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This paper investigates adaptive finite-time stabilisation for a class of output-constrained low-order nonlinear systems with unknown time-varying powers, parametric and dynamic uncertainties. Due to low-order nonlinear systems being merely continuous but not smooth, and the presence of time-varying powers and multiple unknowns, all the existing control methods of output-constrained nonlinear systems are inapplicable. By characterising unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), applying finite-time stability theory and introducing the tan-type barrier Lyapunov function, low-power and high-power terms into control design, a unified adaptive state-feedback controller, which can deal with both constrained and unconstrained systems, is constructed. It is proved that all the closed-loop signals are uniformly bounded, the output constraint is not violated, and system states converge to zero in a finite time. Finally, a simulation example is given to illustrate the effectiveness of this control scheme. [ABSTRACT FROM AUTHOR]

In this article, an adaptive practical tracking control scheme is presented for full-state constrained high-order nonlinear systems. By skillfully introducing the adaptive gain, nonlinear transformed functions and sign functions into control design, a novel continuous state-feedback controller is constructed without imposing restrictive approximation techniques and feasibility conditions. Under mild assumptions, the boundedness of all the closed-loop signals can be guaranteed, full-state constraints are not transgressed for all time, and the tracking error tends to an arbitrarily small region of zero in a finite time. [ABSTRACT FROM AUTHOR]

This article investigates the asymptotic tracking control problem for full-state-constrained nonlinear systems with unknown time-varying powers. By introducing a nonlinear state-dependent transformation, a continuous bounded scalar function, and lower and higher powers into adding a power integrator control design, full-state constraints are skillfully handled without imposing frequently used feasibility conditions in traditional barrier Lyapunov function-based methods, and an asymptotic tracking control design is provided. It is proved that all the closed-loop signals are bounded, full-state constraints are not transgressed, and the asymptotic tracking is achieved. [ABSTRACT FROM AUTHOR]

This article investigates the tracking control for input and full-state-constrained nonlinear time-delay systems with unknown time-varying powers, whose nonlinearities do not impose any growth assumption. By utilizing the auxiliary control signal and nonlinear state-dependent transformation (NSDT) to counteract the effect of input saturation and cope with full-state constraints, respectively, and then introducing lower and higher powers and Lyapunov–Krasovskii (L–K) functionals in control design together with the adaptive neural-networks (NNs) method, an adaptive neural tracking control design is provided without feasibility conditions. It is proved that NNs approximation is valid, all the closed-loop signals are semiglobally bounded, and input and full-state constraints are not violated. [ABSTRACT FROM AUTHOR]

This article discusses the adaptive fuzzy asymptotic tracking control for high-order nonlinear time-delay systems with full-state constraints. Fuzzy-logic systems and a separation principle are utilized to relax growth assumptions imposed on unknown nonlinearities. The adverse effect caused by unknown time delays is eliminated by choosing appropriate Lyapunov–Krasovskii functionals. By integrating nonlinear-transformed functions with a key coordinate transformation into the control design and constructing a specific compact set on the initial values of system states, the desired trajectory and parameter estimates, it is rigorously proved that all closed-loop signals are semiglobally bounded, the fuzzy approximation is valid, the full-state constraints are not violated without feasibility conditions on virtual controllers, and asymptotic tracking is achieved. The effectiveness and advantages of this control scheme are confirmed by two examples including a single-link robotic system. [ABSTRACT FROM AUTHOR]

This paper investigates practical preassigned finite-time tracking control for state-constrained high-order nonlinear systems. Fuzzy systems are utilised to remove frequently used growth assumptions on completely unknown nonlinearities. By integrating nonlinear transformed functions with a key coordinate transformation into control design, full-state constraints can be handled without imposing feasibility conditions in traditional barrier Lyapunov function-based control methods. It is rigorously proved that the states of fuzzy systems remain within a specific compact set, on which fuzzy approximation is valid. Besides, asymmetric full-state constraints aren't violated for all time, and the tracking error converges to the prescribed small region around zero in a preassigned finite-time. Two simulation examples show the effectiveness and advantages of this control scheme. [ABSTRACT FROM AUTHOR]

