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In this article, we introduced a novel definition for a class of extended Nussbaum functions that have looser requirements than the traditional Nussbaum function. The extended Nussbaum function achieves comparable performance to the traditional Nussbaum function while addressing the challenges of unknown control directions and time‐varying actuator faults. We then provide a specific example function based on the extended Nussbaum function definition. Unlike the traditional Nussbaum function, which oscillates with fixed frequency and constantly increasing amplitude, this example function constrains the amplitude and oscillates with decreasing frequency. Consequently, its amplitude and derivative remain bounded. The oscillation of the system caused by the too large amplitude of the traditional Nussbaum function can be avoided. Furthermore, this example function is constructed using portions of elliptic curve. As a result, it is continuous and differentiable, in contrast to the normal decreasing‐frequency Nussbaum function using trigonometric function, which is only continuous. The overall closed‐loop system's global stability and asymptotic convergence of system states are successfully achieved. Simulation results demonstrate the effectiveness of the proposed function. [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 article studies the leader‐following attitude coordination problem of a group of rigid spacecraft subject to communication constraint, disturbances and uncertain control coefficient matrices. A fully distributed adaptive anti‐disturbance attitude coordinated control scheme with event‐triggering mechanism is developed. First, the event‐triggered adaptive distributed observer is designed for each follower to estimate the leader's information without continuous communication requirement. Based on the estimated information, the adaptive anti‐disturbance attitude tracking controller is designed such that asymptotic coordinated tracking can be achieved under additive disturbances and actuators' partial loss of efficiency. The proposed control scheme ensures that all the closed‐loop signals are bounded and the positive lower bound of inter‐event times exists in each subsystem. Simulation results illustrate the effectiveness and flexibility of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the consensus tracking control for a class of heterogeneous multi-agent systems with multiple unknown time-varying control directions and unknown direction actuator faults. Different from existing work, the directions of the multiple time-varying control coefficients are subject to fault-induced sign-switching. To address this challenge, a series of high-order Lyapunov functions and differentiable functions are introduced to avoid non-integrable terms. Then, a novel contradiction statement and some Nussbaum functions are used to handle the summation of multiple unknown control coefficients with time-varying amplitudes and directions. Meanwhile, a novel distributed observer with quantized communication is introduced to track a reference trajectory with unknown dynamics. It is shown that all closed-loop signals are globally uniformly bounded and the tracking errors converge to residual sets that can be made arbitrarily small. Simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper is devoted to attitude tracking control of fractionated spacecraft with wireless communication. We consider the practical case that the spacecraft suffers from uncertain inertia parameters, external disturbances, and even unknown and time-varying actuator faults. Within the framework of the backstepping method, a novel event-triggered adaptive fault-tolerant control scheme is proposed. In our design, an event-triggering mechanism is introduced to determine the time instants for communication, which successfully avoids continuous communication and Zeno phenomenon. Then, with the aid of a bound estimation approach and a smooth function, the impacts of the actuator faults, as well as the network-induced error, are effectively compensated for. Moreover, by employing the prescribed performance control technique, it is shown that the attitude tracking errors can converge to predefined arbitrarily small residual sets with prescribed convergence rate and maximum overshoot, no matter if there exist unknown actuator faults. Compared with conventional adaptive attitude control schemes, the proposed scheme significantly reduces the communication burden, while providing high reliability and stable, rapid, and accurate response for attitude maneuvers. Simulation results are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive dynamic surface control scheme is proposed for a class of hypersonic flight vehicles with unknown elevator faults. By estimating the bounds of the fault uncertainties, the effect of the faults is successfully compensated for and each elevator is allowed to change among the healthy case and different faulty cases infinitely many times. The proposed scheme is free of the problem of explosion of complexity and is able to steer tracking errors into predefined arbitrarily small residual sets with prescribed convergence rates and maximum overshoots. Such features result in a simple flight control scheme which can be easily implemented with less computational burden, satisfactory tracking performance and high reliability. Simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, an output-feedback adaptive consensus tracking control scheme is proposed for a class of high-order nonlinear multi-agent systems. The agents are allowed to have unknown parameters, unknown nonlinearities, and input quantization simultaneously. The desired trajectory to be tracked is available for only a subset of agents, and only the relative outputs and the quantized inputs need to be measured or transmitted as signal exchange among neighbors regardless of the system order. By introducing a kind of high-gain K-filters and a smooth function, the effect among agents caused by the unknown nonlinearities is successfully counteracted, and all closed-loop signals are proved to be globally uniformly bounded. Moreover, it is shown that the tracking errors converge to a residual set that can be made arbitrarily small. Simulation results on robot manipulators are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a decentralized output-feedback adaptive control scheme is proposed for a class of interconnected nonlinear systems with input quantization. Both logarithmic quantizers and improved hysteretic quantizers are studied, and a linear time-varying model is introduced to handle the difficulty caused by quantization. The proposed scheme allows the parameters of the quantizers to be freely changed during operation, and can guarantee global stability of the overall closed-loop system regardless of the coarseness of the quantizers and the existence of interactions among subsystems. Moreover, with the aid of a kind of high-gain K-filters, it is shown that all tracking errors converge to a residual set which can be made arbitrarily small by adjusting some design parameters. Simulation results are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a decentralized output-feedback adaptive backstepping control scheme is proposed for a class of interconnected nonlinear systems with unknown actuator failures. By introducing a kind of high-gain K -filters, a bound estimation approach and some smooth functions, the effect of actuator failures and interactions among subsystems is successfully compensated for and the actuators are allowed to change among the normal operation case and different failure cases infinitely many times. The proposed scheme is able to guarantee the global stability of the overall closed-loop system, regardless of the possibly infinite number of unknown actuator failures. An initialization technique is also introduced so that the L ∞ performance of tracking errors can be adjusted no matter if there exist unknown actuator failures. Simulation results performed on double inverted pendulums are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, a new adaptive compensation control scheme is proposed for a class of nonlinear systems with unknown parameters and unknown actuator failures. The normal operation case and different failure cases of actuators are unified through a time-varying model. By introducing a smooth function, an integrable auxiliary signal, and a bound estimation approach, the effect of failures is successfully compensated for, and the total number of failures is not restricted to be finite. It is shown that all closed-loop signals are globally uniformly bounded, and the tracking error converges to zero asymptotically regardless of the possibly infinite number of actuator failures. An application to the longitudinal dynamic model of a twin otter aircraft is presented to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive dynamic surface control scheme is proposed for a class of multi-input multi-output (MIMO) nonlinear time-varying systems. By fusing a bound estimation approach, a smooth function and a time-varying matrix factorisation, the obstacle caused by unknown time-varying parameters is circumvented. The proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step. Moreover, all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot. Such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance. Simulation results are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM PUBLISHER]

