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This article explores a distributed optimal coordination control problem for multiple Euler–Lagrange systems with actuator faults. To address this problem, an event-triggered fault-tolerant optimisation algorithm is first proposed to eliminate unexpected faults and reduce the consumption of control resources. In order to further enhance the system's reliability, another algorithm based on the Nussbaum function is proposed to handle faulted systems with uncertain control directions. Note that an auxiliary system with adaptive gains is introduced to eliminate the need for agents to interact with their actual state information, and thus has the effect of protecting privacy. Moreover, the stochastic semi-Markov jumping networks are considered in the algorithms to describe the switching process of uncertain communication graphs. Additionally, the algorithms are fully distributed since it does not require global information of topologies. Finally, numerical simulations are conducted in the article to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article is devoted to the event‐triggered practical tracking control for a class of high‐order nonlinear systems with serious uncertainties. Remarkably, the serious uncertainties are greatly reflected from the unknown control directions and input powers which give rise to essential obstacles in control design and hence lead to incapability of the traditional control methods on this topic. To solve the control problem, a novel switching event‐triggered control scheme is proposed by a skillful incorporation of logic‐based switching mechanism into the event‐triggered one. Specifically, two pivotal events are smartly chosen to give the event‐triggered mechanism for the determination of the sampling times. In particular, one of the events is used to give the switching varying mechanism, by which the controller parameters are respectively switched in two groups of sequences which are carefully chosen for the compensation of serious uncertainties. Under the proposed switching event‐triggered mechanism, a state‐feedback controller is designed which guarantees that all the signals of the closed‐loop system are bounded while system output practically tracks the reference signal, along with a finite number of switching of controller parameters as well as the exclusion of the Zeno phenomenon. Finally, simulation examples are provided to validate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the output synchronization for multiple parametric strict feedback (PSF) systems with unknown control directions. Toward this, prescribed performance control is applied, that is, both transient and steady‐state properties are guaranteed simultaneously by the recursively designed controller. It is different from existing studies, mainly in the following points: (1) The dynamic of each agent has multiple unknown control directions; (2) the neighborhood error not only evolves within the specified boundaries but also converges to zero ultimately; and (3) there is no leader in the digraph. The effectiveness of the proposed controller is verified by theoretical analysis and numerical simulation example of the vessels. [ABSTRACT FROM AUTHOR]

In this article, a class of global finite‐time stabilization problem for high‐order stochastic nonlinear systems with multiple unknown control directions is studied. In order to solve the difficulties caused by the unknown control directions and at the same time, the system is required to converge to the origin in a limited time. Therefore, a new switching mechanism based on the Lyapunov‐like function is proposed. By adding a power integral technique and utilizing sign function, a finite‐time switching controller is designed. The controller parameters need to be adjusted online according to the proposed switching logic. It is rigorously proved that the designed controller can make the system state converge probabilistically to the origin in a finite‐time. A simulation example shows the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This article addresses the event‐triggered adaptive consensus control of nonlinear multi‐agent systems with unknown control direction and actuator saturation. A new robust adaptive control algorithm based on an event‐triggered mechanism is designed. The smooth Lipschitz function approximates the saturated nonlinear function, while the Nussbaum function handles unknown control directions and residual terms. The event‐triggered mechanism is designed to determine the time of communication, significantly reducing the communication burden. An additional estimator is utilized to deal with unknown parameters involved in neighbor dynamics and prevent information exchange to consistency errors between connected subsystems. The results show that all the signals of the closed‐loop system are uniformly bounded, and the consensus tracking error converges to a bounded set. Meanwhile, Zeno's behavior is eliminated. Simulation results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This article is concerned with event‐triggered adaptive tracking control design of strict‐feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event‐triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed‐loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Summary: This paper presents an event‐triggered control strategy for stochastic interconnected nonlinear systems with unknown control directions. Firstly, a new lemma is proposed for stochastic nonlinear systems with multiple time‐varying unknown control directions, which guarantees the boundedness of Nussbaum function parameter variables. Different from the existing results, each subsystem is allowed to have multiple time‐varying unknown control directions. Then, by using the backstepping method, a novel controller is proposed based on the relative threshold event‐triggered strategy. The controller not only reduces the communication burden but also eliminates the interference of unknown control directions. Based on Lyapunov stability theory, it is proved that the controller can make all signals in the closed‐loop system be bounded in probability and the system state variables converge to zero in probability. Finally, two simulation examples are presented to certify the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

