Adaptive state estimation for a class of system with nonlinear parametrization

This work presents the problem of state estimation with the adaptive time-varying observer, for a class of nonlinear parameter systems in a linearly growing triangular form. The parameter appears in functions involving the unmeasured state and the bound of it is not known a priori. By extending the technology of constructing the high-gain observer, we explicitly construct an adaptive time-varying observer which converges to the system. We will present a pendulum system to show the feasibility of this technology.