Adaptive tracking designs for input-constrained linear systems using backstepping

The problems of adaptive control via state feedback for linear systems with input constraints are addressed. We first study an adaptive tracking design for stable systems in the observable canonical form. Then we consider plants both in the observable canonical form and the parametric-strict-feedback form with a chain of integrators. Our main design tool is backstepping. For both cases, our adaptive controllers ensure global boundedness without restricting the magnitude of the reference signal. However, to achieve perfect tracking certain magnitude constraints on the reference signal are required.