This article investigates the mode cluster-based event-triggered control (MCETC) of stochastic Markovian jump systems (SMJSs) under denial-of-service (DoS) attack. First, a novel MCETC framework is designed by considering the interplay among subsystems, DoS attacks, and the event-triggered mechanism (ETM). In this framework, the controller mode is reconstructed, and the number of controller modes is reduced by reclustering the system modes. It significantly reduces the conservatism of the system compared to existing mode-dependent/-independent controllers. Second, a switching ETM is designed for scenarios with and without DoS attack activation, which can effectively save network bandwidth resources and reduce computational load. Third, a multi-Lyapunov function based on DoS attacks is proposed to ensure the stability of the closed-loop SMJSs. Then, the controller gains and event-triggered parameters are jointly solved via the linear matrix inequality (LMI) technique. Moreover, the maximum allowable sampling interval (MASI) is given such that the controller can restore the control signals as soon as a DoS attack ends, which enables faster stabilization of the closed-loop system. Finally, a numerical example is used to verify the effectiveness and superiority of the proposed method.

For DC microgrids (MGs), real-time adjustment of current sharing ratios and secure voltage restoration are paramount for optimizing load allocation and enhancing dynamic performance. In this paper, a dual-objective distributed model-free adaptive control (MFAC) scheme is designed for the first time to guarantee voltage transient performance and adjustable current sharing. First, an output-constrained nonlinear MG model with ZIP (constant impedance, constant current and constant power) load is established, and subsequently it is converted into an equivalent unconstrained data model using system transformation and dynamic linearization techniques. Second, a new prescribed performance control algorithm with asymmetrical preset boundaries is proposed to restrict voltage transient responses. This algorithm is updated with real-time input and output data at discrete instants, making it independent of line resistance and ZIP load measurements. To enhance the robustness of the control method, an internal observer is designed to actively compensate for the unknown nonlinear dynamics generated by time-varying system parameters. The stability conditions of the transformed systems in the presence of ZIP loads and time-varying line resistance are derived, which can indirectly ensure the prescribed voltage performance of the original system. Finally, the effectiveness of the proposed control method is validated through some simulations and hardware experiments.

This paper is concerned with the sliding mode predictive control problem for the load frequency control (LFC) of interconnected power systems with input delays and load disturbance. To deal with input delays, unknown disturbance, the interconnected influence existing simultaneously in power systems, the state-observer and disturbance-observer are respectively designed by employing the reduction transformation technique for state observer and introducing the sliding mode surface for the extended disturbance observer. Then the jointed observers based integral sliding mode controller with active disturbance compensation is designed. Furthermore, by constructing a novel Lyapunov function and matrix inequality technique, the sufficient conditions of exponential stability are provided for the closed-loop observer error systems in linear matrix inequality form, which can be solved by linear matrix inequality (LMI) toolbox in Matlab. Simulation is given to verify the effectiveness of the proposed approach.Note to Practitioners—This paper was motivated by the practical control problem of load frequency control systems with input delay. The input delay, unknown load disturbance and frequency fluctuation of tie-lines make it difficult to design a suitable control for load frequency control systems. The main practical contributions are summed as follows: A new jointed observer-based sliding mode predictive control approach is proposed to the interconnected power systems with input delays. By employing the reduction transformation technique, a jointed observer based integral sliding predictive mode controller with active disturbance compensation is developed to deal with input delay, unknown disturbance, the interconnected influence existing simultaneously in practical power systems.

Random differential equations (RDEs) involving colored noise hold more practical significance than stochastic differential equations (SDEs) driven by white noise. The research on random nonlinear systems is becoming more and more popular. This paper considers the problem of finite-time control for high-order random nonlinear systems with general growth conditions and unknown control coefficients. Based on the backstepping and domination idea, the technique of adding a power integrator is adopted to recursively design an adaptive controller that renders the closed-loop system finite-time stable in probability. This paper serves as a pioneering attempt at finite-time control design of random nonlinear systems. The theoretical results are corroborated by a numerical example.Note to Practitioners—This article was motivated to realize the finite-time stability of high-order random nonlinear systems, even though there are unknown control coefficients in the system. The practical significance of this paper is mainly twofold. Firstly, since random noise is ubiquitous in all kinds of engineering environments, the research on random nonlinear systems driven by colored noise is of great importance. Secondly, the asymptotic stability is infeasible in the practical implementation, so the achievement of finite-time control makes the method proposed in this paper applicable.

For the superheated steam temperature control system, an optimized disturbance observer and output-constrained control algorithm have been designed. Initially, the original system with output constraints is transformed into a system without any state constraints, suitable for backstepping design, through state transformation. Then, based on the concept of negative gradient optimization, a gain iterative disturbance observer is constructed, which dynamically improves the control accuracy of the system compared to a constant gain disturbance observer. Finally, an adaptive neural control scheme based on the gain iterative disturbance observer is proposed, proving that all output states are constrained within predefined bounds, and all closed-loop signals are semi-globally uniformly bounded. The effectiveness of the proposed scheme is demonstrated through a simulation example of the superheated steam temperature system.

