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 paper investigates the problem of dynamic output feedback fault-tolerant control (DOF-FTC) for T-S fuzzy fractional-order systems (TSFFOSs) subject to multiple faults and mismatched disturbances. First, the system is preprocessed using augmentation and desingularization techniques. Then, by optimizing the structure of the traditional fractional-order intermediate observer, the joint estimation of states, faults and mismatched disturbances in the system is achieved. In particular, the estimation performance is significantly improved. More importantly, during the design of the observer, the reliance onH∞methods and decoupling methods for disturbance handling is eliminated. Furthermore, a novel DOF-FTC strategy is developed, which does not require state information. The designed controller can be adjusted online based on the estimation of faults and disturbances to ensure system stability. Finally, a permanent magnet synchronous motor model is employed to verify the effectiveness of the proposed method.

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.

This article addresses the security-based practical fixed-time adaptive stabilization problem for nonlinear cyber-physical systems (CPSs) with higher powers under deception attacks. First, a novel practical fixed-time stability criterion is proposed based on Nussbaum functions. The criterion introduces a relaxed convergence condition, facilitating the analysis of practical fixed-time stability for high-power nonlinear systems. Second, to compensate for the compromised states, a dual coordinate transformation structure consisting of a virtual coordinate transformation and an available coordinate transformation is proposed. This structure is applicable to both low- and high-power systems. Moreover, a security-based fixed-time control strategy is developed by combining adaptive methods with Nussbaum functions to mitigate the influence of unknown attack gains. The proposed strategy also effectively overcomes the singularity problem. Finally, the effectiveness of the designed control strategy is validated through simulations.

This article presents a robust fault reconstruction scheme for a class of discrete-time nonlinear singular systems with disturbances. The Lipschitz condition is utilized to describe the nonlinearity under investigation. To effectively estimate multiple types of faults such as time-varying faults and constant ones, a brand-new proportional-difference (PD) observer design method is established. What is worth mentioning is that all the gains of PD observer can be calculated at the same time by our method instead of manually selecting some gains and then solving other gains as has been done in the pertinent literature, which serves as a pioneering attempt for the similar design. Besides, by using the Lyapunov theory, less conservative linear matrix inequalities (LMIs) criteria with slack scalars and matrices are obtained to ensure that error systems are robust stability with the prescribed H∞performance. Finally, two examples on RC circuits and tanks level control models are presented to prove the superiority and practicability of the proposed fault estimation procedure.

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.

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 is considered on underactuated fractional-order stochastic systems (FOSSs) with actuator saturation and incrementally conic nonlinear terms, whose fractional-order α ∈ (0,1) . First, to bring FO dynamic signals, solving the unmodeled dynamics, in the meantime, the saturated nonlinear term of the control input is taken into account. At the time, to cope with the stability issue of FOSS under such situation, the fault tolerant resilient controller based on underactuated condition is designed. Then, according to the method of the Lyapunov and It∧ o differential formulation to design proper multiple Lyapunov-Krasovskii (L-K) functions, such that, a novel sufficient condition of the robustly asymptotically stability of fuzzy FOSS under underactuated conditions is rigorously proved in terms of linear matrix inequality (LMI). Furthermore, in order to research the mean square stability of the above-mentioned system, so the solution of FOSS is obtained to achieve this purpose. By applying the above method, which is proposed in this work that the controlled system can be obtained with faster response and higher control accuracy. At last, to display the superiority of the above-mentioned scheme is effective, tethered satellite system and numerical results are presented.

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.

The finite-time output consensus (FTOC) issue of heterogeneous fractional-order multiagent systems (HFO-MASs) is investigated in this article. First, a new principle of finite-time convergence for absolutely continuous functions is developed if a fractional derivative inequality is satisfied. Next, in order to remove the assumption that the leader's system matrix is known to all agents in previous studies, a distributed adaptive finite-time observer is designed, which can estimate not only the leader's state but also the leader's system matrix. Then, a novel finite-time event-triggered compensator with intermittent communication is constructed to estimate the leader's state by introducing a dynamic threshold for a novel triggering function. In this case, the high frequency triggering is restrained and the triggering number is significantly reduced. The Zeno behavior does not exist by choosing parameters appropriately. In addition, two finite-time control strategies are constructed based on the above distributed observer and event-triggered compensator, respectively, to achieve output consensus in finite time. The feasibility of the proposed method is ensured by the comprehensive theoretical demonstration of the finite-time consensus stability and the analysis of the Zeno behavior. Finally, the examples are given to demonstrate the conclusion.

