Attitude dynamics stabilization with unknown delay in feedback control implementation
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This work addresses the problem of stabilizing attitude dynamics with an unknown delay in feedback. Two cases are considered: 1) constant time-delay 2) time-varying time-delay. This is to our best knowledge the first result that provides asymptotically stable closed-loop control design for the attitude dynamics problem with an unknown delay in feedback. Strict upper bounds on the unknown delay are assumed to be known. The time-varying delay is assumed to be made of the constant unknown delay with a time-varying perturbation. Upper bounds on the magnitude and rate of the time-varying part of the delay are assumed to be known. A novel modification to the concept of the complete type Lyapunov-Krasovskii (L-K) functional plays a crucial role in this analysis towards ensuring stability robustness to time-delay in the control design. The governing attitude dynamic equations are partitioned to form a nominal system with a perturbation term. Frequency domain analysis is employed in order to construct necessary and sufficient stability conditions for the nominal system. Consequently, a complete type L-K functional is constructed for stability analysis that includes the perturbation term. As an intermediate step, an analytical solution for the underlying Lyapunov matrix is obtained. Departing from previous approaches, where controller parameter values are arbitrarily chosen to satisfy the sufficient conditions obtained from robustness analysis, a systematic numerical optimization process is employed here to choose control parameters so that the region of attraction is maximized. The estimate of the region of attraction is directly related to the initial angular velocity norm and the closed-loop system is shown to be stable for a large set of initial attitude orientations.