In this article, a novel adaptive event-triggered (ET) control scheme with dynamic limits error constraints is presented. To solve the problem of difficult selection of error constraint limit, the new error transformation function is constructed, which relates the constraint limit to the error and directly constrains the error. The constraint limit of the error designed in this article will change with the change of the error, so that the constraint limit has the ability of self-adjustment to improve the flexibility of error constraints. In addition, a novel ET mechanism based on relative threshold is proposed in this article. The mechanism associates the threshold with the tracking error. When the tracking error of the system changes, the threshold of the ET mechanism will also change accordingly, so as to adjust the number of triggers. On the premise of ensuring the control performance of the system, it can save communication resources as much as possible. Finally, a simulation implementation of the control strategy is carried out through numerical simulation to prove its effectiveness.

The optimal tracking problem for continuous-time boiler turbine systems (BTSs) with asymmetric input constraints is considered in this paper. Considering that continuous updating of control input will reduce the service life of engineering oriented system, a novel dynamic event-based triggering mechanism is proposed to reduce the number of controller updates, where a positive internal dynamic variable is introduced to expand the threshold. The objective is to find the optimal event-triggered control strategy for a given performance index function so that the system can track the ideal signal while minimizing the cost function. Firstly, by introducing tracking error variable, the optimal tracking problem is transformed into the optimal stability problem with symmetric input constraints. Then, three neural networks are designed to approximate the system model, cost function and control strategy respectively, and the feasibility of the proposed optimization algorithm is strictly proved by Lyapunov method, and the system will not exhibit Zeno behavior. Finally, simulation results effectively indicate the feasibility of the developed method in the industrial oriented system.Note to Practitioners—With the development of the national economy, China’s demand for electricity is also increasing. The BTSs in thermal power generation unit should not only realize load tracking, but also consider minimizing fuel consumption, minimizing pollutant emissions, maximizing the service life of BTSs. In this paper, adaptive dynamic programming (ADP) method and dynamic event-based mechanism are used to solve the optimal tracking problem of BTSs. The dynamic event-based mechanism not only affects the real performance of the BTSs, but also reduces the number of controller updates and saves resources of the BTSs.

This article investigates the finite-time containment control problem for fractional-order nonlinear multiagent systems (FOMASs) with event-triggered inputs. First, a new Lyapunov stability lemma is developed, which provides a basic approach for the completely unknown nonlinear fractional-order system to realize finite-time convergence. Considering the containment control for FOMASs, the restricted assumption that the derivatives of leaders' trajectories are known to the followers is removed, and only the boundedness of derivatives is required in this article, whose upper bound need not be known. To reduce the burden of communication, an event-triggered condition consisting of the control input and a decreasing function related to the containment errors is devised, which can provide more design freedom to balance the system performance and communication resources. According to the proposed fractional-order finite-time convergence lemma, a distributed adaptive containment control scheme is developed, such that each follower can be steered to the convex hull spanned by the leaders in finite time. Simulation examples further demonstrate the effectiveness of our proposed method.

This article addresses the solution of continuous-time linear Itô stochastic systems with Markovian jumps using an online policy iteration (PI) approach grounded in -learning. Initially, a model-dependent offline algorithm, structured according to traditional optimal control strategies, is designed to solve the algebraic Riccati equation (ARE). Employing Lyapunov theory, we rigorously derive the convergence of the offline PI algorithm and the admissibility of the iterative control law through mathematical analysis. This article represents the first attempt to tackle these technical challenges. Subsequently, to address the limitations inherent in the offline algorithm, we introduce a novel online -learning algorithm tailored for Itô stochastic systems with Markovian jumps. The proposed -learning algorithm obviates the need for transition probabilities and system matrices. We provide a thorough stability analysis of the closed-loop system. Finally, the effectiveness and applicability of the proposed algorithms are demonstrated through a simulation example, underpinned by the theorems established herein.

This article focuses on the issue of novel dynamic event-triggered consensus control of multiagent systems (MASs) with denial-of-service (DoS) attacks. Different from the conventional Markovian switching topologies, the generally uncertain semi-Markovian (GUSM) switching topologies with partially unknown elements and time-dependent uncertainties are constructed for the leader-following MASs by considering the equipment performance and external uncertain environment influence. To save communication resources, the novel dynamic memory event-triggered strategy (DMETS) is presented to decrease the frequency of communication between agents. Some secure consensus control criteria are established for the MASs with GUSM switching topologies and DoS attacks due to the potential system communication disruption caused by attackers. Finally, two physical system examples are designed to prove the effectiveness of the presented method.

This article addresses the problem of containment control for continuous-time multiagent systems. A containment error is first given to show the coordination between the outputs of leaders and followers. Then, an observer is designed based on the neighbor observable convex hull state. Under the assumption that the designed reduced-order observer is subject to external disturbances, a reduced-order protocol is designed to realize the containment coordination. In order to ensure the designed control protocol can achieve the effect of the main theories, a corresponding Sylvester equation is given with a novel approach which proves that the Sylvester equation is solvable. Finally, a numerical example is given to verify the validity of the main results.

This article researches the sliding mode control (SMC) for fuzzy fractional-order multiagent system (FOMAS) subject to time-varying delays over directed networks based on reinforcement learning (RL),$\alpha\in(0,1).$First, since there is information communication between an agent and another agent, a new distributed control policy$\xi_{i}(t)$is introduced so that the sharing of signals is implemented through RL, whose propose is to minimize the error variables with learning. Then, different from the existed papers studying normal fuzzy MASs, a new stability basis of fuzzy FOMASs with time-varying delay terms is presented to guarantee that the states of each agent eventually converge to the smallest possible domain of$0$using Lyapunov–Krasovskii functionals, free weight matrix, and linear matrix inequality (LMI). Furthermore, in order to provide appropriate parameters for SMC, the RL algorithm is combined with SMC strategy, and the constraints on the initial conditions of the control input$u_i(t)$are eliminated, so that the sliding motion satisfy the reachable condition within a finite time. Finally, to illustrate that the proposed protocol is valid, the results of the simulation and numerical examples are presented.

