Nonlinear Observer Design Using Metric Based Potentials

Abstract

This thesis addresses observer design for nonlinear dynamical systems which can be approximated with dissipative Hamiltonian realizations. The design methods builds upon earlier developments that allow the approximate dissipative potential to be extracted using a homotopy operator. This potential is obtained by decomposition of the observer error associated one-form using the homotopy operator which generates the potential. A time-varying differential metric equation dependent on the Hessian of the potential and the measured output function is proposed, which is used to design a state observer. The stability of both the observer and metric equation are assessed using Lyapunov theory. A time-invariant metric is then proposed making use of the Hessian of the potential on a metric-state based observer. Using several process simulations, the approach is shown to provide an effective design alternative for nonlinear observer design.