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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 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 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]

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]

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]

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]

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]

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 studies a class of random nonlinear systems with time-varying delay, in which the r -order moment of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear time-delay systems. Secondly, some criteria on noise-to-state stability in the moment sense and in probability sense are given by Lyapunov method respectively. Finally, an adaptive output feedback regulation controller is constructed for a class of random nonlinear time-delay systems and the effectiveness of the proposed recursive procedure is demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]