In this study, a class of nonlinear systems with integral input to state stability (iISS) inverse dynamics and unknown control direction are examined for the issue of time-varying asymmetric output constraints of adaptive output feedback controller. To deal with unmeasured state variables and unknown directions, the state observer is constructed using a Rickati matrix differential equation with time variation. A backstepping-based method is recommended for establishing the dynamic output feedback control law. By ensuring boundedness for the time-dependent barrier Lyapunov function (BLF) in the closed loop, we may not only maintain the boundedness and stability of other signals, but also avoid breaking the time-varying asymmetric constraint of the output. Finally, simulation analyses are used to confirm the scheme's efficacy. [ABSTRACT FROM AUTHOR]

In this article, an event‐triggered zero‐error adaptive output tracking controller with fixed‐time convergence mode is designed for a kind of uncertain nonlinear systems under full‐state constraints, unknown control coefficients, input dead‐zone, and saturation. The constrainedly practically fixed‐time stability is investigated for the considered high‐order nonlinear system. Then applying the barrier Lyapunov function technology and blending an error transformation into backstepping scheme, the Nussbaum‐gain‐based adaptive fuzzy control is proposed with prescribed performance. The control process consists of two phases, among which the first phase is used to render tracking error into the preset adjustable residual set within a preassigned fixed time at a prescribed decay rate, and the second phase further force the tracking error to converge to zero asymptotically. Additionally, the desired full‐state constraints are not violated in the whole control process. The simulation results are also given to show the effectiveness of the designed control method [ABSTRACT FROM AUTHOR]

This paper investigates the distributed adaptive PI consensus tracking control for output-constrained nonlinear multiagent systems (MASs) with unknown control directions and unknown time-varying actuator faults under the directed graph. Firstly, an auxiliary filter network is constructed to estimate the output of the leader. Then, by introducing a nonlinear state transformation function, the asymmetric constraints on agents' outputs can be achieved with unconstrained initial conditions. Furthermore, based on the Nussbaum-type function, a distributed adaptive PI controller is designed by utilizing the constructed generalized error for nonlinear MASs with unknown time-varying control directions caused by actuator faults. The proposed control scheme can guarantee that all signals in the closed-loop system are bounded and the distributed asymptotic consensus tracking is achieved. Finally, a simulation example illustrates the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper addresses global output-feedback stabilisation in the context of unknown control directions and intrinsic unmeasurable-states-dependent growth, and focuses on rectifying the substantial deficiencies in the related works and developing a new adaptive output-feedback controller essentially reducing conservativeness. First, a varying parameter which takes value 1 or − 1 , instead of in an unbounded countable set, is specialised to capture the unknown control direction and accordingly a supervisory mechanism is delicately constructed to decide when to switch the parameter from 1 to − 1 or from − 1 to 1. A dynamic high gain, rather than a switching one, is appointed to compensate the serious system uncertainties. Then, the wanted controller is constructed, for which the design functions and design parameters are recursively generated by backstepping method (instead of analytically defined owing to the unknown control coefficients). Based on the designations and supervisory mechanism, it turns out that no Zeno phenomenon occurs, and global boundedness and convergence (to zero) hold, both for the resulting closed-loop system. An example is given to show the effectiveness and the advantage of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this article, we develop an adaptive global prescribed performance tracking control scheme for nonlinear multiple‐input multiple‐output (MIMO) robotic systems in the presence of unknown control directions and nonparametric uncertainties, in which the proposed solution mainly includes the following steps. Firstly, by constructing a global prescribed performance function, together with a series of transformations, the corresponding control guarantees the position tracking error evolves strictly within the prespecified region for all time, which is independent of initial conditions; Secondly, in order to cope with the problem of multiple unknown control directions, we make use of a symmetric matrix lemma to convert the underlying problem from matrix form to scalar form, so that the Nussbaum‐gain lemma for SISO systems becomes effective for MIMO systems with multiple inputs; In addition, we employ the integrable function to handle the nonparametric uncertainties, enabling the control scheme with the capability to drive the tracking error toward zero asymptotically. The effectiveness of the proposed control is validated via a two‐link rigid robotic manipulator. [ABSTRACT FROM AUTHOR]

