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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]

Multiple uncertainties/noises, frequently exist in a plant, usually require multiple compensation techniques, which renders feedback controllers highly dynamic and nonlinear. This motivates us to search for a compact design scheme of compensation to reduce the complexity of controllers. In this paper, global output-feedback stabilisation is investigated for a class of uncertain nonlinear systems with unknown unmeasured states-dependent growth and input matching uncertainty. To solve the problem, a compact scheme is proposed to design a global adaptive output-feedback controller, which combines the technique of dynamic gain and extended state observer together. Particularly, only one dynamic gain, rather than two dynamic gains, is introduced to deal with the unknown polynomial-of-output growth rate, which makes our controller to have lower dynamics than those in the related works. Moreover, the input matching uncertainty is asymptotically estimated by the extended state observer, and thus its effect is well counteracted. It is shown that, under the designed controller, the system states globally converge to zero. A simulation example on non-zero set-point regulation demonstrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper is concerned with the global adaptive stabilisation via output feedback for a class of uncertain planar nonlinear systems. Remarkably, the unknowns in the systems are rather serious: the control coefficients are unknown constants which do not belong to any known interval, and the growth of the systems heavily depends on the unmeasured states and has the rate of unknown polynomial of output. First, a delicate state transformation is introduced to collect the unknown control coefficients, and subsequently, a suitable state observer is successfully designed with two different dynamic gains. Then, an adaptive output feedback controller is proposed by flexibly combining the universal control idea and the backstepping technique. Meanwhile, an appropriate estimation law is constructed to overcome the negative effect caused by the unknown control coefficients. It is shown that, with the appropriate choice of the design parameters, all the states of the resulting closed-loop system are globally bounded, and furthermore, the states of the original system converge to zero. [ABSTRACT FROM PUBLISHER]