Quasi-optimal robust stabilization of control systems

In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that, in the absence of minimal time singular trajectories, the solutions of the closed-loop system converge to the origin in quasi minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances and actuator noise

Robust hybrid global asymptotic stabilization of rigid body dynamics using dual quaternions

A hybrid feedback control scheme is proposed for stabilization of rigid body dynamics (pose and velocities) using unit dual quaternions, in which the dual quaternions and veloc- ities are used for feedback. It is well-known that rigid body attitude control is subject to topological constraints which often result in discontinuous control to avoid the unwinding phenomenon. In contrast, the hybrid scheme allows the controlled system to be robust in the presence of uncertainties, which would otherwise cause chattering about the point of discontinuous control while also ensuring acceptable closed-loop response characteristics. The stability of the closed-loop system is guaranteed through a Lyapunov analysis and the use of invariance principles for hybrid systems. Simulation results for a rigid body model are presented to illustrate the performance of the proposed hybrid dual quaternion feedback control scheme

Hybrid Control for Robust and Global Tracking on Smooth Manifolds

In this paper, we present a hybrid control strategy that allows for global asymptotic tracking of reference trajectories evolving on smooth manifolds, with nominal robustness. Two different versions of the hybrid controller are presented: One which allows for discontinuities of the plant input and a second one that removes the discontinuities via dynamic extension. By taking an exosystem approach, we provide a general construction of a hybrid controller that guarantees global asymptotic stability of the zero tracking error set. The proposed construction relies on the existence of proper indicators and a transport map-like function for the given manifold. We provide a construction of these functions for the case where each chart in a smooth atlas for the manifold maps its domain onto the Euclidean space. We also provide conditions for exponential convergence to the zero tracking error set. To illustrate these properties, the proposed controller is exercised on three different compact manifolds-the two-dimensional sphere, the unit-quaternion group, and the special orthogonal group of order three- A nd further applied to the problems of obstacle avoidance in the plane and global synchronization on the circle

Robust global exponential stabilization on the n-dimensional sphere with applications to trajectory tracking for quadrotors

In this paper, we design a hybrid controller that globally exponentially stabilizes a system evolving on the n-dimensional sphere, denoted by Sn. This hybrid controller is induced by a “synergistic” collection of potential functions on Sn. We propose a particular construction of this class of functions that generates flows along geodesics of the sphere, providing convergence to the desired reference with minimal path length. We show that the proposed strategy is suitable to the exponential stabilization of a quadrotor vehicle