An adaptive approximated inverse control scheme for a class of high-order nonlinear multi-agent systems with unknown control directions is proposed in this paper. The adaptive control problem under the case it is not required to be identical for the unknown control directions is solved by some novel Nussbaum functions and a monotonously increasing sequence, leading our multiple Nussbaum functions reinforce rather than counteract each other. Also, it is introduced in the design and analysis like some integrable auxiliary signals and a novel contradiction argument. Moreover, hysteresis nonlinearity is counteracted by constructing its approximated inverse compensator. With these efforts, stability analysis ensures that all the closed-loop system signals are uniformly bounded, and it is successfully achieved the asymptotic convergence of tracking error to zero, circumventing the obstacle caused by the unknown control directions. Experiment results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper investigates a novel distributed fuzzy adaptive iterative learning control protocol of exact consensus for second-order unknown nonlinear strict-feedback multi-agent systems with partially unknown time-varying control di- rections. Fuzzy logic system estimates the unknown nonlinear dynamics of each agent. Based on Nussbaum function, the control protocols of all follower agents with partially unknown virtual and actual control directions are designed by the backstepping method. The proposed protocol guarantees that the output of every follower agent could exactly track the desired output trajectory on a finite time interval. As an extension, the formation control results can also be solved. Finally, two simulation examples prove that the proposed control scheme is effective and rigorous. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive synchronization sliding mode control is proposed for a dual-arm robot against parameter variations, external disturbance, and unknown control directions. The proposed control is designed by using cross-coupling error and sliding mode control to guarantee the position synchronization of the dual-arm manipulator. The control objective of the proposed control is to synchronize the movement of both arms beside the trajectory tracking issue. In order to manage the lumped uncertainties caused by the parameter variations, external disturbance, and unknown control directions, an extended state observer is used in the proposed control. It enhances the stability of the controlled system against uncertainties. Additionally, a Nussbaum gain function is integrated into the control algorithm to deal with the issue of unknown control direction. Lyapunov stability theory is used to demonstrate the stability of the controlled system. Finally, some simulations are implemented in MATLAB Simulink with a dual 3-DOF manipulator system. The results of the proposed control are compared to other controllers to verify its effectiveness. [ABSTRACT FROM AUTHOR]

This paper deals with the consensus output tracking problem for multi-agent systems with unknown high-frequency gain signs, in which the subsystems are connected over directed graphs. The subsystems may have different dynamics, as long as the relative degrees are the same. A new type of Nussbaum gain is first presented to tackle adaptive consensus control of network-connected systems without the knowledge of the high-frequency gains. Adaptive laws and internal models are then proposed to handle the uncertainties and unknown parameters. An integral Lyapunov function based on sufficient conditions is finally introduced to tackle the asymmetry of the Laplacian matrix of directed graphs, into which we incorporate the new Nussbaum gain and the adaptive internal model to design the controller. It is apparent that the control scheme and the adaptive laws are fully distributed, which means that only the relative information of the neighbourhood subsystems' outputs is used, and the simulation results validate the effectiveness of the control design, whereby they guarantee the asymptotic convergence of errors to zero as well as the boundedness of the state variables. [ABSTRACT FROM AUTHOR]

This paper concentrates on the study of the adaptive fast finite-time control method for a class of nonlinear time-delay systems with unknown control directions and dead zone. Fuzzy logic systems (FLSs) are employed to handle the problem of uncertain nonlinear terms. The Nussbaum function is utilised to deals with the problem of unknown control directions. Based on the fast finite-time stability theory, a novel adaptive fast finite-time fault tolerant control scheme is proposed under the framework of adaptive backstepping control. Choosing an appropriate Lyapunov-Krasovskii function, it is theoretically proved that the proposed control scheme can not only ensure that the control system is semi-global practical fast finite-time stable but also the tracking error converges to a small neighbourhood of the origin in a fast finite-time. Finally, simulation studies are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the finite time stabilization problem for a class of nonlinear systems with unknown control directions and unstructured uncertainties. The unstructured uncertainties indicate that not only the parameters but also the structure of the system nonlinearities are uncertain. A new adaptive control method is proposed for the considered system. Logic‐based switching rule is utilized to tune the controller parameters online to stabilize the system in finite time. Different from the existing adaptive controllers for structured/parametric uncertainties, a new switching barrier Lyapunov method and supervisory functions are introduced to overcome the obstacles caused by unstructured uncertainties and unknown control directions. Both simulations and experiments are conducted on mechatronic systems to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. Using the fuzzy logic systems, the uncertain nonlinear dynamics are approximated. Considering the command filter and backstepping control technique, the problem of the so-called "explosion of complexity" in the design of virtual control laws and adaptive updating laws is avoided. Meanwhile, the Nussbaum gain function method is applied to handle the unknown control directions and unknown input saturation problems. Based on the finite-time control theory and Lyapunov stability theory, it was found that all signals in the closed-loop system remained semi-global practical finite-time stable, and the tracking error could converge to a sufficiently small neighborhood of the origin in the finite time. In the end, simulation results were provided to verify the validity of the designed control law. [ABSTRACT FROM AUTHOR]

