Abstract: This paper provides a robust stabilization method
for rotational motion of underwater robots against parameter
uncertainties. Underwater robots are expected to be used for
various work assignments. The large variety of applications of
underwater robots motivates researchers to develop control systems
and technologies for underwater robots. Several control methods
have been proposed so far for the stabilization of nominal system
model of underwater robots with no parameter uncertainty. Parameter
uncertainties are considered to be obstacles in implementation of the
such nominal control methods for underwater robots. The objective
of this study is to establish a robust stabilization method for rotational
motion of underwater robots against parameter uncertainties. The
effectiveness of the proposed method is verified by numerical
simulations.
Abstract: We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.