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Finite-time stabilization of underactuated mechanical systems in the presence of uncertainties: application to the cart-pole system

Finite-time stabilization of underactuated mechanical systems in the presence of uncertainties: application to the cart-pole system

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Underactuated mechanical systems [13,14,27] are those systems with less control inputs than generalized coordinates (called also degrees of freedom), i.e., they have unactuated generalized coordinates. For such systems, the unactuated generalized coordinates may indirectly be controlled by the actuated coordinates through the dynamic coupling, inherent to these systems [8]. This coupling is often nonlinear, resulting in generally nonintegrable dynamic constraints and therefore second-order nonholonomic.

Chapter Contents:

  • 8.1 Introduction
  • 8.2 Dynamic modeling of underactuated mechanical systems: Lagrangian formalism
  • 8.3 Control problem formulation
  • 8.4 Preliminaries
  • 8.4.1 Notions of finite stability
  • 8.5 Proposed control design
  • Theorem 8.2
  • 8.6 Numerical simulations: the case of the cart-pole system
  • 8.7 Conclusion
  • References

Inspec keywords: pole assignment; uncertain systems; stability

Other keywords: finite-time stabilization; nonintegrable dynamic constraints; unactuated generalized coordinates; cart-pole system; underactuated mechanical systems; dynamic coupling

Subjects: Control system analysis and synthesis methods; Stability in control theory

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