The issue of adaptive output-feedback stabilization is investigated for a category of stochastic nonstrict-feedback nonlinear systems subject to unmeasured state and unknown control directions. By combining the event-triggered mechanism and backstepping technology, an adaptive fuzzy output-feedback controller is devised. In order to make the controller design feasible, a linear state transformation is introduced into the initial system. At the same time, the Nussbaum function technology is used to overcome the difficulties caused by unknown control directions, and the state observer solves the problem of the unmeasured state. Based on the fuzzy-logic system and its structural characteristics, the issue of unknown nonlinear function with nonstrict-feedback structure in the system is tackled. The designed controller could not only guarantee all signals of closed-loop systems are bounded in probability but also save communication resources effectively. Finally, numerical simulation and ship dynamics example are given to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, an adaptive event-triggered fault-tolerant asymptotic tracking control problem guaranteeing prescribed performance is addressed for a class of block-triangular multi-input and multioutput uncertain nonlinear systems with unknown nonlinearities, unknown control directions, and actuator faults. Through a systematic co-design of the adaptive control law and the event-triggered mechanism, including fixed and relative threshold strategies, a control scheme with low structure and calculation complexity is designed to conserve system communication and computation resources. In this design, the output asymptotic tracking is achieved. The Nussbaum gain technique is incorporated to overcome unknown control directions with a new adaptive law, and a type of barrier Lyapunov function is adopted to handle the prescribed performance control problem, which contributes to a novel control law with strong robustness. The robust controller can address the uncertainties and couplings derived from the system structure, actuator faults, and event-triggered rules, without using approximating structures or compensators. Besides, the explosion of complexity is avoided. It is proved that all signals of the closed-loop system remain bounded, and system tracking errors asymptotically approach 0 with the prescribed performance, while the Zeno behavior is prevented. Finally, the effectiveness of the proposed control scheme is evaluated via an application example of the half-car active suspension system. [ABSTRACT FROM AUTHOR]

Recently, the fruitful results on robust control for large-scale interconnected systems have been reported, but most of them are contingent upon "known control directions" and/or only acquire uniformly ultimately bounded performance in the presence of disturbances. Of particular interest in this paper is to develop a continuous and decentralized control algorithm for such systems, which can release the need to know the control directions, guarantee robustness against general system uncertainties (e.g., exogenous disturbances, unknown interactions), and achieve asymptotic output tracking. To this end, we apply a new Nussbaum function to the decentralized controller to identify the control directions despite global interactions. Then resorting to the robust-integral-of-sign-of-error (RISE) technique, we develop a closed-loop system that fully eliminates the effects of the system uncertainties while preserving the control variables' continuity. Additionally, to synthesize the new Nussbaum function and the RISE method, a second-order filter designed for generating feasible feedback signals is constructed. Lyapunov-based stability analysis and numerical simulations are carried out to validate the robustness and the asymptotic convergence of the interconnected system under the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this article, we study an adaptive finite-time event-triggered command filtered control problem based on output feedback for a class of nonstrict-feedback nonlinear systems with unknown control directions. Firstly, the unknown nonlinear continuous functions in the systems are approached by fuzzy logic systems, and the coordinate transformations and Nussbaum function technique are introduced to settle the problem caused by the unknown control directions in the systems. Then, in order to reduce the communication burden between the controller and the actuator, a finite-time adaptive event-triggered control algorithm is designed by means of backstepping technique. It is proved that the tracking and observer errors are adjusted around zero with a small neighborhood in a finite time and all the signals in the closed-loop systems are bounded. In addition, the command filtering technology based on error compensation system with fractional power is constructed to avoid the complexity explosion issue in the backstepping design process. Finally, the simulation examples are included to verify the availability and superiority of the control approach. [ABSTRACT FROM AUTHOR]