This article discusses the tracking control problem of full-state constrained nonlinear systems with unknown time-varying powers. With the help of a nonlinear state-dependent transformation, by introducing lower and higher powers in control design and skillfully combining the adding a power integrator method with the dynamic gain method, a full-state constrained tracking control design is developed without frequently used feasibility conditions. It is rigorously proved that all the signals of the closed-loop system are bounded, full-state constraints are not violated, and the tracking error converges to a compact set around the origin in a finite-time. [ABSTRACT FROM AUTHOR]

This article studies full-state constrained control for high-order nonlinear systems with unknown multiple time-varying powers and serious parameter unknowns. Due to the simultaneous existence of unknown powers and full-state constraints, we construct a log-type quadratic barrier Lyapunov function (BLF) rather than a quadratic Lyapunov function. By skillfully combining the log-type BLF, adding a power integrator technique and adaptive technique, an adaptive state feedback controller is developed. Under feasibility conditions, which are provided as sufficient conditions for the existence of proposed full-state constrained control, it is proved that all the signals of the closed-loop system are bounded, original system states converge to zero and full-state constraints are not violated. [ABSTRACT FROM AUTHOR]

In this article, tracking control is considered for a class of uncertain multi-input–multi-output (MIMO) nonlinear systems, where the time-varying parameters, the time-varying control coefficient and the time-varying disturbance are assumed to be unknown but to be bounded. Three stable adaptive tracking schemes for a given reference signal are proposed by devising different control algorithms. In the first scheme, bounded-error tracking is achieved in the sense that the tracking error converges exponentially to an adjustable region around the origin, where the $\sigma $ -modification adaptive laws are used to ensure the boundedness of all closed-loop signals. In the second scheme, asymptotic tracking is obtained in the sense that the tracking error converges to zero asymptotically, where the strictly positive and integral functions are employed in the control law to ensure the signal boundedness and zero-error tracking. In the third scheme, exponential tracking is gotten in the sense that the tracking error exponentially converges to zero with a given convergence speed, where exponential functions are incorporated into control law and adaptive laws to ensure system stability and the faster convergence. Three adaptive tracking schemes are, respectively, applied to nonlinear chaotic Chua’s circuit with control inputs. The parametric model is developed for Chua’s circuit with uncertain parameters and external disturbances. The effectiveness of the proposed control algorithms is demonstrated by comparative simulation studies. [ABSTRACT FROM AUTHOR]

This paper investigates the semi-global stabilisation problem of high-order nonlinear systems with full-state constraints and input saturation. By constructing the high-order barrier Lyapunov function (BLF) and auxiliary subsystem, a state feedback controller is designed without state and input constraints violation. It is proved that all the closed-loop signals are bounded in the semi-global sense, error signals converge to a small neighbourhood of the origin, and full-state constraints and input saturation are not violated. Two simulation examples are presented to show the feasibility and advantage of this method. [ABSTRACT FROM AUTHOR]

In this paper, for uncertain nonlinear systems with time-varying full state constraints, input saturation and unknown control direction, time-varying asymmetric barrier Lyapunov functions, the auxiliary subsystem, and the Nussbaum gain technique are employed. It is shown that all the closed-loop signals are bounded in the semi-global sense, error signals converge to bounded compact sets, and time-varying full state constraints and input saturation are not violated. [ABSTRACT FROM AUTHOR]

This paper studies the problem of global output feedback control for a class of feedforward nonlinear systems with unknown multiple time-varying delays and unknown output function under more general uncertain growth condition. We allow that there exists unknown constant, input function and polynomial-of-output growth rates imposed on nonlinearities. By skilfully introducing dynamic gain method, backstepping method and Lyapunov-Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain to guarantee the boundedness of closed-loop system signals and the convergence of original system states and their corresponding observer states. [ABSTRACT FROM AUTHOR]

