Adaptive attitude tracking control with parameter identification by shaping invariant manifold

The nonlinear adaptive attitude control problem is considered with the focus on the identification of unknown system parameters. The unknown parameters are assumed to be constant and the quaternion representation of the kinematic equations is adopted to avoid the singularity in three-parameter representations. In addition to the global asymptotic convergence of the tracking error to zero, the parameter identification is guaranteed with a simple reference signal. The parameter identification procedures rely on the shaping of the invariant manifold introduced in the adaptation algorithm. The main contribution of the paper is to propose the algorithm to identify the unknown system parameters without designing reference signals for the satisfaction of a rank condition. In order to guarantee the convergence of the estimator to the true system parameters, a three-stage estimation algorithm is proposed. At each stage, the system has a different invariant manifold in its closed-loop system dynamics. Numerical simulations demonstrate the effectiveness of the proposed method.