In this paper, the collaborative control of multiple nonlinear Euler-Lagrange systems with actuator faults and stochastic semi-Markov jump networks (SMJNs) is concerned. In order to fulfil high reliability and low consumption, several novel event-triggered fault-tolerant control (ETFTC) algorithms are established to simultaneously eliminate the undesirable faults and save control resources, where only quantised partial-state signal of neighbours is required for the control process. Moreover, some ubiquitous constraints, such as unknown control directions and time-varying communication delays, are also comprehensively considered and effectively excluded so as to further enhance the control reliability. Meanwhile, some sufficient criteria on the algorithm synthesis and stability analysis without involving Zeno behaviour are successfully built with the aid of Lyapunov–Krasovskii functional. Finally, some illustrative simulations are performed to validate the feasibility and effectiveness of the derived ETFTC algorithms. [ABSTRACT FROM AUTHOR]

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This article addresses an event-triggered adaptive fuzzy tracking control problem for nonlinear systems with unknown control directions. To achieve the practical tracking, fuzzy logic systems are employed to approximate unknown nonlinear function. Nussbaum functions are adopted to address the problem of the unknown control directions. The newly designed controller not only guarantees the tracking error that converges to an arbitrary small neighborhood near the zero but also reduces the communication burden from the controller to the actuator. Moreover, the feasibility of the proposed event-triggered mechanism is verified by excluding Zeno behavior. Finally, the simulation result proves the effectiveness of the designed control scheme. [ABSTRACT FROM AUTHOR]

In the article, the issues of asymptotic adaptive tracking control for the uncertain nonlinear systems in the presence of actuator faults and unknown control directions are investigated. By using the properties of the Nussbaum function and backstepping technique, the problems resulting from the unknown signs of the nonlinear control functions are circumvented successfully. Moreover, a new adaptive asymptotic tracking control method is presented with the fault-tolerant control framework, which is capable of realising zero-tracking performance. The stability of the controlled system is ensured through fractional Lyapunov stability analysis. Finally, the validity of the raised scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]

This paper focuses on the controller design and vibration elimination for a flexible single‐link manipulator. The flexible single‐link manipulator considered in this paper is described by partial differential equations (PDEs). Considering actuator faults and sensor faults simultaneously, a novel boundary controller is designed for the flexible manipulator system. The actuator faults are special since the control directions are unknown. In the proposed controller, the Nussbaum‐type function is used, and an adaptive law is applied. The system performance analysis is given with the aid of Lyapunov approach, and the closed‐loop PDE system is guaranteed to have semi‐global uniform ultimate boundedness (SGUUB). In simulation, several cases are carried out to validate the effectiveness of the proposed controller, under actuator faults and sensor faults. [ABSTRACT FROM AUTHOR]

This work investigates the consensus tracking problem for high-power nonlinear multiagent systems with partially unknown control directions. The main challenge of considering such dynamics lies in the fact that their linearized dynamics contain uncontrollable modes, making the standard backstepping technique fail; also, the presence of mixed unknown control directions (some being known and some being unknown) requires a piecewise Nussbaum function that exploits the a priori knowledge of the known control directions. The piecewise Nussbaum function technique leaves some open problems, such as Can the technique handle multiagent dynamics beyond the standard backstepping procedure? and Can the technique handle more than one control direction for each agent? In this work, we propose a hybrid Nussbaum technique that can handle uncertain agents with high-power dynamics where the backstepping procedure fails, with nonsmooth behaviors (switching and quantization), and with multiple unknown control directions for each agent. [ABSTRACT FROM AUTHOR]

In this brief, an adaptive fuzzy tracking control method is proposed for switched multi-input multi-output (MIMO) nonlinear systems with time-varying full state constrains (TFSCs) and unknown control directions. First, the fuzzy logic systems are utilized to approximate unknown dynamic functions. A tangent barrier Lyapunov function (BLF-Tan) is used to solve the problem of TFSCs, and the unknown control directions problem is addressed by applying Nussbaum-type function. Then, an adaptive tracking controller is constructed by the backstepping technique. Under the designed control scheme, all the systems signals are derived to be bounded, and the tracking error of the systems is converged to a neighborhood near zero. Finally, the simulation example illustrates the control design programme is reasonable and effective. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive event-triggered asymptotic tracking control problem is addressed for switched nonlinear systems with unknown control directions. In existing control schemes, the proposed controller is not directly aimed at the original system, which affects the control performance. Different from the existing control schemes, based on the original system, an event-triggered control law is constructed in this paper. The proposed event-triggered controller guarantees that the tracking error ς1 asymptotically converges to the origin. Finally, the effectiveness of the proposed controller design scheme is proved by simulation examples. [ABSTRACT FROM AUTHOR]

