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Stabilisation via adaptive feedback is investigated for an ODE system cascaded by coupled parabolic equations. The remarkable characteristic of the system is the presence of serious uncertainties since no known or bounded intervals are needed for the unknown parameters. Besides, strong coupling exists in the PDE subsystem which brings essential difference compared with those of the related literature. For this, a passive identifier is skillfully constructed firstly, and in turn adaptive laws are given to compensate the serious parametric unknowns. Then, by constructing a backstepping transformation and its inverse one, the identifier joint with the original system is transformed into a new system. From the new system, an adaptive state-feedback controller is designed which ensures that all the states of the closed-loop system are bounded and particularly those of the original system converge to zero. Finally, a numerical example is provided to validate the proposed algorithm. [ABSTRACT FROM AUTHOR]

Adaptive stabilisation is investigated for a class of uncertain coupled parabolic equations in this paper. The presence of unknown coefficients can reduce the rigorousness of system modelling and enlarge the scope of the systems, whereas it could give rise to essential difficulties to control problems. Mainly due to the latter, certain new initiative, such as uncertainty compensation, should be considered to solve the stabilisation problem. For this, by infinite-dimensional backstepping method combining with adaptive compensation technique, an adaptive control scheme is proposed. Then, an adaptive state-feedback controller is constructed which guarantees that all the closed-loop system states are bounded while the original system states converge to zero. A numerical example is provided to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the global output-feedback stabilisation for a class of nonlinear systems with inherent nonlinearities and coarse disturbance. Remarkably, the disturbance may be non-periodic, non-differentiable and/or of unknown magnitude, and hence some critical requirements on the disturbance in the existing related literature are successfully removed. Recognising that the strategies of disturbance compensation, such as internal model principle, sliding mode control method, learning method and active disturbance rejection control method, are quite hard or even impossible to apply, a time-varying design scheme is developed in the paper. Moreover, the serious unknowns and time-variations reflected in the growth rate of the system are also dealt with by the proposed scheme. By designing a time-varying output-feedback controller, all the signals of the resulting closed-loop system are globally bounded, and the original system state and the observer state ultimately converge to zero. [ABSTRACT FROM AUTHOR]

Adaptive stabilisation is investigated for ordinary differential equation systems via distributed effect of uncertain diffusion-dominated actuator dynamics. The presence of the unknowns/uncertainties and the distributed effect makes the system under investigation more general and representative than those of the related literature, and moreover yields the ineffectiveness of the existing methods on this topic. By constructing an invertible spatial and time-varying state transformation, the original closed-loop system is first changed into a target system, from which the design of parameter updating law and the analysis of the closed-loop system performance become more convenient. Then, by Lyapunov method and adaptive compensation technique, an adaptive stabilising controller is successfully constructed, which guarantees that the original system states converge to zero while other closed-loop system states are bounded. A simulation example is provided to validate the proposed method. [ABSTRACT FROM AUTHOR]