Constrained-Inversion MRAC: An Approach Combining Hard Constraints and Adaptation in Uncertain Nonlinear Systems”

In this work, we propose a design strategy for adaptive control of a class of nonlinear systems with input and state constraints. The systems of interest are required to have relative degree 1 and a convergent zero-dynamics: these properties cover a significant number of applications, after suitable changes of coordinates and with a proper selection of the regulated output. Through a design based on Barrier Lyapunov Functions, inspired by Explicit Reference Governors, we propose a feasible closed-form right-inverse unit that can be effectively interconnected with a nominal adaptive stabilizer, this way enforcing constraint satisfaction, while rejecting the effects of parametric uncertainties at the same time. The stabil- ity and feasibility properties of the control scheme are formally proven, and verified in a detailed numerical simulation.