Design of Terminal Sliding-Mode Controllers for Nonlinear Systems with Regional Fixed-Time Stability

Abstract This paper presents a fixed-time control design for a class of uncertain under-actuated nonlinear systems (UNS) using a non-singular fast terminal sliding mode control (TSMC) with a radial basis function (RBF) based estimator to achieve the fast convergence and robustness against the uncertain disturbances. The generalized mathematical model of the considered class is first reduced into an equivalent regular form, which is more convenient for any control synthesis design. A fast TSMC is designed for the transformed regular form to improve the control performance and annihilate the associated singularity problem of the conventional TSMC scheme. The steering of sliding manifold and system states in fixed-time is ensured through the Lyapunov stability theory. The RBF-based neural networks are used to adaptively estimate the nonlinear drift functions, which are feedbacked to the control input. The theoretical design, analysis and simulations of cart-pendulum and quadcopter systems demonstrate the feasibility and benefits of the regular form transformation and the designed control design. Comparing the proposed control synthesis with the standard literature presents the attractive nature of the proposed method for such a class.

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Fast fixed-time convergent smooth adaptive guidance law with terminal angle constraint for interception of maneuvering targets

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410020965094 ◽

2020 ◽

pp. 095441002096509

Author(s):

Peng Zhang ◽

Xiaoyu Zhang

Keyword(s):

Stability Theory ◽

Sliding Mode ◽

Fixed Time ◽

Guidance System ◽

Time Stability ◽

Terminal Sliding Mode ◽

Guidance Law ◽

Maneuvering Targets ◽

System States ◽

Terminal Angle Constraint

This paper introduces a fast fixed-time guidance law with terminal angle constraint for interception of maneuvering targets, which is based on the structure of singularity-free fast terminal sliding mode and the fixed-time stability theory. Different from the finite-time stability, the fixed-time stability can predefine the maximum stabilization time of system states which is independent on the initial value of system states. Under the proposed guidance law, the guidance system can achieve stabilization within settling time which decides by the parameters of controller. In addition, an adaptive law is proposed which alleviate the chattering of sliding mode and smooths the guidance law. Meanwhile, the proof of the sliding mode manifold and system states fixed-time convergence is given by Lyapunov stability theory. Finally, numerical simulations demonstrate the performance of the proposed guidance law is satisfying.

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Nonsingular terminal sliding-mode control of nonlinear planar systems with global fixed-time stability guarantees

Automatica ◽

10.1016/j.automatica.2018.06.032 ◽

2018 ◽

Vol 95 ◽

pp. 561-565 ◽

Cited By ~ 25

Author(s):

Maria Letizia Corradini ◽

Andrea Cristofaro

Keyword(s):

Sliding Mode Control ◽

Sliding Mode ◽

Fixed Time ◽

Terminal Sliding Mode Control ◽

Time Stability ◽

Terminal Sliding Mode ◽

Mode Control ◽

Nonsingular Terminal Sliding Mode ◽

Planar Systems

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Smooth adaptive fixed time convergent controller design for BTT missiles with uncertainties

The Aeronautical Journal ◽

10.1017/aer.2019.151 ◽

2019 ◽

Vol 124 (1273) ◽

pp. 323-345

Author(s):

Y. Yun ◽

S. Tang ◽

J. Guo ◽

Y. Yun

Keyword(s):

Control Algorithm ◽

Performance Metrics ◽

Controller Design ◽

Sliding Mode ◽

Fixed Time ◽

Convergence Time ◽

Control Input ◽

Time Stability ◽

Terminal Sliding Mode ◽

Satisfactory Performance

ABSTRACTA smooth adaptive sliding-mode-based controller is developed for BTT missiles considering nonlinear couplings and aerodynamic uncertainties, wherein fixed-time stability theory is synthesised into sliding-mode control algorithm, such that control variables follow the desired command within fixed-bounded convergence time. Unlike other terminal sliding-mode-related works, the bound of settling time is independent of initial states, indicating that performance metrics, for instance the convergence rate, can be evaluated in advance. The control input is designed to be intrinsically smooth, based on adaptive estimations, and therefore the problem of singularity and chattering is effectively eliminated. Simulation results demonstrate the satisfactory performance and validate the effectiveness of the designed approach.

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