A hybrid redesign of Newton observers in the absence of an exact discrete-time model

We study the Newton observer design, developed by Moraal and Grizzle, when the exact discrete-time model of the sampled-data plant is not known analytically. We eliminate the dependence on this exact model with a “hybrid” reconstruction that makes use of continuous-time filters to produce the numerical value of the exact model. We then implement the Newton method with finite-difference and secant approximations for the Jacobian. Despite the continuous-time filters, the proposed hybrid redesign preserves the sampled-data characteristic of the Newton observer because it only employs discrete-time measurements of the output. It also offers flexibility to be implemented with nonuniform, or event-driven, sampling. We finally study how a line search scheme can be incorporated in this hybrid Newton observer to enlarge the region of convergence.