to demonstrate the derived results.

This work considers the problem of sliding mode control for stochastic systems with Markovian jumping parameters, in which the packet dropout may happen when the state information is transmitted from the sensor to the controller. By means of an estimator for loss signals, an integral-like sliding function is constructed. And then, a sliding mode controller involving in dropout probability is designed such that the effect of packet losses can be effectively attenuated. Moreover, the analysis on both the stability of sliding mode dynamics and the reachability of sliding surface are made. Finally, the numerical simulation results are given.

This paper considers the problem of reliable control for a class of uncertain switched system via sliding mode control technique. By means of a matrix transformation, a common sliding surface is designed. Moreover, the asymptotical stability of the sliding mode dynamics is analyzed by adopting the multiple Lyapunov functions method based on the min-projection strategy. Besides, the state trajectories can be driven onto the proposed sliding surface despite the presence of the parameter uncertainties and the actuator faults. The efficiency of the controller design is demonstrated by a numerical example.

This paper deals with the filtering problem for discrete-time fuzzy stochastic systems with sensor nonlinearities. There exist time-varying parameter uncertainties and random noise depending on state and external-disturbance. The characteristic of nonlinear sensor is handled by a decomposition method. By means of the parallel distributed compensation technique, the design method of the robust H_ filter is presented. Sufficient conditions for the stochastic stability of the filtering error systems are derived such that the filter parameters can be explicitly obtained. Simulation results are given to illustrate the proposed method.

For original paper see D. W. C. Ho et al., ibid., vol.16, no.3, p.625-35, (2005). For original paper see S. J. Yoo et al., ibid., vol.19, no.8, p.1496-8, (2008). This paper presents the reply to "Comments on ldquoAdaptive neural control for a class of nonlinearly parametric time-delay systemsrdquordquo.

This paper deals with the sliding-mode control (SMC) problem for nonlinear stochastic time-delay systems by means of fuzzy approach. The Takagi-Sugeno (T-S) fuzzy stochastic time-delay model with parametric uncertainties and unknown nonlinearities is presented. A sufficient condition for the exponential stability in mean square of the sliding motion is also derived. Moreover, it is shown that when the linear matrix inequalities (LMIs) with equality constraint are feasible, the designs of both sliding surface and sliding-mode controller can be easily obtained via convex optimization. A simulation example illustrating the proposed method is given.

In this paper, an adaptive neural controller for a class of time-delay nonlinear systems with unknown nonlinearities is proposed. Based on a wavelet neural network (WNN) online approximation model, a state feedback adaptive controller is obtained by constructing a novel integral-type Lyapunov-Krasovskii functional, which also efficiently overcomes the controller singularity problem. It is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed-loop systems. An example is provided to illustrate the application of the approach.