In this article, under directed graphs, an adaptive consensus tracking control scheme is proposed for a class of nonlinear multiagent systems with completely unknown control coefficients. Unlike the existing results, here, each agent is allowed to have multiple unknown nonidentical control directions, and continuous communication between neighboring agents is not needed. For each agent, we design a group of novel Nussbaum functions and construct a monotonously increasing sequence in which the effects of our Nussbaum functions reinforce rather than counteract each other. With these efforts, the obstacle caused by the unknown control directions is successfully circumvented. Moreover, an event-triggering mechanism is introduced to determine the time instants for communication, which considerably reduces the communication burden. It is shown that all closed-loop signals are globally uniformly bounded and the tracking errors can converge to an arbitrarily small residual set. Simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This article studies the adaptive fuzzy fault tolerant control (FTC) problem for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with unknown control directions in the presence of time-varying asymmetric output constraints. Our contribution includes a step forward beyond usual FTC results to exhibit that the system output of nonsquare and square MIMO systems is uniformly bounded against actuator faults by a novel FTC methodology without the fault detection unit, as well as stay in the preselected constraints. To obtain new results, an equivalent unconstrained system is established by employing an error transformation technique. Furthermore, a learning-based switching function scheme is proposed to automatically activate different groups of actuators without human intervention for attenuating the influence of faulty actuators. By this means, no explicit fault detection and isolation units are needed to result in reducing the risk of false alarm or missed detections and expediting the responsiveness of the controller. Moreover, the obstacle caused by unknown control directions is circumvented by a novel technique combining the matrix decomposition technique and Nussbaum-type function. It is proved that the desired tracking performance with prescribed output bounds and the boundedness of all the signals in the closed-loop system can be guaranteed via an improved average dwell time approach. Finally, simulation results demonstrate the merits of the proposed controller. [ABSTRACT FROM AUTHOR]

This article presents an event-triggered adaptive asymptotic tracking control method based on the low-complexity design architecture to reduce the communication and computational resources of uncertain nonlinear systems with unknown control directions and actuator faults. By utilizing a systematic codesign of backstepping and an event-triggered mechanism, the proposed adaptive fault-tolerant control method exploits only error transformation variables associated with prescribed performance specifications, without the use of any compensators or approximation structures to handle unknown nonlinearities and actuator and component faults. This design provides a robust method, through which the controller can effectively address external disturbances, unknown system uncertainties, and actuator and component faults, while eliminating the explosion of complexity problem in backstepping. Asymptotic stability analysis of the closed-loop system is conducted, and the Zeno behavior is avoided. The effectiveness of the proposed approach is illustrated through applications to linear motor systems. [ABSTRACT FROM AUTHOR]

This article studies the issue of command filter-based adaptive fault-tolerant control for a class of nonlinear systems subject to unknown control directions and disturbance. First, the neural network is employed to deal with the nonlinear functions, and the explosion of the complexity problem is handled by the command filter approach. Second, the bound estimation method and the Nussbaum function are utilized to compensate for the influence of the actuator faults and the unknown directions, respectively. Finally, the tracking error signals are guaranteed to converge into bounded compact sets around the origin, and all closed-loop signals are bounded. The effectiveness of the proposed method is illustrated by three simulations. [ABSTRACT FROM AUTHOR]

In this article, the global stabilization issue is discussed for a class of stochastic continuous time‐delay nonlinear systems suffered from unknown control directions and disturbance. Instead of designing the adaptive law online, a control gain is invoked to adapt for the formidable scene of merely continuous but nonsmooth caused by the low‐order, and to deal with the negative effects of disturbance and multiple unknown nonlinear functions where both input and state time delays are taken into account. Then, by utilizing the homogenous domination approach, a delay‐independent controller is designed with a sign function to compensate for the negative impact generated from disturbance and maintain the global asymptotic stability of the closed‐loop system. Finally, a stochastic simulation is supplied to show the validity of the control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time adaptive fuzzy control method is proposed for nonlinear nonstrict-feedback multi-agent systems (MASs) with unknown control directions. The Nussbaum function is introduced to compensate the influence of unknown control directions. By combining the finite-time stability criterion, an adaptive fuzzy controller is constructed to ensure that systems reach a steady state in a finite time, and the tracking errors of all output signals converge to a small neighbourhood of the origin. By using the Lyapunov finite-time stability theorem, all signals are proved to be semi-global practically finite-time stable. Finally, the effectiveness of the proposed control method is proved through some results of simulation experiments. [ABSTRACT FROM AUTHOR]

