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This article investigates the event‐triggered stabilization for a class of hyperbolic PDE‐ODE cascade systems with nonlocal term. The presence of unknown parameters in the system brings technical challenges from design to analysis. This compels us to integrate certain powerful dynamic compensation into event‐triggering control mechanism. To solve the problem, by adaptive technique, a compensation strategy is developed to counteract the parametric uncertainties. Then, a desired event‐triggered controller is delicately designed to guarantee that all the signals in the closed‐loop system are bounded and the original system states converge to zero in the L2 norm. Particularly, the event‐triggering mechanism with an additional dynamic signal in the threshold is devised to overcome the negative influence of execution error, while ensuring a positive lower bound for the interexecution intervals. Finally, a simulation example is given to illustrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Summary: Adaptive output‐feedback control is investigated for a class of uncertain damped wave equations. The remarkable features of the system in question are as follows: (i) Unknown damping is allowed at the boundary; (ii) The boundary measurement is corrupted by an unknown harmonic disturbance. These features make the control problem essentially different from those in the related literature. To solve the problem, a novel adaptive output‐feedback control scheme is established for the system. Specifically, an ingenious observer is first introduced to reconstruct the unmeasured system state in the space domain. Based on this, a certain compensation mechanism is designed for the unknown damping coefficient and output disturbance by adaptive technique based on projection operator. Then, an output‐feedback controller is successfully designed by the backstepping method for ODEs, which guarantees that all states of the resulting closed‐loop system are bounded, and the original system state ultimately converges to an arbitrarily prescribed small neighborhood of the origin. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the global practical tracking via adaptive output‐feedback for a class of uncertain nonlinear systems. Essentially different from the closely related literature, the system under investigation possesses unknown time‐varying control coefficients and a polynomial‐of‐output growth rate, and meanwhile, the system nonlinearities and the reference signal allow serious unknowns. For this, an adaptive observer is designed to reconstruct the system unmeasured states, where a new dynamic gain is introduced to compensate the serious unknowns in the system nonlinearities and the reference signal. Based on this and by backstepping technique, an adaptive output‐feedback controller is successfully designed, such that all the states of the closed‐loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical simulation is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers the global finite-time output-feedback stabilization for a class of uncertain nonlinear systems. Comparing with the existing related literature, two essential obstacles exist: On the one hand, the systems in question allow serious parametric unknowns and serious time variations coupling to the unmeasurable states, which is reflected in that the systems have the unmeasurable states dependent growth with the rate being an unknown constant multiplying a known continuous function of time. On the other hand, the systems possess remarkably inherent nonlinearities, whose growth allows to be not only low-order but especially high-order with respect to the unmeasurable states. To effectively cope with these obstacles, we established a time-varying output-feedback strategy to achieve the finite-time stabilization for the systems under investigation. First, a time-varying state-feedback controller is constructed by adding an integrator method, and by homogeneous domination approach, a time-varying reduced-order observer is designed to precisely rebuild the unmeasurable states. Then, by certainty equivalence principle, a desired time-varying output-feedback controller is constructed for the systems. It is shown that, as long as the involved time-varying gain is chosen fast enough to overtake the serious parametric unknowns and the serious time variations, the output-feedback controller renders that the closed-loop system states converge to zero in finite time. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]