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This article addresses the attitude manoeuvre control without unwinding based on variable gain (i.e. adaptive) super-twisting algorithm (STA) and the modified Rodrigues parameters (MRPs). First, a selection logic for the MRP set and its shadow set is designed in order to construct an attitude control system model for rigid spacecraft. Second, a nonlinear sliding function is presented, and on the sliding phase, finite-time convergence and anti-unwinding performance are guaranteed. As a result, a first-order sliding mode controller is created to ensure finite-time convergence and anti-unwinding performance on the reaching phase. To alleviate the chattering and improve convergence speed, an adaptive STA is presented, and the finite-time convergence and anti-unwinding performance are guaranteed on the reaching phase. Furthermore, the adaptive gains are designed based on dual-layer adaptive law, which allows the gains to be increased and decreased as appropriate. It is further demonstrated that when the controller gains are time-varying according to adaptive law, the convergence property and anti-unwinding performance are guaranteed. Numerical simulations are carried out to illustrate the closed-loop system's performance under the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper provides a new sliding mode control (SMC) approach, by which both the nominal and robust stability associated with a trajectory tracking problem for an uncertain robot manipulator are achieved. More precisely, the new control law consists of linear and nonlinear functions of tracking errors, in which the former is for the nominal stability and the latter is to ensure the robust stability of the resulting closed‐loop systems. The nonlinear function can be interpreted as an extended version of conventional SMC approach, and the reaching phase corresponding to a pregiven sliding surface is shown to be completed in a finite time; the tracking errors arrive at the sliding surface in a finite time and do not deviate from it after the arrival. In the sliding phase, the tracking errors are also ensured to converge to the origin. Finally, some simulation results are given to demonstrate both the theoretical validity and practical effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

It is well known that unknown modeling errors cannot be avoided in practice. Such unmeasured uncertainties are usually denoted as unknown nonlinear functions that exist in every channel of the system equation. This paper aims to develop an output feedback adaptive control scheme by constructing state estimation filters to address such unknown modeling errors. In the controller design, these uncertainties caused by modeling errors will be accumulated to the last step for compensation. Unknown parameters existing in the upper bound functions of unknown nonlinear functions and system parameters are estimated synchronously based on tuning function approaches. It is shown that the designed output feedback controller can ensure the stability and tracking performance of the closed‐loop system, and the transient performance in terms of a truncated norm is also established. [ABSTRACT FROM AUTHOR]

The paper expounds the question of echo state network‐based fixed‐time adaptive tracking control for a type of multi‐input multi‐output nonlinear strict‐feedback system with input delayed saturation. Based on the feature that echo state network can obtain better estimation performance at lower computational cost, it is utilized to approximate the unknown nonlinear function in the controller design course. By constructing an auxiliary system, a time‐delay system with input saturation is eliminated. Moreover, command filtering techniques can be applied to avoid the "complexity explosion" problem in the backstepping method. Then, the closed‐loop system is attested to be semi‐global practical fixed‐time stable. In the end, a simulation shows the valid scheme. [ABSTRACT FROM AUTHOR]