This study is primarily focused on the issue of low-complexity prescribed performance fault compensation for multi-input and multi-output uncertain nonlinear systems with actuator failures, coupling states, and unknown control directions. First of all, proper logarithm-type error conversion functions and smooth orientation functions are linked to design the continuous control signals in the state feedback controller. Then, based on the idea of proof by contradiction, it is shown that the state errors converge to a predictable compact aggregate at the definite rate. Meanwhile, the boundedness of any closed-loop signals might be guaranteed. The numerical and actual simulation examples are delivered to demonstrate the effectiveness of the developed control strategy at last. [ABSTRACT FROM AUTHOR]

For a class of stochastic nonlinear systems (SNSs) with state delay and unknown control directions (UCDs), the global asymptotic regulation problem is investigated in this brief. Based on the key Lyapunov-Krasovskii functional (KLF), a dynamic feedback control strategy is designed to solve the time delay and UCDs problems. The proposed dynamic compensator guarantees the global asymptotic convergence of the systems state in probability at the origin and the global boundedness of the closed-loop system (TCLS) in probability. Finally, an example is given to verify the effectiveness of the developed scheme. [ABSTRACT FROM AUTHOR]

This article concentrates on the study of the decentralized fuzzy control method for a class of fractional-order interconnected systems with unknown control directions. To overcome the difficulties caused by the multiple unknown control directions in fractional-order systems, a novel fractional-order Nussbaum function technique is proposed. This technique is much more general than those of existing works since it not only handles single/multiple unknown control directions but is also suitable for fractional-/integer-order single/interconnected systems. Based on this technique, a new decentralized adaptive fuzzy control method is proposed for fractional-order interconnected systems with unknown strong interconnections among subsystems. Furthermore, fuzzy logic systems are utilized to approximate unknown nonlinearities. It is proven that the designed controller can guarantee the boundedness of all signals in interconnected systems and the convergence of tracking errors. Two examples are given to show the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, an event‐triggered adaptive control strategy is presented for nonlinear pure‐feedback multi‐agent systems, and the problem of the unknown control gain is also considered. In contrast to most of the existing results, each agent's control item is a power exponential function, and this problem is handled by utilizing the "adding a power integrator" technique. Based on the Nussbaum gain technique, a control scheme is presented to handle the problem concerning unknown control gains. The tracking differentiator is used to eliminate the problem of "explosion of complexity" in the backstepping method. Furthermore, an event‐triggered control strategy is designed to reduce the communication burden and the computational cost. It is proved via the Lyapunov stability method that the consensus tracking errors can converge to a small neighborhood of the origin and all signals of the closed‐loop systems are semi‐globally uniformly ultimately bounded. Finally, some simulation results are proposed to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

When the actuator faults and the control directions are unknown, the difficulty of the asymptotically tracking control of the surface vessel will increase. In this paper, for actuator failures and unknown control directions, a distributed adaptive asymptotically synchronous tracking control law for multiple uncertain underactuated surface vessels (USVs) is proposed, which can achieve network connectivity and good tracking performance in a limited communication range. First, a distributed nonlinear error surface is introduced to achieve synchronous tracking between USVs and maintain the initial connectivity patterns. Second, a conditional inequality is proposed to solve the problems of unknown actuator failures and unknown control directions. Then, combined with the derived technical lemmas and Barbalat's lemma, the stability of the closed loop system is proved by the Lyapunov method. Finally, a simulation example verifies the theoretical results. [ABSTRACT FROM AUTHOR]

This study reports adaptive quantized control for a class of uncertain strict‐feedback nonlinear systems with unknown control directions. Combining backstepping technique and Lyapunov stability theory, a systematic analysis method is designed. Based on the disintegration of the hysteresis quantizer, a Nussbaum‐based scheme can be developed to get over the obstacle of the quantized input signal and unknown control directions. Moreover, the number of adaptive laws is small, thereby reducing the computational burden. Then we testify the boundedness of all signals in the closed‐loop system. Besides, the tracking error can converge to an arbitrarily small domain of origin. Finally, a simulation example is provided to verify the feasibility of the control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive fuzzy backstepping control problem is considered for a class of single-input single-output (SISO) unknown uncertain nonaffine nonlinear systems in strict-feedback form. Within this approach, Nussbaum gain functions are introduced to solve the problem of unknown control directions. The unknown nonlinear functions are approximated by employing adaptive fuzzy systems. The stability analysis of the closed-loop system in the sense of Lyapunov guarantees the global boundedness property for all the signals and states, and at the same time, steers the tracking error to a small neighborhood of the origin. The feasibility of the developed control approach is illustrated by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper focuses on the adaptive event-triggered consensus control problem for a class of stochastic nonlinear multi-agent systems with unknown nonlinear control directions and external disturbances. The heterogeneous nonlinear dynamics and non-identical unknown control directions are discussed for different agents. The application of the event-triggered mechanism can effectively decrease the update frequency of the controller, and unknown nonlinear dynamics are solved by using fuzzy logic systems. Under the action of the designed distributed controller, all signals of this stochastic multi-agent systems can reach semi-globally uniformly ultimately bounded (SGUUB) in mean square. Furthermore, Zeno behavior can be ruled out by the existence of positive inter-event intervals. Finally, a simulation example is presented to verify the feasibility of the algorithm. [ABSTRACT FROM AUTHOR]

