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 stability and feasibility properties of the control scheme are formally proven, and verified in a detailed numerical simulation.