Adaptive control schemes for systems with unknown drift and control directions

In this thesis, we consider two adaptive control problems containing unknown 2×2 or 3×3 orthogonal matrices. The first one refers to the adaptive control problem for systems with unknown drift vector directions where the certainty-equivalence principle can be applied with overparameterization. The second one refers to the adaptive control problem for drift-free systems with unknown control directions where the certainty-equivalence principle cannot be applied without making other assumptions such as satisfaction of restrictive matching conditions. For both these adaptive control problems, we propose new non-certainty equivalent adaptive controllers that ensure asymptotic convergence of the tracking error to the origin for most initial conditions while simultaneously enforcing orthogonality on the matrix estimate for all time. In addition to stability proofs, numerical simulations are presented to illustrate the closed-loop performance of the resulting controller designs.