Adaptive output feedback control using optimal control modification

In this paper, an observer-based adaptive output feedback controller is developed for a class of strict-feedback nonlinear systems having unmatched uncertainties with unmeasured states. We transform an unmatched uncertain nonlinear system into the system having matched uncertainty through system transformation that forms lumped uncertainties. Since only the output is measurable, we design an adaptive observer based on the transformed nonlinear system to make the output track the given desired trajectory. The adaptive laws are derived using optimal control modification, which allows the use of a large adaptive gain for fast adaptation. This approach is based on an optimal control problem to minimize ℒ₂ norm of the tracking error. Uniformly ultimate boundedness of the overall closed-loop system is analyzed by the Lyapunov stability theory. Simulation results validate the performance of the proposed control approach.