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Many practical dynamic models always suffer from complex nonlinearities, parameter uncertainties and random noises. Such kind of models are always characterized by uncertain stochastic nonlinear systems. Besides, many factors will lead to dead‐zone actuator, which further adds more challenges to control engineering. This paper studies stabilization issue of stochastic systems with polynomial nonlinear conditions, unknown parameters and dead‐zone actuator. An adaptive control approach is proposed by exploring homogeneous domination control and using dynamic‐gain‐based adaptive design strategy. It shows that all the signals are bounded almost surely and the system states converge to the origin almost surely. The presented method is successfully applied to the mass spring mechanical system. [ABSTRACT FROM AUTHOR]

The existing researches mainly focused on control issues of systems with constant powers. In practical engineering, it shows that some dynamic systems have time‐varying powers, which result in the inapplicability of many reported methods. Besides, nonlinear systems constantly suffer from uncertain dynamics. This article discusses the control issue of systems which possess uncertain dynamics and time‐varying powers. By introducing a new Lyapunov function which contains quadratic components and high‐order components and raising a novel recursive design strategy, we successfully design a semi‐global practical finite time controller which allows uncertain dynamics and larger range of system powers. Numerical and practical examples show that the presented strategy is valid. [ABSTRACT FROM AUTHOR]

The adaptive control issue of uncertain nonlinear system which has complicated polynomial growing condition is studied. Utilizing the dynamic‐gain transformation, we transform the considered system into the time‐varying system. By using a recursively design for its nominal system, a controller is skillfully constructed first. Subsequently, for the original system, by flexibly utilizing the dynamic gain and presenting an adaptive homogeneous domination method, a new time‐varying adaptive controller is successfully obtained to ensure that the equilibrium point is globally asymptotically stable. An extended robust adaptive controller is also provided. Finally, we discuss two examples to verify the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: This paper discusses the adaptive control problem for a class of nonlinear systems with polynomial growing conditions. By introducing a Lyapunov function which carries the quadratic terms and higher‐order terms of the transformed variables and constructing an appropriate dynamic gain, a new control strategy is presented to design an adaptive controller using only one parameter estimation. Compared with the existing results, the presented method avoids the over‐parameterization and significantly simplifies the control design. A modified version of the method which adopts no parameter estimation is also provided. It shows that all the signals of the closed‐loop system are bounded and the solution of the original system converges to zero. A simulation example is given to show the validness of the method. [ABSTRACT FROM AUTHOR]

Summary: This article investigates the fast finite‐time adaptive tracking control via event‐triggered mechanism for a class of high‐order uncertain nonlinear systems. An adaptive tracking controller is constructed for the first time by utilizing a new fast finite‐time performance function and a serial of transformations equipped with a barrier function and event‐triggering rules, which guarantees that the tracking error is restricted in a time‐varying prescribed region and converges to an arbitrarily small constant in a faster speed compared with some traditional finite‐time control strategies. A remarkable feature of this article is to avoid Zeno phenomenon without taking a derivative with respect to the absolute value of the event‐triggered error which may not be differentiable at some discrete points. Finally, a simulation example is provided to verify the feasibility and effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the global stabilization for a class of high-order time-delay nonlinear systems. Compared with the existing references, a distinct characteristic of this paper rests in time-delay entering high-order, low-order, and linear growth parts of system nonlinearities. Based on Lyapunov-Krasovskii theorem and necessary improvement of the adding a power integrator method, a continuous global state-feedback controller is constructed to preserve the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. Finally, a simple example is provided to demonstrate the validness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]