State and Parameter Estimation for Nonlinearly Parameterized Systems: AnH∞-Based Approach?

We present a framework for estimating states and parameters in systems that can be described by a detectable linear system perturbed by a nonlinear function of the states, exogenous signals, and a vector of unknown, constant parameters. The estimators designed in this framework consist of two interconnected modules: a parameter estimator that is constructed as though the states and the nonlinear perturbation were directly available for measurement; and an observer/perturbation estimator that estimates the states as well as the perturbation. The design methodology is based on satisfying an H∞ condition, which leaves the designer with a wide range of options for carrying out the design. We discuss the use of LMI-based techniques in particular, and illustrate their application on a simulation example. We also discuss how the results of the paper can be applied to a more general class of cascaded nonlinear systems.