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Adaptive controller and observer design for a class of nonlinear systems

The design of a stable adaptive controller and observer for a class of nonlinear systems is considered. Stable adaptive observer designs in the existing literature are generally based on the assumption that the nonlinearities in the system dynamics are functions of measured variables and inputs. In this work, a broader class of nonlinear systems that contain the product of an unmeasurable state and an unknown parameter are considered. The nonlinear system is transformed into a suitable form which allows for the design of a stable adaptive controller and a stable nonlinear observer using a parameter dependent Lyapunov function. The design process is shown on a simple example and then extended to the general case. Simulation results on two distinct examples are shown and discussed for the proposed scheme.