The robustH∞fault-tolerant control problem for a class of nonlinear fractional-order systems described by T-S fuzzy models is investigated in this paper. A transformed system is firstly constructed according to the original system. Then, a fractional-order intermediate observer is proposed. It can obtain the state and actuator fault of the transformed system, which indirectly achieves the simultaneous estimation of states, faults and disturbances of the original system. Unlike the strategy of suppressing or decoupling the disturbances in traditional fault estimation methods of nonlinear fractional-order systems, this paper focuses on estimating the disturbances directly. This way not only avoids handling the disturbances or the dynamics of faults via theH∞method, but also does not have strict equation constraints required in the decoupling method. Additionally, an active fault-tolerant controller is designed that dynamically adjusts its actions based on the information obtained by the observer, thereby ensuring system stability under multiple faults and disturbances. Finally, the effectiveness of the proposed method is validated on two typical application circuits.

This article investigates the robust fault estimation (FE) scheme for a class of discrete-time nonlinear dynamics subject to simultaneous bounded disturbances, sensor and actuator/process faults through the T–S fuzzy method. By constructing an augmented system that contains sensor faults as part of its state, a dissipativity-based FE observer is proposed to achieve sensor and actuator/process faults reconstruction. Combine with the fuzzy Lyapunov function method and dissipativity theory, some brand-new conditions with slack scalars and matrices are attained to ensure that observation error systems are strictly$(\mathcal {R},\mathcal {W},\mathcal {S}) -\delta -$dissipative. Besides, to improve the transient FE performance, regional pole placement problem is also considered in FE observer design. It is worth mentioning that different from some existing results which assume that actuator faults occur in a constant form, the method given in this article is suitable for more types of faults such as time-varying ones. By two simulation experiments, the validity and practicability of the proposed FE observer are fully illustrated.

This article investigate the cooperative differential game (CDG) for continuous-time linear Itô stochastic systems with markovian jumps (SSMJ) to obtain the Pareto solutions. Different from most existing works studying nonzero-sum games, this article studies the CDG on the quadratic infinite horizon for the Itô-type SSMJ with unknown system matrix and transition probability. A novel$Q$-learning online algorithm is developed, which consists of that (i) the optimal control problem is equivalent to solving a stochastic algebraic Riccatic equation (ARE); (ii) the joint cost function is approximated by a critic neural network (NN) and Pareto efficient is approximated by two actor NNs. The rigorous stability analysis shows that the system state for SSMJ and the NN weight errors are uniformly ultimately bounded (UUB). Finally, the theory analysis is validated by a numerical example with detailed discussions.Note to Practitioners—In practical applications, many systems are often affected by the change of external environment or the failure of internal components, which leads to the random jump of system parameters. Markovian jump system can effectively describe the above problems. And when the system model is disturbed by the internal parameters, the system control input and external environment, the random errors of state measurement, and other random factors, the deterministic model can no longer accurately describe the controlled system. Therefore, the SSMJ can describe practical problems more accurately. By cooperation, in general, the cost one specific player incurs is not uniquely determined anymore. If all players decide, for example, to use their control variables to reduce the cost of player 1 as much as possible, a different minimum is attained for player 1 compared with that in the case where all players agree collectively to help a different player in minimizing his cost. So, depending on how the players choose to ‘divide’ their control efforts, a player incurs different ‘minima’. Therefore, we will design an online learning algorithm to obtain pareto solutions with different weights. On the other hand, in practice, it is difficult to obtain an accurate system model. In order to solve this problem, a novel scheme is designed by using$Q$-learning technology, which does not need system matrix.

This article investigates the fully distributed resilient practical leader-follower bipartite output consensus (LFBOC) problem for heterogeneous linear multiagent systems (MASs) with denial-of-service (DoS) attacks and actuator faults. To estimate the leader matrix and state in the presence of DoS attacks, two novel adaptive event-triggered observers are proposed based on newly developed lemmas, and then the adaptive event-triggered fault-tolerant controller without chattering behavior is developed to solve the LFBOC problem. Different from most existing resilient practical LFBOC working with DoS attacks and actuator faults, our method does not rely on any global information, event-triggered communication between neighbors and discrete update controllers are implemented simultaneously. Finally, an example is presented to well illustrate the effectiveness of developed method.

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.

Although the current sharing control of dc microgrids has been widely studied, the high communication bandwidth and global communication network structure information demands hander the renewable energy consumption. Thus, this article proposes a fully distributed dynamic edge-event-triggered current sharing control strategy for multibus dc microgrids with power coupling. First, the system model with power coupling is built, which is further switched to the linear heterogeneous multiagent systems with unknown disturbance. It is an indispensable preprocessing for controller design. Furthermore, the fully distributed current sharing control strategy is proposed through adaptive coupling weights. Note that the global communication network structure information demand is eliminated. Moreover, the fully distributed dynamic edge-event-triggered mechanism is proposed to reduce communication bandwidth. Compared with the previous dynamic event-triggered mechanisms applied into dc microgrids, the continuous communication between neighboring agents is avoided, and controller updating frequency is reduced. Finally, the simulation and experimental results verify the proposed control performance.

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.

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.

A distributed control law synthesized several effective tools which called adaptive compensators solve a containment control problem. Distinguish from many studies on tracking, the situation where external system information is not available to network nodes is considered in a multileader system under a structurally balanced topology, the designed compensator is used to estimate the adaptive state of the convex hull to each follower. Considering the special case of external system information, a novel adaptive internal model compensator is proposed to dispose of the system robustness problem. Moreover, a novel Sylvester equation is given without considering all closed-loop system information and present an algorithm for calculating adaptive solutions of Sylvester equations based on containment control.

This article considers the distributed bipartite adaptive event-triggered fault-tolerant consensus tracking issue for linear multiagent systems in the presence of actuator faults based on the output feedback control protocol. Both time-varying additive and multiplicative actuator faults are taken into account in the meantime. And the upper/lower bounds of actuator faults are not required to be known. First, the state observer is designed to settle the occurrence of unmeasurable system states. Two kinds of event-triggered mechanisms are then developed to schedule the interagent communication and controller updates. Next, with the developed event-triggered mechanisms, a novel observer-based bipartite adaptive control strategy is proposed such that the fault-tolerant control problem can be addressed. Compared with some related works on this topic, our control scheme can achieve the intermittent communication and intermittent controller updates, and the more general actuator faults and network topology are considered. It is proved that the exclusion of Zeno behavior can be realized. Finally, three illustrative examples are given to demonstrate the feasibility of the main theoretical findings.

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.