This article presents a novel finite-time adaptive fuzzy event-triggered control strategy for stochastic nonlinear systems in nonstrict feedback structure, where time-varying output constraints and input delay are considered. To deal with the output constraints, a stochastic nonlinear mapping is developed to transform the original system into an equivalent one without output constraints. Furthermore, the Pade approximation method is applied to address the input delay by introducing a new intermediate variable. Then, a novel adaptive event-triggered mechanism is proposed to reduce the number of data transmissions and mitigate the effects of tracking error. The stability analysis shows that the closed-loop signals are semiglobal finite-time stable in probability, while the tracking performances are well and satisfy the output constraint condition. Finally, simulation results demonstrate the effectiveness of the developed approach.

This article investigates the bipartite time-varying output formation tracking issue for heterogeneous linear multiagent systems with multiple leaders under signed digraph. Different from previous related works, the leaders are considered to be heterogeneous, which greatly increases the difficulty of designing distributed control strategies. To address this issue, we develop a novel fully distributed dynamic event-triggered formation tracking control strategy and the Zeno behavior is ruled out. Compared with previous relevant results, in addition to addressing a more meaningful new issue, the developed control strategy also has the following advantages: 1) the control strategy gets rid of this assumption that each given follower must be well informed or uninformed; 2) the adaptive gains do not increase unboundedly in the presence of external disturbances; 3) the interevent time is larger. Moreover, a self-triggered realization based on sampled information is also formulated for the developed control strategy. Finally, the theoretical result is demonstrated by a simulation example.

This article considers the bipartite time-varying output formation-containment tracking control issue for general linear heterogeneous multiagent systems with multiple nonautonomous leaders, where the full states of agents are not available. Both cooperative interaction and antagonistic interaction between neighboring agents are taken into account. First, an observer is constructed using the output information to observe the state information. Then, based on the information between neighboring agents, an independent asynchronous fully distributed event-triggered bipartite compensator is put forward to estimate the convex hull spanned by the states of multiple leaders. Note that the compensator does not require to use of any global information. Subsequently, a formation-containment tracking control strategy based on the observer and compensator and an algorithm to determine its control parameters are given. The Zeno behavior is further proved to be excluded in any finite time. In addition, a novel self-triggered control strategy based only on the sampled information at triggering instants is also formulated, which avoids continuous communication among agents. Finally, a numerical example is given to validate the effectiveness and performance of the proposed control strategies.

This article is concerned with distributed resilient load frequency control (LFC) for multi-area power interconnection systems against jamming attacks. First, considering uncertainties and high dimension nonlinearity, the model-free adaptive control (MFAC) model is adopted for the power system, in which only input and output (I/O) data are used. Second, jamming attacks are modeled in a stochastic process, and a multistep predictive compensation algorithm is developed to mitigate the impact of jamming attacks. Then, the distributed MFAC protocol with predictive compensation algorithm is designed such that the frequency tracking errors under the predictive compensation algorithm of multi-area power interconnection systems converge consensually into a small neighborhood of origin in the mean square sense. Simulation results show the effectiveness of the approach.

Considering that cooperative interactions and antagonistic interactions between neighboring agents may exist simultaneously in practice, this article studies the bipartite time-varying output formation tracking (BTVOFT) problems for homogeneous/heterogeneous multiagent systems with multiple nonautonomous leaders under switching communication networks. First, a full-dimensional observer-based nonsmooth distributed dynamic event-triggered (DDET) output feedback control scheme is proposed to ensure that BTVOFT is achieved, and the Zeno behavior is excluded. Note that the nonsmooth distributed control scheme requires global communication network information and may cause unexpected chattering effect, and the design cost of full-dimensional observer is relatively high. Thus, a reduced-dimensional observer-based continuous fully DDET scheme is proposed. Compared with the existing event-triggered schemes, the dynamic event-triggered scheme can ensure larger interevent times by introducing an additional internal dynamic variable. Finally, the effectiveness and performance of the theoretical results are validated by numerical simulations.

This article has a research on the problem of output consensus for linear heterogeneous multiagent systems (LHMASs) by using dynamic event-based impulsive control. First, according to whether the transfer of information from different agents is continuous or not, two corresponding control approaches are provided, respectively. Second, for the case of continuous information transfer, the corresponding dynamic event-triggered condition is obtained. Third, for the case that the information communication from each agent only occurs at the event-triggered time instant, two different dynamic event-triggered conditions according to whether the event-triggered time instant for each agent is same or not are proposed, respectively. For all these event-triggered mechanisms, both the output consensus conditions and the proofs of avoiding Zeno-behavior are given. Moreover, the effect of the dynamic variables belong to these dynamic event-triggered conditions on the minimum event-triggered time interval is also discussed. Finally, the analysis for a numerical example with two control approaches and the corresponding event-triggered conditions provided in this article is obtained to support our opinions.

