Adaptive Tracking Control via Immersion and Invariance: An (i)ISS Perspective

This paper studies the immersion and invariance (I&I)-based adaptive tracking problem of nonlinear systems with linear and nonlinear parameterizations. For a linear parameterization of the unknown parameters, a new strict Lyapunov function construction method is first presented for I&I adaptive control systems using the notion of integral input-to-state stability (iISS). This then motivates us to develop a new adaptive I&I tracking control scheme for a class of nonlinearly parameterized systems. Under an ISS small-gain condition, a strict Lyapunov function can be explicitly constructed to show that both global asymptotic tracking and estimation can be achieved uniformly.