The robust stabilisation for a general class of disturbed nonlinear systems subject to state-dependent uncertainties is addressed in this paper. Different from most existing results, the lumped uncertainty, including external disturbances and model uncertainties, is relaxed to be bounded by some nonlinear functions rather than constants in this paper. Based upon the classical design procedure of disturbance observer-based control (DOBC), a new continuous saturation-based dynamic controller is proposed to estimate the lumped uncertainty. By the delicate design of several compact sets, the qualitative robust stability of the closed-loop system is guaranteed in the sense that all the signals of the closed-loop system can converge to an arbitrarily small compact set in a finite time. Furthermore, when the external disturbances are constants, the semi-global asymptotic stability can also be guaranteed by the proposed controller. Finally, the relationship between system uncertainties and observer gain is shown by a numerical simulation example. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the adaptive control is investigated by switching linear controllers for a class of nonlinear parameterized systems with multiple unknown control directions. Parametric uncertainties entering the state equations nonlinearly can be fast time‐varying or jumping at unknown time instants, the bounds of the parametric uncertainties are not required to know a priori and the multiple control directions are unknown. Our proposed adaptive controller is a switching type controller. First, sufficient conditions for designing an adaptive stabilizer are derived. Then, a switching‐type adaptive controller is designed, in which a linear controller with two undetermined design parameters to be tuned is recursively designed by adding a power integrator, and a switching mechanism is proposed to tune these parameters online for compensating the multiple unknown control directions and the unknown bounds of the parametric uncertainties. The undetermined design parameters are based on the upper bound estimation of the unknown parameters existing not only in the nonlinear functions but also in the control directions functions. The proposed adaptive controller globally asymptotically stabilizes the system in the sense that, for any initial conditions, the state converges to the origin while all the signals of the closed‐loop system are bounded. Finally, an example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the adaptive state‐feedback control problem of output‐constrained stochastic high‐order nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics. A key nonlinear transformation function is constructed to convert the original output‐constrained stochastic nonlinear system into an equivalent form without any output constraint. By subtly using the SiISS small‐gain condition and fully extracting the characteristics of system nonlinearities, two new control design and analysis methods are developed to guarantee that the closed‐loop system has an almost surely unique solution, all the closed‐loop signals are bounded almost surely, and the equilibrium point is stable in probability without the violation of output constraint. A simulation result is provided to show the effectiveness of this control method. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive fault‐tolerant tracking control problem for nonlinear systems with prescribed performance and input dead‐zone. First, a new composite variable is constructed by using the characteristics of actuator fault and input dead‐zone for the modeling purpose. Second, an adaptive neural network observer is designed to estimate the system states in the presence of inaccurate feedback information. Third, the proposed control strategy effectively counteracts the effects of sensor failure and unknown nonlinear functions, which makes the tracking error confined within the performance boundary and all the signals of the closed‐loop system semi‐globally uniformly ultimately bounded. Finally, an application oriented example is provided to demonstrate the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on addressing the leaderless consensus problem in general nonlinear multi-agent systems (MAS) with bounded disturbances and directed topology. Neural networks are utilized for estimating unknown nonlinear functions. By designing an adaptive observer, under the presence of bounded disturbances and unknown nonlinearities, a fully distributed leaderless consensus protocol is presented to make the closed-loop systems achieve consensus. By using sigmoid basis functions for disturbance compensation, the sensitivity of the controller to disturbances can be reduced, enabling the system to work more stably and robustly in the presence of bounded disturbances. Finally, the results are verified through a numerical example. [ABSTRACT FROM AUTHOR]

This paper considers the adaptive fixed-time neural tracking dynamic surface control (DSC) for high-order nonlinear switched systems. The uncertain nonlinear functions are approximated by neural networks (NNs). And the obstacles of high-order terms are eliminated by the adding a power integrator. A novel fixed-time convergence filter is proposed to refrain from the problem of repeated differentiation of virtual controllers. On the basis of the backstepping control algorithm and the common Lyapunov function (CLF) method, a novel adaptive fixed-time neural DSC strategy is developed. It is proven that the states in the closed-loop system are bounded and the tracking error converges to an area of zero in fixed time. The simulation experiments further verify the feasibility of the mentioned method. [ABSTRACT FROM AUTHOR]

In this paper, we propose the twisting observer for robustly estimating the states of a second-order uncertain system. It is well-known that the twisting algorithm achieves the second-order sliding mode condition using the sign information of both the plant states. When all the states are not available, the twisting algorithm cannot be extended to the estimation problem directly. Hence, our proposed observer approximates this unknown sign term for the non-measurable state in the twisting observer with a delayed output-based switching function. It is shown that under some suitable gain conditions, the observer can guarantee any arbitrary accuracy of estimation error for some appropriate delay parameter which can be varied online. The advantage of this observer is that one needs to control only the delay parameter to achieve the desired steady-state accuracy, unlike the additional nonlinear functions found in the existing observers. The application of this observer to output feedback stabilization is also discussed. The separation principle for the closed-loop system is shown by designing the gains of controller and observer independently. Finally, we illustrate the design and performance of the proposed state observation scheme through a numerical example. [ABSTRACT FROM AUTHOR]