Adaptive control schemes specially designed for systems with unknown orthogonal matrix parameters

In this paper, we consider two adaptive control problems for systems containing constant unknown proper orthogonal matrices. The first one refers to the adaptive control problem for drift-free systems with unknown control direction (high-frequency gain). The second one refers to the adaptive control problem for systems with unknown drift directions. For both adaptive control problems, we propose new non-certainty-equivalent adaptive controllers that ensure closed-loop signal boundedness and 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.