This article devotes to solve the fault-tolerant control problem based on interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy stochastic switched uncertain time-delayed systems with signal quantization. Stochastic switched systems can model a dynamic structure susceptible to abrupt faults, making it more practically significant in power systems or economic systems. The core design is an observer-based fault-tolerant control scheme that can estimate incomplete measurable variables and eliminate the influence of fault dynamically well and enhancing the robust stability of the systems subject to quantization effects. A novel method in seeking the upper bound solution of time-varying delay efficiently decreases conservativeness, especially for the proposed time-delayed system. The simulated analysis is specified to verify the availability and validity of the obtained design method.

This article investigates the fault-tolerant control problem for stochastic switched interval type-2 (IT2) fuzzy time-delayed uncertain systems based on unknown input observer synthesis, which can avoid uneasy measurement on the time derivative of output, and estimate unavailable or partially measurable states, including sensor and actuator faults accurately. First, a desired fuzzy observer is designed to ensure the observer-based dynamic error system mean-square exponentially stable with sufficient condition of a strict$(\ell,\hbar,\wp)$-$\mho $-dissipative performance, which is a unified framework of passivity, and$\mathcal {H}_{\infty }$provides results with less conservativeness. Then, we concentrate on stability analyses on dissipativity-based switched IT2 fuzzy systems with stochastic perturbation through linear matrix inequalities, Lyapunov function, free-weighting matrices, and average dwell time, discussing it according to different values of disturbance. Finally, simulation examples are listed to account for availability and effectiveness of the research methodology.

In this article, the finite-time containment control problem of the nonlinear multiagent systems (MAS) is investigated, in which the follower agents are subjected to full state constraints. The fuzzy logic system is employed to approximate the uncertain dynamic of the nonlinear MAS. A new nonlinear transformation function (NTF) is proposed, which serves as a unified tool for coping with the systems subjected to state constraints and no constraint. By combing the variable transformation with the proposed NTF, the original systems with state constraints are converted into the equivalent free-constrained systems. Moreover, as long as the boundedness of the states in transformed systems is guaranteed, the states of the original MAS do not transgress the preassigned boundaries. Based on the finite-time stability theory, the adaptive fuzzy control scheme is constructed for the transformed systems. It is proved that the outputs of all the followers are driven to converge to the convex hull spanned by the leaders in a finite time, and all the signals in the closed-loop systems are bounded in sense of mean square. The full state constraints for the followers are not violated all the time. Especially, the control structure does not need to change even there is no constraint imposes on the state. Finally, simulation examples are given to verify the effectiveness of the proposed finite-time control scheme.

This article investigates the prescribed finite-time control for the nonlinear system with uncertain nonlinearity and unknown control directions. Different from the existing finite/fixed-time control methods on the basis of the fractional-order state feedback, the proposed finite-time control in this article only employs regular state feedback. The key is that a novel prescribed finite-time performance function is introduced such that the controller design is under the standard Lyapunov stability theoretical framework. A lemma is developed as a tool for coping with the coexistence of multiple Nussbaum gains for the stochastic system with unknown control directions. Fuzzy logic systems are used to approximate the uncertain nonlinear functions. Applying the backstepping structure, an adaptive fuzzy control scheme is developed. The salient characteristic of the proposed control is that the finite convergence time and the accuracy of the tracking error are independent of the initial states and design parameters, and that can be assigned in a prior. Two examples are given to demonstrate the feasibility and effectiveness of the proposed control scheme.

This article is concerned with the fuzzy functional observer-based finite-time adaptive sliding-mode control for nonlinear systems with the partly unmeasurable states and some matched uncertainties. First, considering that the upper bound of the uncertain function exists but unknown, a fuzzy functional observer (FFO) with an adaptive compensator is constructed. Second, an FFO-based fuzzy integral sliding mode controller (ISMCr) is designed such that the closed-loop fuzzy systems are finite-time bounded with$H_{\infty }$performance over the reaching phase, the sliding phase, and the whole finite-time interval, respectively. To reduce the conservatism and increase the solution space of linear matrix inequality conditions, the fuzzy Lyapunov functional approach and equivalent fuzzy relaxed matrices technique are developed by introducing some relaxed matrices in the derivative of the fuzzy normalized membership function. Compared with the common Luenberger-type observer-based approach, the gain matrices of ISMCr depend on the FFO designed, which also enhances the flexibility of controller design. Finally, a simulation example with some comparison is given to show the effectiveness of the proposed method.

This study investigates the bipartite fixed-time time-varying output formation-containment tracking issue for heterogeneous linear multiagent systems with multiple leaders. Both cooperative communication and antagonistic communication between neighbor agents are taken into account. First, the bipartite fixed-time compensator is put forward to estimate the convex hull of leaders' states. Different from the existing techniques, the proposed compensator has the following three highlights: 1) it is continuous without involving the sign function, and thus, the chattering phenomenon can be avoided; 2) its estimation can be achieved within a fixed time; and 3) the communication between neighbors can not only be cooperative but also be antagonistic. Note that the proposed compensator is dependent on the global information of network topology. To deal with this issue, the fully distributed adaptive bipartite fixed-time compensator is further proposed. It can estimate not only the convex hull of leaders' states but also the leaders' system matrices. Based on the proposed compensators, the distributed controllers are then developed such that the bipartite time-varying output formation-containment tracking can be achieved within a fixed time. Finally, two examples are given to illustrate the feasibility of the main theoretical findings.

