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This paper focuses on global adaptive state-feedback stabilization for a class of high-order uncertain nonlinear systems with multiple delays. Restriction on system growth is relaxed. Two dynamic gains are introduced to deal with uncertainty and nonlinear growth rate of the system. Without precise information about time-delay being needed and only by like Lyapunov function, a new control strategy is presented based on homogeneous domination idea and two necessary transformations. As an application, the developed scheme is utilized to control design of a two-stage chemical reactor with delayed recycle streams. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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 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]

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]

This paper investigates the problem of state-feedback control for a class of stochastic high-order nonlinear systems with stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystem are stochastic input-to-state stable (SISS), by extending through adding a power integrator technique, choosing an appropriate Lyapunov function and using the idea of changing supply function, a smooth state-feedback controller is explicitly constructed to render the system globally asymptotically stable in probability and the states can be regulated to the origin. A simulation example is provided to show the effectiveness of the proposed scheme. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [ABSTRACT FROM AUTHOR]

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control (MRAC) with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter are also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, by using the topological degree theory and the fixed point index theory, the existence of three kinds of solutions (i.e., sign-changing solutions, positive solutions and negative solutions) for asymptotically linear three-point boundary value problems is obtained. [Copyright &y& Elsevier]

Abstract: This paper considers the decentralized adaptive regulation via output-feedback for nonlinear systems with integral input- to-state stable (iISS) inverse dynamics, nonlinear uncertainties, and unknown control direction. It is shown that all the signals in the closed-loop system obtained are bounded, and the asymptotic regulation is achieved. A numerical example shows the effectiveness of the design. [Copyright &y& Elsevier]

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 problem of robust decentralized adaptive output feedback stabilization for a class of interconnected systems with static and dynamic interconnections, and unmodelled dynamics by using MT filters and the back-stepping design method. It is shown that the closed-loop system is globally stable, and the asymptotic convergence of all the signals except for the parameter estimates can be guaranteed. The result is better than those obtained in other related papers. The effectiveness of the proposed scheme is demonstrated by simulation. [ABSTRACT FROM AUTHOR]

This paper solves finite-time stabilization problem of stochastic low-order nonlinear systems with time-varying orders and stochastic inverse dynamics. Due to stochastic low-order systems being merely continuous but not smooth, and the appearance of time-varying orders and stochastic inverse dynamics, all of control methods of stochastic nonlinear systems are inapplicable. By characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability (FT-SISS) and applying more general stochastic finite-time stability theory, a new design and analysis method is proposed to guarantee almost sure boundedness of all the closed-loop signals and stochastic finite-time stability of stochastic low-order nonlinear systems with time-varying orders and FT-SISS inverse dynamics. [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 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]

This paper investigates adaptive finite-time fuzzy control for full-state constrained high-order nonlinear systems. Fuzzy logic systems are employed to relax growth assumptions imposed on unknown system nonlinearities. By integrating a nonlinear state-dependent transformation into control design, full-state constraints can be handled without imposing feasibility conditions on virtual controllers. It is rigorously proved that fuzzy approximation is valid based on a compact set, full-state constraints aren't violated for all time. Besides, the solution of the closed-loop system is semi-global practical finite-time stable, and the tracking error converges to an adjustable compact set around the origin in finite-time. Two examples show the advantages of this control scheme. [ABSTRACT FROM AUTHOR]