This paper investigates adaptive fuzzy tracking control for high-order nonlinear time-delay systems with full-state constraints and input saturation. By adopting fuzzy approximation technique, frequently used growth assumptions imposed on unknown system nonlinearities are removed. High-order barrier Lyapunov functions are employed to prevent the transgression of full-state constraints. The auxiliary subsystem and the Nussbaum gain technique are utilized to analyze the effect of input saturation. Appropriate Lyapunov–Krasovskii functionals are constructed to compensate the adverse effect caused by the unknown time-delay. Novel feasibility conditions are formulated as sufficient conditions for the existence of proposed control. It is rigorously proved that all the closed-loop signals are bounded in the semi-global sense, error signals converge to small bounded compact sets, full-state constraints, and input saturation are not violated, and the arguments of unknown nonlinearities are constrained within a compact set, on which fuzzy approximation is valid. Eventually, the theoretical result is confirmed by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper studies the problem of global output feedback control for a class of feedforward nonlinear systems with the unknown output function and input matching uncertainty, whose nonlinearities satisfy the linear growth condition on unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates, where the value range of the power of polynomial-of-output growth rate is increased compared with the existing results. Under the new transformation, based on the dynamic gain method and backstepping method, by constructing a new extended state observer with two dynamic gains, an output feedback controller can be designed to ensure that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimate of input matching uncertainty converges to its actual value. [ABSTRACT FROM AUTHOR]

This paper considers a class of uncertain nonlinear feedforward systems with unknown constant growth rate, output polynomial function growth rate and system input function growth rate. Under the most general growth rate condition, only one dynamic gain is used to compensate simultaneously these three types of growth rates, an output feedback controller is constructed to guarantee the boundedness of closed-loop system states and the convergence of original system states. [ABSTRACT FROM AUTHOR]

In this paper, finite-time stabilization is investigated in depth for stochastic nonlinear systems with stochastic inverse dynamics. The contributions of this work are characterized by the following novel features: (i) Motivated by the concept of stochastic integral input-to-state stability (SiISS) and the existing stochastic finite-time stability theorem, a new concept of finite-time stochastic integral input-to-state stability (FT-SiISS) using Lyapunov function is first introduced, and an inclusion relationship among three types of stochastic stability, i.e., FT-SiISS, FT-SISS and SISS, is rigorously established. On the basis of FT-SiISS, we develop two new FT-SiISS small-gain conditions and discuss their relationship. Then, to analyze finite-time stability of stochastic nonlinear systems with FT-SiISS inverse dynamics, a stochastic finite-time stability theorem is improved. (ii) As the application of (i), we propose a unified finite-time control method, which can simultaneously handle stochastic nonlinear systems with FT-SiISS or FT-SISS inverse dynamics, and guarantee that the closed-loop system has an almost surely continuous solution, all the closed-loop signals are bounded almost surely, and its trivial solution is stochastically finite-time stable. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we give some new results on finite‐time stabilization for stochastic nonlinear systems whose powers of integrators are all positive odd rational numbers (ie, numerators and denominators of the powers are all positive odd integers) but not necessary only high order or low order. By adopting new conditions on drift and diffusion terms, Lyapunov function, and controller design method, a state feedback controller is designed to guarantee stochastic nonlinear systems finite‐time stable in probability. Moreover, when unknown parameters exist in systems, we give the adaptive finite‐time state feedback controller. Numerical examples demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper studies the problem of global output feedback control for nonlinear time-delay systems with input matching uncertainty and the unknown output function, whose nonlinearities are bounded by lower triangular linear unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates. By constructing a new extended state observer and skillfully combining the dynamic gain method, backstepping method and Lyapunov-Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain. It is proved that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimation of input matching uncertainty converges to its actual value. Two examples demonstrate the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This paper studies adaptive finite-time control problem of a class of nonlinear systems with dynamic and parametric uncertainties. The power of systems in this paper is any positive odd rational number but not necessary equal to or greater than one. To solve this problem, finite-time input-to-state stability (FTISS) is used to characterise the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, adding a power integrator, adaptive control and FTISS methods, an adaptive state feedback controller is designed to drive the states to the origin in finite time while maintaining all the closed-loop signals bounded. [ABSTRACT FROM AUTHOR]