This brief considers the security control problem for nonlinear cyber-physical systems (CPSs) against jamming attacks. First, a novel event-based model-free adaptive control (MFAC) framework is established. Second, a multistep predictive compensation algorithm (PCA) is developed to make compensation for the lost data caused by jamming attacks, even consecutive attacks. Then, an event-triggering mechanism with the dead-zone operator is introduced in the adaptive controller, which can effectively save communication resources and reduce the calculation burden of the controller without affecting the control performance of systems. Moreover, the boundedness of the tracking error is ensured in the mean-square sense, and only the input/output (I/O) data are used in the whole design process. Finally, simulation comparisons are provided to show the effectiveness of our method.

In this study, the state formation control issue of general linear networked multi-agent systems (MASs) is considered. Combining self-triggered strategy with general event-triggered strategy, a novel fully distributed asynchronous mixed self- and event-triggered control strategy is proposed, which can make the MASs achieve the prescribed state formation structure. The control strategy proposed in this study does not depend on any global network information. Therefore, no matter how large scale of the network is, the control strategy is feasible. Meanwhile, the control strategy uses the sampled state information at triggering instants instead of the real-time state information, which efficiently eliminates continuous communication among agents. Different from the existing studies, the event-triggered detector starts to work if and only if the next self-triggering instant comes in the control strategy proposed in this article. Thus, the control strategy can save more communication resources between sensor and event-triggered detector within the same inter-event interval compared with the previous event-triggered strategies. In addition, the control strategy designs a exponential decay term in the triggering function to rule out the unexpected Zeno behavior and reduce the triggering number. Finally, the numerical simulation result of multi-robot formation is given, which demonstrates the feasibility and performance of the proposed control strategy.

The issue of fault detection (FD) and fault-tolerant control is developed for a switched random nonlinear system against multiple delays in this work. There also exist parameter uncertainties, exogenous disturbances, nonlinear functions as well as measurement noise in this model. This is one of the few tries to investigate the dissipativity issue and an design FD-based observer for the switched random system. Based on the dimensionally adjustable observer, the controller is designed to make this system noise-to-state exponentially mean-square stable. Then, these sufficient stability conditions can be earned by the piecewise Lyapunov function. Concurrently, this strict$\left({\mathsf {Q}, \mathsf {S}, \mathsf {R}}\right)-{\upsilon }-$dissipativity performance, this elaborate$H_{\infty }$performance as well as this elaborate$H\_{}$performance can be gained, separately. In addition, the merits and feasibility are presented via a numerical simulation and a practical example.

Compared with stochastic differential equations (SDEs) driven by white noise, random differential equations (RDEs) generated by colored noise are claimed to be more practical. This article considers reduced-order high-gain observer (ROHGO)-based neural tracking control on random nonlinear systems having output delay. In order to foster the design and analysis, the estimated states and the estimation errors are scaled by the high gain of the observer. Based on neural network (NN) approximation and state observation, an adaptive controller is designed for the overall system using the backstepping method. It is proved that all the closed-loop signals are bounded almost surely, letting alone the tracking error. By tuning the related design parameters, the asymptotic tracking error could be regulated arbitrarily small. Within the best of our knowledge, this article serves as the first attempt for NN-based control on RDE systems. Finally, the validity of main results is confirmed by a simulation example.

In this article, the leader-following exponential consensus problem of fractional-order descriptor multiagent systems (FOD-MASs) with event-triggered control (ETC) protocol is investigated, which includes integer-order descriptor multiagent systems as the special case. Two classes of control schemes and the corresponding event-triggered conditions are presented, respectively. First, a distributed state feedback ETC protocol is developed to reach the leader-following exponential consensus. The leader-following exponential consensus is achieved in the sense of the Mittag-Leffler stability of fractional-order systems. Second, when full-state measurements are not available, a novel observer-type output feedback ETC strategy with some desirable characteristics is provided. For two distributed ETC protocols, consensus conditions are derived and convergence rate of the system can be adjusted. Also, the integral inequality is applied to get the fact that Zeno behavior is excluded, which verifies the feasibility of ETC schemes. Finally, the effectiveness of conclusions is demonstrated by the examples.

This article considers an adaptive fuzzy control problem for nonstrict-feedback nonlinear stochastic systems, which contain input delay, output constraints, and unknown control coefficients, simultaneously. First, an original stochastic nonlinear mapping and the Pade approximation transformation techniques are developed to solve the symmetric output constraints and input delay. Then, an adaptive fuzzy controller is designed for the unknown nonlinear systems, in which the Nussbaum function is employed to deal with the unknown time-varying control coefficients. Tracking errors are ensured to converge to a small neighborhood around the origin, and the system output does not violate the predefined constrained conditions. All the signals of the closed-loop systems have proven to remain bounded in probability. Moreover, the asymmetric output-constrained control is also studied. Two simulation examples are provided to show the effectiveness of the developed method.

In this article, the bipartite fixed-time output consensus problem of heterogeneous linear multiagent systems (MASs) is investigated. First, a distributed bipartite fixed-time observer is proposed, by which the follower can estimate the leader's state. The estimate value is the same as the leader's state in modulus but may not in sign due to the existence of antagonistic interactions between agents. Then, an adaptive bipartite fixed-time observer is further proposed. It is fully distributed without involving any global information. This adaptive bipartite fixed-time observer can estimate not only the leader's system matrix but also the leader's state. Next, distributed nonlinear control laws are developed based on two observers, respectively, such that the bipartite fixed-time output consensus of heterogeneous linear MASs can be achieved. Moreover, the upper bound of the settling time is independent of initial states of agents. Finally, the examples are given to demonstrate the results.