This article focuses on the distributed robust fault estimation problem for a kind of discrete-time interconnected systems with input and output disturbances. For each subsystem, by letting the fault as a special state, an augmented system is constructed. Particularly, the dimensions of system matrices after augmentation are lower than some existing related results, which may help to reduce calculation amount, especially, for linear matrix inequality-based conditions. Then, a distributed fault estimation observer design scheme that utilizes the associated information among subsystems is presented to not only reconstruct faults, but also suppress disturbances in the sense of robust$H_{\infty }$optimization. Besides, to improve the fault estimation performance, a common Lyapunov matrix-based multiconstrained design method is first given to solve the observer gain, which is further extended to the different Lyapunov matrices-based multiconstrained calculation method. Thus, the conservatism is reduced. Finally, simulation experiments are shown to verify the validity of our distributed fault estimation scheme.

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 paper presents a bilevel planning framework to coordinate truck mobile chargers (TMCs) and fixed chargers (FCs) on highways to promote charging flexibility and provide more choices for electric vehicle (EV) users. A collaborative location optimization (CLO) approach is developed at the upper level to optimize the location of charging stations. Furthermore, a collaborative capacity optimization (CCO) approach is formulated at the lower level to optimize the capacity of TMC and FC at candidate stations. In the proposed framework, origin-destination (OD) analysis, Floyd algorithm and Monte Carlo simulation (MCS) are employed to generate the spatial-temporal distribution of charging demand based on historical data. An improved income approach (IIA) is then developed to well capture the heterogeneity of EV users’ charging behavior. The waiting cost of EV users is estimated by their value of time (VOT), which helps them to make a better choice between TMC and FC. To solve the optimal model easily, the big-M method is applied to linearize and convert the nonlinear problem into a mixed-integer linear programming (MILP) model. Meanwhile, the analytical target cascading (ATC) technique is employed to realize the data exchange process between the upper and lower layers. Finally, numerical study demonstrates the effectiveness of the proposed framework and method.

The time-varying output bipartite formation containment (TVOBFC) problem for linear multiagent systems (MASs) under directed graphs is an important problem. However, the methods in existing works rely on the global information of the MASs or do not use event-triggered communication. This article investigates two kinds of TVOBFC problems for heterogeneous linear MASs under signed digraphs by event-triggered communication. For the first case where leaders have the same dynamics, the innovative fully distributed event-triggered protocol for the follower is proposed. In this case, the followers form the preset formation shape. For the second case where leaders have different dynamics, the leaders are divided into two groups. One group can directly obtain the output information of the virtual leader, while the other group cannot. In order to make leaders achieve the formation shape and track the virtual leader, two kinds of innovative observers are designed for two kinds of leaders to estimate the state of the virtual leader, and the control protocol is designed for each leader based on the designed observers. Then, the control law for each follower is designed to solve the formation containment problem. Finally, two examples are introduced to illustrate the main results.

This article discusses the fault estimation (FE) problem of nonlinear fractional-order (FO) systems subject to faults and unknown inputs through the T–S fuzzy approach. A novel fuzzy FO unknown input observer is well synthesized to not only achieve the desired FE but also decouple the unknown input in contrast to the traditional integer-order observer design technique. It is worth pointing out that the provided FE scheme can reconstruct the fault signal appearing in both input and output equations simultaneously. Furthermore, by resorting to linear matrix inequalities, the stability criteria of observation error dynamics are first formulated based on general quadratic Lyapunov functions, which are further extended via fuzzy Lyapunov functions containing the information of membership functions. Finally, the performance of theoretical results is verified through two elaborate examples.

