A global continuous control scheme with desired conservative-force compensation for the finite-time and exponential regulation of bounded-input mechanical systems

Global continuous control for the finite-time or (local) exponential stabilization of mechanical systems with bounded inputs is achieved involving desired conservative-force compensation. With respect to the on-line compensation case, the proposed controller entails a closed-loop analysis with considerably higher degree of complexity, whence more involved requirements prove to arise. Other important analytical limitations are further overcome through the developed algorithm. Numerical simulations considering a robotic arm model corroborate the efficiency of the proposed scheme.

[1]  Derong Liu,et al.  Stability of Dynamical Systems , 2008 .

[2]  Arturo Zavala-Río,et al.  Local-homogeneity-based global continuous control for mechanical systems with constrained inputs: finite-time and exponential stabilisation , 2017, Int. J. Control.

[3]  Patrizio Tomei,et al.  Adaptive PD controller for robot manipulators , 1991, IEEE Trans. Robotics Autom..

[4]  Feng Gao,et al.  Robust finite-time control approach for robotic manipulators , 2010 .

[5]  P. Olver Nonlinear Systems , 2013 .

[6]  Isabelle Fantoni,et al.  Global Finite-Time Stability Characterized Through a Local Notion of Homogeneity , 2014, IEEE Transactions on Automatic Control.

[7]  Dennis S. Bernstein,et al.  Geometric homogeneity with applications to finite-time stability , 2005, Math. Control. Signals Syst..

[8]  Jie Huang,et al.  Finite-time control for robot manipulators , 2002, Syst. Control. Lett..

[9]  Suguru Arimoto,et al.  A New Feedback Method for Dynamic Control of Manipulators , 1981 .

[10]  Amit K. Sanyal,et al.  Finite-time stabilisation of simple mechanical systems using continuous feedback , 2015, Int. J. Control.

[11]  Víctor Santibáñez,et al.  Output-feedback proportional–integral– derivative-type control with simple tuning for the global regulation of robot manipulators with input constraints , 2015 .

[12]  M. Kawski Homogeneous Stabilizing Feedback Laws , 1990 .

[13]  R. Murray,et al.  Exponential stabilization of driftless nonlinear control systems using homogeneous feedback , 1997, IEEE Trans. Autom. Control..