This article focuses on finite-time adaptive fuzzy output-feedback control for a class of nontriangular nonlinear systems with full-state constraints and unmeasurable states. Fuzzy-logic systems and the fuzzy state observer are employed to approximate uncertain nonlinear functions and estimate the unmeasured states, respectively. In order to solve the algebraic loop problem generated by the nontriangular structure, a variable separation approach based on the property of the fuzzy basis function is utilized. The barrier Lyapunov function is incorporated into each step of backstepping, and the condition of the state constraint is satisfied. The dynamic surface technique with an auxiliary first-order linear filter is applied to avoid the problem of an "explosion of complexity." Based on the finite-time stability theory, an adaptive fuzzy controller is constructed to guarantee that all signals in the closed-loop system are bounded, the tracking error converges to a small neighborhood of the origin in a finite time, and all states are ensured to remain in the predefined sets. Finally, the simulation results reveal the effectiveness of the proposed control design.

This article addresses an adaptive fuzzy control for the nonstrict-feedback nonlinear systems with asymmetric time-varying full state constraints. To prevent the state constraints being violated, the nonlinear state-dependent function (NSDF) is introduced instead of the tradition barrier lyapunov function (BLF). The constrained systems are transformed into a novel free-constrained systems based on the NSDF. A direct approach is given to cope with the state constraints. Fuzzy logic system is utilized to approximate the uncertain nonlinear system functions. The new affine variables are constructed for the transformed systems, and the prior knowledge of the control gains is not required necessarily. Under the designed control scheme, the boundedness of the signals in the closed-loop systems is guaranteed certainly, and the asymmetric time-varying constraints are maintained. This proposed method removes the feasibility condition on the virtual controller derived from the method of BLF. The effectiveness of the proposed control strategy is verified by two simulation examples.

This article addresses an adaptive fuzzy finite-time control for a class of uncertain strict-feedback nonlinear systems with backlashlike hysteresis and stochastic disturbances. At first, a novel criterion of semiglobally finite-time stability in probability (SGFSP) is established based on Lyapunov function method. Under the proposed stability criterion, an adaptive fuzzy finite-time control scheme is designed. In the design process of the controller, command filter technique is introduced to overcome the problems of “explosion of complexity” and “singularity” inhered in the traditional adaptive finite-time control based on the backstepping method. Meanwhile, via constructing the corresponding error compensating systems, the effect of errors generated by the command filters is reduced, such that the original systems have more better tracking performance. To cope with the influence of backlashlike hysteresis input, an auxiliary system is constructed, in which the output signal is applied to compensate the effect of the hysteresis. It is shown that the tracking error can converge to a small neighborhood of original in finite time, and the closed-loop system is SGFSP under the constructed controller. Finally, the effectiveness of the proposed control strategy is further verified by two simulation examples.

In this paper, a novel robust controller for continuous stochastic polynomial fuzzy systems is investigated. The aim of the proposed method is to eliminate the restrictive assumptions that the local input matrix Bi must be uniform and the sliding mode surface proposed did not consider the stochastic perturbations, which are required in most existing results. At the same time, the proposed method could handle the system with matched external disturbances. First, a novel vector integral sliding mode surface (VISMS) is constructed according to the basis matrix B(x). The sliding mode surface parameter matrix K(x) can be obtained through the provided sum of squares conditions. Second, by using an improved Lyapunov method and a new proposed lemma, a novel sliding mode control law is designed to keep the state of the closed-loop systems on the VISMS approximately since the initial time. Third, a practical example and a numerical one are provided to illustrate the validity of the proposed approach.

This article is concerned with the periodic tracking control problem for nonlinear systems. First, the Takagi-Sugeno (T-S) fuzzy model is employed to describe the nonlinear control systems. Second, considering the partly unmeasurable states of the system, a novel fuzzy observer-based repetitive controller, which is the mixed controller of the fuzzy observer-based controller and the fuzzy repetitive controller, is designed to deal with the periodic tracking control problem. To reduce the conservatism and increase the feasible solution space of the stabilization conditions, a new fuzzy relaxed matrix technique is developed by introducing some relaxed matrices in the derivative of the fuzzy normalized membership function. Then, the fuzzy Lyapunov functional with an additional separation parameter and the augmented fuzzy matrix technique (the interactions of fuzzy observer subsystems) are proposed such that the delay-dependent stability condition of the closed-loop system in the form of linear matrix inequality is obtained with less conservatism. It is worth noting that due to introducing an additional parameter in the fuzzy Lyapunov functional, the fuzzy controller and fuzzy observer can be separately designed, which largely enhances the flexibility of design with low computational complexity. Finally, three examples are provided to illustrate the effectiveness and less conservatism of the proposed method.

This article addresses the adaptive bipartite event-triggered output consensus issue for heterogeneous linear multiagent systems. We consider both cooperative interaction and antagonistic interaction between neighbor agents in both fixed and switching topologies. An adaptive bipartite compensator consisting of time-varying coupling weights and dynamic event-triggered mechanism is first proposed to estimate the leader's state in a fully distributed manner. Different from the existing methods, the proposed compensator has three advantages: 1) it does not depend on any global information of the network graph; 2) it avoids the continuous communication between neighbor agents; and 3) it is applicable for the signed communication topology. Assume that the system states are unmeasurable, and we thus design the state observer. Based on the devised compensator and observer, the distributed control law is developed such that the bipartite event-triggered output consensus problem can be achieved. Moreover, we extend the results in fixed topology to switching topology, which is more challenging in that state estimation is updated in two cases: 1) the interaction graph is switched or 2) the event-triggered mechanism is satisfied. It is proven that no agent exhibits Zeno behavior in both fixed and switching interaction topologies. Finally, two examples are provided to illustrate the feasibility of the theoretical results.

