Constrained Parameter Update Law for Adaptive Control

In this paper, a constrained parameter update law is derived in the context of adaptive control. The parameter update law is based on constrained optimization technique where a Lagrangian is formulated to incorporate the constraints on the parameters using inverse Barrier function. The constrained parameter update law is used to develop a adaptive tracking controller and the overall stability of the adaptive controller along with the constrained parameter update law is shown using Lyapunov analysis and development in stability of constrained primal-dual dynamics. The performance of the constrained parameter update law is tested in simulation for keeping the parameters within constraints and convergence to true parameters.