This article concentrates on the neural network (NN)-based adaptive sliding-mode control (SMC) for fuzzy fractional-order system (FOS),$\alpha \in (0,1)$. First of all, a novel method of optimal SMC approach is developed for fuzzy FOSs by using the adaptive dynamic program (ADP), integral sliding mode, and NN with unmatched disturbances and time-varying delays. Next, to weaken the influence of the nonlinearities, the SMC strategy is proposed for the specific system, which is established on the corresponding SMD to ensure that the FOS reach the SMS in a finite time. Moreover, it shows that the matrix of SMS can be described by the linear matrix inequality (LMI). Furthermore, the Hamilton–Jacobi–Bell man (HJB) equation can be approximated by a single NN method, and the Lyapunov stability principle proves that the weight errors are convergent, further guaranteeing the asymptotically stability of the fuzzy FOS. Finally, to display that the above-presented policy is effective, simulation results are presented.

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 article, a novel data-based adaptive dynamic programming (ADP) method is presented to solve the optimal consensus tracking control problem for discrete-time (DT) multiagent systems (MASs) with multiple time delays. Necessary and sufficient conditions of the corresponding equivalent time-delay system are provided on the basis of the causal transformations. Benefitting from the construction of tracking error dynamics, the optimal tracking problem can be transformed into settling the Nash-equilibrium in the graphical game, which can be completed by solving the coupled Hamilton-Jacobi (HJ) equations. An error estimator is introduced to construct the tracking error of the MASs only using the input and output (I/O) data. Therefore, the designed data-based ADP algorithm can minimize the cost functions and ensure the consensus of MASs without the knowledge of system dynamics. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

In this article, we pay our attention on exploring observer-based actuator fault and sensor fault reconstruction associated with fault-tolerant control (FTC) for nonlinear systems, which are approximated by the Takagi–Sugeno (T-S) fuzzy method. By designing a brand-new unknown input observer (UIO), unknown state, sensor, and actuator faults can be reconstructed simultaneously, where some constraints imposed on the actuator fault such as the first derivative of fault being equal to zero required in the previous results are not needed in our work. With the support of this estimation information, a FTC scheme is well established, by which the system may recover its performance even in the occurrence of faults. Another contribution of the developed method is that all the stability criteria are deduced via fuzzy Lyapunov functions. It makes the obtained conditions more relaxed than the ones derived by quadratic Lyapunov functions. Finally, simulation results conducted on two practical dynamics are provided to show the validity of the achieved procedure.

In this work, we study simultaneous reconstructions of sensor fault and actuator fault, as well as fault-tolerant control (FTC) for nonlinear systems approximated by the T–S fuzzy model. By making the sensor fault as part of the state, a rectangular singular system is firstly given, based on which, a proportional-integral observer (PIO) is synthesized to realize the reconstructions of sensor and actuator faults simultaneously. With the support of these estimation information, an FTC scheme is well provided to maintain the stability of the closed-loop system even in the occurrence of faults. Furthermore, by resorting to linear matrix inequalities (LMIs), the stability criteria are formulated via the fuzzy Lyapunov function method. Finally, the performance of the theoretical result is verified through two real dynamics.

In this article, a novel parallel tracking control optimization algorithm is first proposed for partially unknown fuzzy interconnected systems. In the existing standard optimal tracking control, the bounded or nonasymptotic stable reference trajectory will lead the feedback control not converging to zero, which causes the performance index infinite and invalid. By using the precompensation technique, in this article, the working feedback control is considered as a reconstructed dynamic with the virtual control and a new augmented fuzzy interconnected tracking system is built, thus that the performance index is valid for optimal control. Then, combining the integral reinforcement learning (RL) method and decentralized control design, the novel integral RL parallel algorithm is first developed to solve the tracking controls for interconnected systems, which relax the requirements of exact matrices information Aikand Bikduring the solving process. Both the convergence and stability of the designed control optimization scheme are guaranteed by theorems. Finally, the new parallel tracking algorithm for interconnected systems is verified through the dual-manipulator coordination system and simulation results demonstrate the effectiveness.

This paper proposes a novel fault-tolerant control method for modular multilevel converter (MMC) with an improved level-shifted carrier PWM, based on the concept of virtual voltage. First, an improved phase disposition level-shifted (PD-LS) PWM with only one carrier in each arm is adopted. Then, based on the virtual voltage idea, a simplified control method is proposed to realize fault-tolerant operation without carriers reconfiguration. Compared with traditional fault-tolerant control methods, due to the reduced carriers generation and decreased comparisons between carriers and modulation waves, the modulation process of the proposed scheme can be dramatically simplified during both the pre-fault and the post-fault process. The effectiveness of the proposed method is verified by simulation and experiment results.