In this paper, the H∞consensus problem for linear heterogeneous multiagent systems (LHMAS) based on eventtriggered output feedback control is investigated. Two novel event-triggered control schemes including nonperiodic and periodic event-triggered control approaches are provided to make the LHMAS with external unknown disturbance achieve H∞consensus. Therein, the nonperiodic event-triggered control method is designed by combining the event-triggered approach with time-triggered scheme, which can make the sampled instants be decided by the event-triggered condition and provide a fixed lower bound of sampled interval to avoid the Zeno-behavior. Then, based on this approach, the periodic event-triggered control scheme has a further improvement that only the information at fixed periodic interval is used for the event-triggered condition, which means that this method avoids the continuous-time information transfer. Besides, both schemes take output feedback control, which means that only the output information of each agent and leader is needed in this paper. Finally, a numerical example is given to support our results.

This paper studies the H∞consensus problem for linear heterogeneous discrete-time multiagent systems (MASs). For a special kind of nonlinear matrix inequality, a novel method is provided to make these inequalities turn into some equivalent conditions that can be solved by utilizing the LMI toolbox. According to this method, a necessary and sufficient condition of H∞consensus for linear heterogeneous discrete-time MAS with output feedback control scheme and a corresponding iterative algorithm are proposed, respectively. Moreover, by employing these results, a necessary and sufficient condition that makes a general linear system with one kind of constrained controller achieve H∞control is provided. Finally, two numerical examples are given to illustrate the validity of our schemes.

An adaptive fuzzy tracking control is investigated for a category of multiple-input multiple-output switched uncertain nonlinear systems in strict-feedback form. The unknown nonlinear function and switching signals with average dwell time are contained in the systems. The control method is designed by generalized fuzzy hyperbolic model and backstepping technique. Through adding a first-order filter into conventional backstepping method, the phenomenon of “explosion of complexity” is eliminated. In the controller design process of each subsystem, only one adaptive parameter is needed to adjust online. Compared with other existing control methods, the proposed control design is more simple and calculated amount is greatly decreased. It is guaranteed that the whole closed-loop system is stable by using Lyapunov function and average dwell-time methods. The effectiveness of the proposed control method can be demonstrated in the simulation part.

This paper investigates the problem of designing a robust controller for continuous polynomial fuzzy systems with external disturbances. The input matrix Bi(x) of the considered system is not equal to one another. To solve this problem, first, we rewrite every column vector of input matrix Bi(x) using the vectors of the basis matrix B(x). Second, by use of the column vector of B(x), the subsliding mode surface sp(t) is designed. Based on the rewritten system, a novel sliding mode surface s(t) is devised. The sliding mode surface parameter matrix can be characterized in terms of the solution of the provided sum of squares conditions. Then, a sliding mode controller is proposed to stabilize the considered system. It could make the state of the considered system drive onto s(t) and avoid the state escaping from the surface in the subsequent time. A lemma is provided to obtain the final result. Finally, practical and numerical examples are provided to demonstrate the validity of the proposed approach.

This paper investigates the fault detection problem for a class of switched nonlinear systems in the T-S fuzzy framework. The unknown input is considered in the systems. A novel fault detection unknown input observer design method is proposed. Based on the proposed observer, the unknown input can be removed from the fault detection residual. The weighted performance level is considered to ensure the robustness. In addition, the weighted performance level is introduced, which can increase the sensibility of the proposed detection method. To verify the proposed scheme, a numerical simulation example and an electromechanical system simulation example are provided at the end of this paper.

This paper addresses the problems of fault estimation and fault-tolerant control for switched fuzzy stochastic systems with actuator fault and sensor fault. A novel observer is proposed to estimate the system states, actuator, and sensor faults, simultaneously. The proposed observer can be treated as an extension of the traditional proportional-integral observer. The estimation information is utilized to design the fault-tolerant controller. Based on the piecewise Lyapunov function and the average dwell time, a set of linear matrix inequalities can be achieved, which ensure that the closed-loop system is mean-square exponentially stable with a weighted H∞performance level. At last, two simulation examples are provided to illustrate the effectiveness of the proposed approach.

This paper focuses on the problem of sensor fault estimation of switched fuzzy systems with unknown input. By treating the sensor fault as a virtual state, an augmented system can be obtained. A dynamic unknown input observer is designed for the augmented system to estimate the sensor fault and the system state simultaneously. Based on the average dwell time and the piecewise Lyapunov function, the observer parameter calculation method is presented in terms of solutions to a set of linear matrix inequalities. The unknown input is decoupled from the estimation error, and the effect of the disturbance is attenuated by the weighted H∞performance level. At last, simulation results are provided to illustrate the effectiveness of the proposed techniques.

