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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]

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 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]

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 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]

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 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 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 studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing aLyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability. [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]

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]

This paper studies the global stabilisation problem for a class of high-order nonlinear systems with multiple time delays. A distinct property of the systems to be investigated is that powers on the upper bound restrictions of nonlinearities are allowed to take values on a continuous interval. By introducing the sign functions and using the generalised method of adding a power integrator, this paper successfully designs a continuous global state-feedback controller independent of time delays. Moreover, a novel Lyapunov–Krasovskii functional is constructed to prove the globally asymptotic stability of the resulting closed-loop system. [ABSTRACT FROM PUBLISHER]

This paper investigates stochastic high-order feedforward nonlinear systems for the first time. By introducing the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability. [ABSTRACT FROM AUTHOR]

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]

This article further discusses output feedback control for stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS) inverse dynamics. Based on the stochastic LaSalle theorem and small-gain type conditions on SiISS, an output feedback controller using the backstepping method is constructively designed to guarantee that all the closed-loop signals are bounded almost surely and the stochastic closed-loop system is globally asymptotically stable in probability. [ABSTRACT FROM AUTHOR]

For a class of discrete-time systems with multiplicative uncertainties, the design and analysis of robust direct model reference adaptive control (MRAC) with normalized adaptive law are investigated. By reproving the discrete-time conclusions on the an relationship properties between the input and the output, and the swapping Lemmas I and II, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all the signals in the closed-loop system, the stability and robustness properties of the discrete-time MRAC scheme are analysed rigorously in a systematic fashion as in the continuous-time case. [ABSTRACT FROM AUTHOR]

This paper considers the model reference adaptive control problem for the system (1) with unmodelled dynamics η[sub n] dominated by a small constant ε multiplied by a quantity dependent on the input, output and noise. Using bounded external excitation and randomly varying truncation techniques, we give design method of a model reference adaptive controller which is similar to that in Meyn and Brown (1992). It is shown that the closed-loop system is globally stable, the estimation error for parameter contained in the modelled part is of order ε, and the closed-loop system under the model reference adaptive control law is suboptimal in the sense of lim sup 1/n Σ[sup n] (A[sub m] (z) y[sub i+1]- B[sub m](z)z*[sub i] - C[sub m] (z) w[sub i+1])[sup 2] ≤ O(ε[sup 2]) + γ[sup 2] b[sub 1][sup 2] while the SPR condition usually used in other papers is replaced by a stability condition. [ABSTRACT FROM AUTHOR]