Finite-time stabilization of a non-autonomous chaotic rotating mechanical system

This paper presents robust adaptive controllers for finite-time stabilization of non-autonomous chaotic horizontal platform systems (HPSs). The effects of uncertainties, unknown parameters and input nonlinearities are fully taken into account. Appropriate adaptation laws are designed to undertake th...

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Bibliographic Details
Published in:Journal of the Franklin Institute 2012-11, Vol.349 (9), p.2875-2888
Main Authors: Aghababa, Mohammad Pourmahmood, Aghababa, Hasan Pourmahmood
Format: Article
Language:English
Subjects:
Adaptation
Adaptive control systems
Applied sciences
Chaos theory
Computer science
control theory
systems
Control system analysis
Control system synthesis
Control theory. Systems
Controllers
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Laws
Mathematical analysis
Nonlinear dynamics and nonlinear dynamical systems
Nonlinearity
Physics
Solid mechanics
Stabilization
Statistical physics, thermodynamics, and nonlinear dynamical systems
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:This paper presents robust adaptive controllers for finite-time stabilization of non-autonomous chaotic horizontal platform systems (HPSs). The effects of uncertainties, unknown parameters and input nonlinearities are fully taken into account. Appropriate adaptation laws are designed to undertake the unknown parameters. Using the adaptation laws and finite-time control theory, first a robust adaptive controller is derived to stabilize the non-autonomous uncertain HPS in finite time. Then, considering the effects of input nonlinearities, another finite-time controller is introduced to stabilize the uncertain HPS with nonlinear control inputs. The finite-time stability and convergence of the proposed schemes are analytically proved. Two illustrative examples are given to show the robustness and feasibility of the proposed finite-time controllers. ► An adaptive robust finite-time controller for chaos suppression of HPS is proposed. ► The effects of nonlinear control inputs are taken into account. ► Two main mathematical theorems are proposed and proved. ► Some numerical simulations are provided to justify the theoretical results.
ISSN:0016-0032
1879-2693
DOI:10.1016/j.jfranklin.2012.08.004