Attitude stabilization of rigid spacecraft with minimal attitude coordinates and unknown time-varying delay

Abstract

The delayed feedback stabilization of rigid spacecraft attitude dynamics in the presence of an unknown time-varying delay in the measurement is addressed. The attitude representation is parameterized using minimal attitude coordinates. The time-varying delay and its derivative are assumed to be bounded. By employing a linear state feedback controller via a Lyapunov-Krasovskii functional, a general delaydependent stability condition is characterized for the closed-loop parameterized system in terms of a linear matrix inequality(LMI) whose solution gives the suitable controller gains. An estimate of the region of attraction of the controlled system is also obtained, inside which the asymptotic stability of parameterized system is guaranteed. Index Terms attitude dynamics, linear matrix inequality, Lyapunov-Krasovskii functional, time-delay, region of attraction. I. INTRODUCTION Feedback stabilization of rigid body attitude dynamics is an important control problem, see e.g. [1]-[5], with a wide range of applications such as spacecraft attitude maneuvers [6], [7],

Multirate iterative learning disturbance observer with measurement delay compensation for flexible spacecraft attitude stabilization subject to complex disturbances

“…To stabilize the spacecraft attitude system with robustness to delayed state feedback, a DC-MILDO-based robust composite controller is designed following Lyapunov-Krasovskii approach (Chunodkar and Akella, 2011;Samiei and Butcher, 2013).…”

Attitude stabilization of a rigid spacecraft based on MRPs with unknown bounded time-delay

“…Ailon [5] apply a nonlinear attitude controller and analysis the system when time delay is induced, sufficient conditions for exponential stability is therefore established. Ehsan Samiei and Eric Butcher [6] propose a linear delayed state feedback controller for a rigid spacecraft at the presence of stochastic noise and time-varying delay in the measurement, instead of determining controller gain matrix from transcendental characteristic equation of the nominal system [7] , the author employed a direct Lyapunov-Krasovskii functional.…”

An attitude cooperative control for multi‐spacecraft systems with arbitrary input delay time‐variation rate: A dynamic event‐triggered approach

“…On the other hand, many important results on stability and control with data transmission delay were proposed in the literature. [19][20][21][22][23][24] For example, by Lyapunov Razumikhin's theory, the problem of attitude synchronization for spacecraft formation with communication time-varying delays was solved in Reference 19. In literature, 20 the attitude synchronous tracking control of multi-spacecraft time-delay systems was studied.…”

“…Under the event‐triggered mechanism, the weighted average consensus problem of multi‐agent systems in directed networks with time‐varying communication delays was discussed in Reference 23. By adopting the event‐triggered control methods, some sufficient conditions for the flocking problem for the nonlinear multi‐agent systems with time‐varying delays were given in Reference 24. More on the time‐delay problems of cooperative control can be found in the literature 25‐28 .…”