This paper studies the problem of finite-time stabilisation of more general high-order nonlinear systems with dynamic and parametric uncertainties. By characterising the unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), skillfully combining Lyapunov function, sign function, backstepping, adaptive control and FTISS approaches, and using finite-time stability theory, an adaptive state feedback controller is designed to guarantee high-order uncertain nonlinear systems globally finite-time stable. [ABSTRACT FROM AUTHOR]

This paper studies the problem of output feedback disturbance attenuation for a class of nonlinear systems with input matching uncertainty, whose nonlinearities are bounded by unmeasured states multiplying unknown input and output polynomial functions. Combining the technique of dynamic gain and extended state observer, an adaptive output feedback controller is designed to guarantee that the states of the closed-loop system are globally bounded, and the disturbance attenuation is achieved in the -gain sense. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates adaptive state feedback stabilization for a class of more general stochastic high‐order nonholonomic systems. By constructing the appropriate Lyapunov function, skillfully combining parameter separation, sign function, and backstepping design methods, an adaptive state feedback controller is designed to eliminate the phenomenon of uncontrollability and guarantee global asymptotic stability in probability of the closed‐loop system. Two simulation examples are used to demonstrate the effectiveness of this method. [ABSTRACT FROM AUTHOR]

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system. [ABSTRACT FROM AUTHOR]

This paper studies finite-time stabilization problem for stochastic low-order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability, combining the Lyapunov function and adding a power integrator technique, and using the stochastic finite-time stability theory, a state feedback controller is designed to guarantee global finite-time stability in probability of stochastic low-order nonlinear systemswith finite-time stochastic input-to-state stability inverse dynamics. [ABSTRACT FROM AUTHOR]

This paper studies the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with state and input delays and the unknown output function. For stochastic feedforward nonlinear systems, the maximal open sector Δ of output function is given. As long as output function belongs to any closed sector included in Δ, by constructing a reduced-order observer and [ABSTRACT FROM AUTHOR]

This paper deals with the problem of continuous output-feedback stabilization for a class of switched high-order planar systems under arbitrary switchings. Based on the common Lyapunov function design method, by using the adding a power integrator technique and designing an implementable observer, a continuous output-feedback controller is constructed such that the closed-loop system is global stabilization and the output can be regulated to the origin. As an application, the developed strategy is utilized to the control design for the continuous stirred tank reactor with two modes feed stream. The simulation results verify the efficiency of the proposed design scheme. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers semi-global output feedback control for more general nonlinear systems with unknown time-delay and output function whose derivative is unbounded from above. By introducing a new observer and using the backstepping design method and the Razumikhin stability theorem, an output feedback controller is constructed to achieve a semi-global stability. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper solves the problem of output feedback stabilisation for nonlinear systems with unknown output function and control coefficients. Since output function is Lipschitz continuous but not necessary derivable, the maximal sector region of output function is given. As long as output function belongs to the sector, an output feedback controller can be designed to render the closed-loop system globally asymptotically stable. The effectiveness of controller is demonstrated by two examples. [ABSTRACT FROM AUTHOR]

This paper considers the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with input and state delay. Under a set of coordinate transformations, we first design a linear output feedback controller for a nominal system. Then, with the aid of feedback domination technique and an appropriate Lyapunov-Krasovskii functional, it is proved that the proposed linear output feedback controller can drive the closed-loop system globally asymptotically stable in probability. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of output feedback stabilization of stochastic planar nonlinear systems with output constraint. By introducing some new nonlinear mappings, adding a power integrator and homogeneous domination techniques, according to different value ranges of the homogeneous degree in the same form of assumptions, we establish two new design and analysis frames of output feedback stabilization to achieve respectively stochastic asymptotic stability (or asymptotical stability in probability) and stochastic finite-time stability of the trivial solution of the closed-loop system while guaranteeing the requirements of almost sure boundedness of the closed-loop signals and the symmetric output constraint. [ABSTRACT FROM AUTHOR]