This article is concerned with the quantized fault‐tolerant control (FTC) for consensus of multiple Lagrangian systems subject to stochastically switching networks, actuator and sensor faults. First of all, a reliable quantized FTC algorithm is developed under Markov jump networks (MJNs), where the communication signal is first quantized before transmitted to develop controllers, and the communication networks are stochastically switching with the sojourn time belonging to an exponential distribution. Then, to handle the FTC problem in the presence of unknown control directions, the Nussbaum function is introduced to further improve the control reliability. Furthermore, the FTC case involving semi‐Markov jump networks (S‐MJNs) and time‐varying communication delays is considered, where the negative constraints of time delays can be effectively attenuated with the sojourn time following a Weibull distribution. Meanwhile, several sufficient criteria on the consensus analysis and algorithms synthesis are established by means of the Lyapunov–Krasovskii stability method. Finally, numerous illustrative examples are elaborated on for demonstrating the feasibility of the derived results. [ABSTRACT FROM AUTHOR]

In this article, we explore the possibility of designing a continuous control algorithm for time‐varying networks of high‐order nonlinear agents with input saturation. A class of neural network‐based (NN) distributed control algorithms are proposed for the consensus of nonlinear agents with input saturation and nonidentical unknown control directions (UCDs) under uniformly quasi‐strongly δ‐connected graphs. An NN is used to cancel the unknown part of agent dynamics due to the well known NN function approximation property. Also, an adaptive smooth term is employed to compensate for the bounded disturbance, the approximation error. Moreover, an auxiliary system is designed to counteract the effect of input saturation. Furthermore, the control law is augmented with the Nussbaum‐type function to obtain an estimation of the UCDs. It is proven rigorously that the consensus of nonlinear agents with input saturation and nonidentical UCDs can be guaranteed, and the boundedness of all signals of closed‐loop systems is ensured. Finally, simulation examples are given to show the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of global state-feedback regulation for a class of switched uncertain nonlinear systems with quantised input and unknown control directions under arbitrary switchings. A hysteretic quantiser is introduced to avoid actuator chattering. The powers of all subsystems are positive odd rational numbers and depend on the switching signals. Incorporating Nussbaum-type gain technique into adding a power integrator approach, a new adaptive controller is designed to guarantee that all the signals of the closed-loop system are bounded and the system state is globally asymptotically regulated to zero. An example is given to illustrate the validity of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper proposes an improved active disturbance rejection control (ADRC) method for output tracking of uncertain plants with unknown control direction. A basic design procedure in the ADRC methodology is to assume the exact knowledge of the system control direction, that is, the sign of its input channel coefficient. Recent works have been proposed to relax such a requirement by performing modifications in its control structure. However, despite considering uncertainties in the input coefficient, many variants of the ADRC method still assume the knowledge of the control direction, which means that the control gain is uncertain in norm, but not in sign. For solving the latter case, and also aiming to generalize the earlier ADRC results for a larger class of systems, the present work incorporates the concept of monitoring functions in the controller design. It is a switching‐based strategy whose main function is to determine the correct sign of the control direction, which is directly related to the sign of the plant input channel coefficient. As a consequence of the resulting new control method, exponential stability with respect to a small residual set is guaranteed for the output tracking problem in closed‐loop. Numerical simulations are performed and discussed initially in an academical example, only for comparing the robustness properties concerning the unknown control direction of the proposed strategy with another ADRC methodology. In the sequence, the proposed ADRC strategy based on monitoring function is applied to the automotive plant system of an Anti‐Lock Braking System for illustrating its performance. [ABSTRACT FROM AUTHOR]