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This paper investigates the global adaptive state feedback controller design for a class of feedforward nonlinear systems with completely unknown control direction and unknown growth rate. Since the control direction, i.e., the sign of the control coefficient, is unknown, the control problem becomes much more challenging, to which a Nussbaum-type function is exploited. Moreover, the systems heavily depend on the unmeasured states with unknown growth rate, and hence a dynamic gain, rather than a constant one, is adopted to compensate the large system unknowns. For control design, a suitable state transformation is first introduced for the original system. Then, the state feedback controller is proposed based on an appropriate Nussbaum-type function and a dynamic high gain. It is shown that the state of the original system converges to zero, while the other states of the closed-loop system are globally bounded. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the stabilization of a class of uncertain reaction–diffusion equations with dynamic boundary condition. Remarkably, the dynamics of boundary condition at control end are considered while unknown parameters are contained in both the intra-domain and the dynamic boundary. This greatly relaxes the restrictions on boundary dynamics and system uncertainties of the related literature where dynamic boundary condition is neglected or considered but unknown parameters are only contained in the dynamic boundary or even completely excluded from the whole system. To solve the control problem, a novel control framework is established by infinite-dimensional backstepping method combining with adaptive compensation technique based on passive identifier. Then, an adaptive state-feedback controller is explicitly constructed which guarantees that all the states of the resulting closed-loop system are bounded while those of the original system converge to zero. A simulation example is provided to validate the effectiveness of the proposed theoretical results. • The restrictions of the existing literature imposed on boundary dynamics and system uncertainties are greatly relaxed since a dynamic boundary condition at control end is considered while unknown parameters are allowed in both the intra-domain and the dynamic boundary in the paper. • A novel passive identifier is designed, combining which with the infinite-dimensional backstepping method, a novel control framework is established that can compensate both the boundary dynamics and system uncertainties, and in turn to stabilize the system under investigation. [ABSTRACT FROM AUTHOR]