The resulting closed-loop system is proven to be uniformly ultimately bounded stability and the effect of the external disturbance on both attitude quaternion and angular velocity can be attenuated to the prescribed level as well.
The proposed control laws guarantee that each rigid body attains desired time-varying attitude and angular velocity while maintaining attitude synchronization with other rigid body.
Then, linear extended state observers (LESO) are constructed to estimate the uncertainties acting on the LTV system in the attitude and angular rate loop.
Using Barbalat׳s Lemma, it is shown that the control laws guarantee each spacecraft approaches the desired time-varying attitude and angular velocity while maintaining attitude synchronization among the other spacecraft in the formation.
In this paper, an optimal PID-like controller is proposed for a spacecraft attitude stabilization problem subject to continuous inequality constraints on the spacecraft angular velocity and control, as well as terminal constraints on the spacecraft attitude and angular velocity.
Using these two potential functions and sliding mode control technique, a nonlinear attitude control law is obtained to guarantee asymptotic convergence of the closed-loop system with consideration of attitude and angular rate constraints, and external disturbances.
Accordingly, the proposed control law depends solely on attitude and angular velocity measurements, and it neither requires knowledge of the spacecraft's inertia parameters nor it works towards estimating these parameters.
First, a new sliding mode controller is designed to ensure the asymptotic convergence of the attitude and angular velocity tracking errors against external disturbances and inertia uncertainties by using a modified differentiator to estimate the total disturbances.
The information required as feedback signals for such a controller is relative –- position, velocity, attitude and angular velocity -and these are expected to be measured or estimated from image data.
The observer possesses one important and novel feature of keeping attitude and angular velocity estimation errors on second-order sliding modes, and thus provides finite-time convergent estimates for each follower.