This study considers the global output‐feedback control for a class of switched stochastic non‐linear time‐delay systems under arbitrary switchings. By using the backstepping technique and choosing an appropriate Lyapunov–Krasoviskii functional, an output‐feedback controller independent of switching signals is constructed to render the closed‐loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. Two simulation examples are provided to show the effectiveness of the designed controller. [ABSTRACT FROM AUTHOR]

In this paper, the problem of state feedback stabilization for stochastic feedforward nonlinear systems with input time-delay is considered for the first time. By introducing a variable transformation, skillfully combining the homogeneous domination method, and constructing an appropriate Lyapunov-Krasovskii functional, a state feedback controller is developed to guarantee the closed-loop system globally asymptotically stable in probability. [ABSTRACT FROM AUTHOR]

Two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented. We consider two possible input nonlinearities, that is, backlash-like hysteresis and symmetric dead-zone, which can be simultaneously dealt with by using the proposed compensation controllers. The knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required. Only the boundedness of the reference signal is assumed. The Nussbaum gain approach is employed to remove the assumption on the control gain sign. The first scheme is based on the backstepping technique. The final step of the recursive design is crucial for the closed-loop stability. In the second scheme, a direct adaptive control law is designed. The controller has a simple structure and only one adaptation parameter is updated. In both controllers, it is shown that asymptotic tracking is ensured. Two numerical examples are provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the state feedback control problem for a class of nonlinear systems with high-order and low-order nonlinearities. The introduction of the sign function together with the method of adding a power integrator and Lyapunov stability theorem makes the closed-loop system globally asymptotically stable. Exploiting the idea of how to deal with growth nonlinearities with both high order and low order being relaxed to some intervals is the focus of this work. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the problem of global stabilization for a class of stochastic high-order feedforward nonlinear systems with time-varying delay. By introducing the homogeneous domination design method and constructing the appropriate Lyapunov–Krasovskii functional, a state feedback controller is constructed to drive the closed-loop system to be globally asymptotically stable in probability. [Copyright &y& Elsevier]

This paper investigates finite-time stabilization of output-constrained stochastic high-order nonlinear systems with stochastic inverse dynamics and high-order and low-order nonlinearities. By characterizing the unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability and introducing nonlinear transformations, a new design and analysis method is constructed. It is rigorously proved that all the closed-loop signals are bounded almost surely, the asymmetric output constraint isn't violated almost surely, and the trivial solution of the closed-loop system is finite-time stable in probability. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates a class of stochastic feedforward nonlinear systems with time-varying delay. By introducing the homogeneous domination approach to stochastic systems, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability. [Copyright &y& Elsevier]

Global asymptotic regulation via output feedback based on a reduced-order observer is considered for a class of nonlinear systems with integral input-to-state stable (iISS) inverse dynamics. The contributions are that: (1) we further consider the conditions on changing supply rates in iISS systems, and discuss the necessity of some conditions by constructing a counter-example; (2) For a more general class of nonlinear systems with iISS inverse dynamics, a reduced-order observer is introduced, and by the combined approach of backstepping and changing iISS supply rates, an output feedback controller is given to drive the output of system to the origin asymptotically and maintain other closed-loop signals bounded. [ABSTRACT FROM AUTHOR]

Abstract: This article further discusses the output feedback stabilization problem for stochastic high-order nonlinear systems with time-varying delay. Under the weaker conditions on nonlinearities in drift and diffusion vector fields, by using the idea of homogeneous domination approach, skillfully choosing an appropriate Lyapunov–Krasoviskii functional, and successfully solving several troublesome obstacles in the design and analysis procedure, an output feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability. [Copyright &y& Elsevier]

Abstract: This paper further discusses output-feedback regulation for more general nonlinear systems with integral input-to-state stability (iISS) inverse dynamics and unknown control direction. By using the adaptive backstepping method, an output feedback controller is given to drive the output to the origin while maintaining other closed-loop signals bounded. [Copyright &y& Elsevier]