Robust finite time stability and stabilisation: A survey of continuous and discontinuous paradigms

Abstract

The aim of this paper is to provide a survey of the tools for analysis and synthesis of finite time stable controllers. The paper analyses the literature in continuous and discontinuous finite time stabilisation in a unified way covering both the fundamentals as well as the latest techniques available in this non-linear control paradigm. The contribution of the paper lies in its exposition of the robustness properties that continuous and discontinuous controllers guarantee. Some open problems are identified which are relevant to both the theory and practice of finite time stabilisation.

Fixed‐time attitude tracking control for spacecraft based on adding power integrator technique

“…The first set of simulation is conducted for the spacecraft dynamic (4), in which the disturbances and thruster faults are not considered. Figures 2 and 3 show the time responses of the attitude tracking errors q e and the angular velocity tracking errors e driven by the proposed FTC in (5), the proposed AFTC in (8), and the NTSMC in Reference 24. It is shown that all q e and e can converge to |q i | ≤ 2 × 10 −4 and | i | ≤ 2 × 10 −4 rad/s; however, the convergence time spent is different.…”

“…Most of the existing attitude tracking controllers are asymptotically stable controllers. By contrast, finite‐time controllers can make the system states converge to an equilibrium point in finite time, which further provides faster convergence rate, better disturbance rejection, and higher precision performance . The finite‐time control methods can be broadly classified into two categories: the homogeneous method and the Lyapunov method .…”

“…convergence rate, better disturbance rejection, and higher precision performance. 8 The finite-time control methods can be broadly classified into two categories: the homogeneous method 9,10 and the Lyapunov method. 11 The homogeneous method cannot deal with external disturbance or model uncertainty because the exact mathematical model of the control system should be known in advance.…”

Modified method for parameters estimating in finite-time control synthesis

“…Задача разработки финитных (гарантирующих выполнение всех переходных процессов на конечном интервале времени) алгоритмов управления с каждым годом становится все более актуальной, о чем свидетельствует рост числа публикаций по этой тематике (см., например, [1][2][3][4]). В работах [5,6] представлен алгоритм финитной стабилизации цепи последовательно соединенных интеграторов в условиях внешних возмущающих воздействий и параметрических неопределенностей системы.…”