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

Abstract

In this paper, we design a hybrid controller that globally exponentially stabilizes a system evolving on the n-dimensional sphere, denoted by S n . This hybrid controller is induced by a "synergistic" collection of potential functions on S n . 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.

Stabilization of Chaotic Systems With Both Uncertainty and Disturbance by the UDE-Based Control Method

“…where x ∈ R 3 , f (x) and B are given as (17). According to [1], the Lorenz system isẋ = f (x), where f (x) is given in (17).…”

“…Unfortunately, there are still many deficiencies in the current research, and in practice this is not the case. For the chaotic systems, a lot of methods have been proposed to investigate the robust stabilization problems, e.g., [16], [17]. However, the disturbance is bounded in some forms is a basic assumption in the most of those methods, such as d(t) belongs to L n 2 [0, +∞), or d(t) is assumed to be L 2 -norm bounded.…”

Global exponential stabilization of a quadrotor by hybrid control

“…Consequently, there exists a compact set U with a bounding ellipsoid E J ( l J ) : = { x ∈ R 6 : x T Jx ⩽ l J } for this system. By considering, according to preposition 1 in Casau et al (2019), there exist ( Q ^ , P ^ ) ∈ R > 0 6 × 6 and K such that the following conditions are satisfied…”

“…The synergistic hybrid feedback was developed in Mayhew and Teel (2013a) to address a global attitude tracking problem. For trajectory tracking of quadrotors in Casau et al (2019), a robust global exponential controller based on this technique was introduced.…”

“…Finally, the proposed controller is contrasted through simulation results, with controllers recommended in Casau et al (2019) and Lee et al (2013). It is recognized that the proposed controller presents significant advantages in both the transient response and in the steady-state response.…”