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Article

Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function

1
Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 11021, Colombia
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Laboratorio Inteligente de Energía, Universidad Tecnológica de Bolívar, km 1 vía Turbaco, Cartagena 131001, Colombia
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Grupo GIIEN, Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín 050036, Colombia
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Facultad de Ingenierías, Universidad Tecnológica de Pereira, Pereira 660003, Colombia
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Hydrogen Research Institute, Université du Quebec à Trois-Rivieres, Trois-Rivières, QC 3351, Canada
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Facultad Tecnológica, Universidad Distrital Francisco José de Caldas, Carrera 7 No. 40B-53, Bogotá 11021, Colombia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(11), 1771; https://doi.org/10.3390/sym12111771
Received: 23 September 2020 / Revised: 16 October 2020 / Accepted: 20 October 2020 / Published: 26 October 2020
(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems)
This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software. View Full-Text
Keywords: discrete-inverse optimal control; global exponential stabilization; reaction wheel pendulum; parametric uncertainties; discrete-affine systems; cost functional discrete-inverse optimal control; global exponential stabilization; reaction wheel pendulum; parametric uncertainties; discrete-affine systems; cost functional
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MDPI and ACS Style

Montoya, O.D.; Gil-González, W.; Dominguez-Jimenez, J.A.; Molina-Cabrera, A.; Giral-Ramírez, D.A. Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function. Symmetry 2020, 12, 1771. https://doi.org/10.3390/sym12111771

AMA Style

Montoya OD, Gil-González W, Dominguez-Jimenez JA, Molina-Cabrera A, Giral-Ramírez DA. Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function. Symmetry. 2020; 12(11):1771. https://doi.org/10.3390/sym12111771

Chicago/Turabian Style

Montoya, Oscar Danilo, Walter Gil-González, Juan A. Dominguez-Jimenez, Alexander Molina-Cabrera, and Diego A. Giral-Ramírez. 2020. "Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function" Symmetry 12, no. 11: 1771. https://doi.org/10.3390/sym12111771

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