From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems

DOI10.1142/S0218127417501048zbMath1370.70049OpenAlexW2739215887MaRDI QIDQ5357148

Ahmed Chemori, Hassène Gritli, Safya Belghith, Nahla Khraief Haddad

Publication date: 14 September 2017

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127417501048

zbMATH Keywords

limit cyclesHopf bifurcationnormal formcenter manifoldIDA-PBC control

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Equilibria and periodic trajectories for nonlinear problems in mechanics (70K42) Bifurcations and instability for nonlinear problems in mechanics (70K50) Control of mechanical systems (70Q05) Invariant manifolds for ordinary differential equations (34C45) Normal forms for nonlinear problems in mechanics (70K45) Bifurcation control of ordinary differential equations (34H20)

Related Items

LMI-based synthesis of a robust saturated controller for an underactuated mechanical system subject to motion constraints

Uses Software

• MATCONT

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Elements of applied bifurcation theory.
• Bifurcation analysis and dynamic behaviour of an inverted pendulum with bounded control
• Global bifurcation analysis of a controlled underactuated mechanical system
• FROM FIRST LYAPUNOV COEFFICIENTS TO MAXIMAL CANARDS
• Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment
• MATCONT
• LOCAL BIFURCATION ANALYSIS IN THE FURUTA PENDULUM VIA NORMAL FORMS
• The Hamilton-Type Principle in Fluid Dynamics
• Analysis and Control of Underactuated Mechanical Systems