In this paper, a hybrid adaptive output feedback fault-tolerant control is investigated for a class of uncertain nonlinear systems with unmeasured states. The generalized fuzzy hyperbolic model is used to approximate the unknown nonlinear functions, and the fuzzy state estimator (FSE) is established for estimating the unmeasured states. Based on the backstepping and dynamic surface control technique, a novel adaptive control method is proposed by introducing the prediction errors between FSE and serial-parallel estimation model. It is proved that all the variables of the closed-loop systems are semi-globally uniformly ultimately bounded by Lyapunov approach, and the tracking errors can converge to a small neighborhood. Two simulation examples are used to illustrate the effectiveness of the proposed control method.

This paper focuses on the problem of fault-tolerant control for a class of nonlinear systems with unknown nonlinear dynamic. The generalized fuzzy hyperbolic model is used to approximate the unknown nonlinear function. A novel fuzzy adaptive descriptor observer and an adaptive disturbance observer are designed simultaneously to estimate the system state, actuator fault, sensor fault, and disturbance. In this paper, the disturbance is assumed to be generated from an unknown exogenous system. Compared with the existing results, in which the disturbance is generated from known exogenous system, the proposed adaptive disturbance observer is more applicable in practice, since the exogenous system is independent of the controlled system and its parameter matrix is difficult to be measured. Furthermore, using the estimation information, a novel nonlinear dynamic output feedback controller is designed. The controller can stabilize the nonlinear system, which is subjected to the unknown nonlinear dynamic, actuator fault, sensor fault, and mismatched disturbance, simultaneously. Finally, simulation results are provided to illustrate the effectiveness of the proposed techniques.

In this paper, the inverse optimal approach is employed to design distributed cooperative control protocols for identical linear systems that guarantee consensus and global optimality with respect to a positive (semi-) definite quadric performance index. Cooperative control and pinning control problems are considered, where the communication graphs are assumed to be directed and have fixe topology. Simple sufficient conditions are established, which indicate that the global optimality is achieved using local distributed protocols which are designed by the linear quadric regulator (LQR) based optimal control method. Examples are given to show the effectiveness of the proposed methods.

In this paper, distributed control for second-order leader-following multi-agent systems has been solved. All the outputs of the agents reach a common trajectory. The dynamic of the leader agent is different with the follower agents. If the digraph contains a spanning tree, then the problem is solved using an appropriate control law. A compensator is designed to making the closed-loop system matrix stable. Simulation results are further presented to show the effectiveness and performance of our work.

In this paper, a sum of squares(SOS) method is proposed to design observers for discrete-time polynomial fuzzy systems. The proposed SOS approach has two improved and innovative results for the existing linear matrix inequality (LMI) method to Takagi-Sugeno(T-S) discrete fuzzy observer designs. Firstly, a polynomial discrete fuzzy model is developed, which is a generation of the well-known T-S fuzzy system. Secondly, the conditions in the proposed approach are obtained in terms of SOS, which is the extension of the LMI method. Therefore, the conditions given in this paper are more general than the existing LMI approaches to T-S fuzzy systems. An example is given to show the effectiveness, which also demonstrate the SOS approaches are more relaxed than the existing LMI approaches. Finally, a conclusion is given to complete the paper.

This paper proposes relaxed stabilization conditions of discrete-time nonlinear systems in the Takagi–Sugeno (T–S) fuzzy form. By using the algebraic property of fuzzy membership functions, a novel nonparallel distributed compensation (non-PDC) control scheme is proposed based on a new class of fuzzy Lyapunov functions. Thus, relaxed stabilization conditions for the underlying closed-loop fuzzy system are developed by applying a new slack variable technique. In particular, some existing fuzzy Lyapunov functions and non-PDC control schemes are special cases of the new Lyapunov function and fuzzy control scheme, respectively. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

This paper is concerned with the design problem of networked control systems with partly unknown transition probabilities. Firstly, a new time-delay switched linear system model is proposed for NCSs, in which both the network-induced delay and the packet dropouts are taken into account. A developed packet dropouts dependent Lyapunov functional is used to obtain the stability criteria, in which the method for treating the uncertainties of partly unknown transition probabilities is embedded. Furthermore, the state feedback controller can be designed. Moreover, because the partly unknown transition probabilities in our study do not need any bounds or structures of uncertainties, the obtained stability criteria can expand to the case that the time-delay switched linear system model under arbitrary switching. Finally, numerical example and simulation is used to illustrate the developed theory.

This paper is concerned with the networked synchronization control problem of coupled dynamic networks (CDNs) with time-varying delay. First, both the data packet dropouts and network-induced delays are taken into account in the synchronization controller design. A Markovian jump process is induced to describe the packet dropouts. The network-induced delays are interval time varying and depend on the Markovian jump modes. A new closed-loop coupled dynamic error system (CDES) with Markovian jump parameters and interval time-varying delays is constructed. Second, using the Kronecker product technique and the stochastic Lyapunov method, a delay-dependent sufficient criterion of stochastic stability is obtained for the closed-loop CDES, which also guarantees that the CDNs are stochastically synchronized. Finally, a simulation example is given to demonstrate the effectiveness of the proposed result.

This paper studies the guaranteed cost control problem for a class of uncertain stochastic nonlinear systems with multiple time delays represented by the Takagi-Sugeno fuzzy model with uncertain parameters. By constructing a new stochastic Lyapunov-Krasovskii functional, sufficient conditions for delay-dependent guaranteed cost control are obtained which do not require system transformation or relaxation matrices. Conditions for the existence of an optimal guaranteed cost controller are presented in the linear matrix inequality format. Simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper.