Quadratically constrained attitude control via semidefinite programming

We consider the attitude control problem augmented with an arbitrary number of nonconvex quadratic constraints. By utilizing the implicit magnitude constraint of the state vector (i.e., quaternion), we are able to reduce this problem to a convex quadratically constrained quadratic program or a semidefinite program. This result leads to an efficient solution strategy for general quadratically constrained attitude control problems. An example demonstrates the proposed methodology.