This paper is devoted to adaptive output tracking for a class of multi-input multi-output nonlinear systems with unknown non-symmetric dead-zone. With the aid of a matrix factorization and a similarity transformation, a robust adaptive dynamic surface control scheme is proposed and the difficulty caused by the control gain matrix and the dead-zone is circumvented. By introducing a surface error modification and an initialization technique, we show that the [ABSTRACT FROM AUTHOR]

SUMMARY This paper is devoted to output-feedback adaptive control for a class of multivariable nonlinear systems with both unknown parameters and unknown nonlinear functions. Under the Hurwitz condition for the high-frequency gain matrix, a robust adaptive backstepping control scheme is proposed, which is able to guarantee the [ABSTRACT FROM AUTHOR]

In this article, a novel output-feedback adaptive dynamic surface control scheme is proposed for linear time-invariant multivariable plants based on the norm estimation of unknown parameter matrices. Besides avoiding the explosion of complexity problem in traditional multivariable backstepping design, the proposed scheme has the following features: (1) only one parameter needs to be updated on-line regardless of the plant order and input–output dimension, (2) only the Hurwitz condition is required for the high-frequency gain matrix and (3) the ℒ∞ performance of the tracking error can be guaranteed. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results are given to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Multivariable adaptive control with less prior information of the high-frequency gain matrix (HFGM) is a longstanding problem of both theoretical and practical importance. In this paper, a solution is presented by proposing a novel output-feedback adaptive backstepping control scheme. Our scheme only requires the leading principal minors of the HFGM to be nonzero and allows their signs to be unknown, which significantly relaxes the assumptions on the HFGM in conventional multivariable adaptive control schemes. To cope with the unknown signs, we propose novel Nussbaum functions with some nice properties and construct periodical intervals in which the effects of the multiple Nussbaum functions reinforce rather than counteract each other. With these efforts, global stability of the closed-loop system and asymptotical convergence to zero of the tracking error are successfully achieved. Simulation results illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the control problem of air-breathing hypersonic vehicles subject to input nonlinearities, aerodynamic uncertainties and flexible modes. An adaptive backstepping controller and a dynamic inverse controller are developed for the altitude subsystem and the velocity subsystem, respectively, where the former eliminates the problem of “explosion of terms” inherent in backstepping control. Moreover, a modified smooth inverse of the dead-zone is proposed to compensate for the dead-zone effects and reduce the computational burden. Based on this smooth inverse, an input nonlinear pre-compensator is designed to handle input saturation and dead-zone nonlinearities, which leads to a simpler control design for the altitude subsystem subject to these two input nonlinearities. It is proved that the proposed controllers can guarantee that all closed-loop signals are bounded and the tracking errors converge to an arbitrarily small residual set. Simulation results are carried out to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]