Predefined-Time Backstepping Control for Tracking a Class of Mechanical Systems

The predefined-time exact tracking of unperturbed fully actuated mechanical systems is considered in this paper. A continuous second-order predefined-time stabilizing backstepping controller, designed using first-order predefined-time stabilizing functions, is developed to solve this problem. As an example, the proposed solution is applied over a two-link planar manipulator and numerical simulations are conducted to show performance of the proposed control scheme.

[1]  Alexander G. Loukianov,et al.  A discontinuous recurrent neural network with predefined time convergence for solution of linear programming , 2014, 2014 IEEE Symposium on Swarm Intelligence.

[2]  Leonid Fridman,et al.  Uniform Second-Order Sliding Mode Observer for mechanical systems , 2010, 2010 11th International Workshop on Variable Structure Systems (VSS).

[3]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

[4]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[5]  A. G. Loukianov,et al.  Predefined-time tracking of a class of mechanical systems , 2016, 2016 13th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE).

[6]  Emilio Roxin,et al.  On finite stability in control systems , 1966 .

[7]  Wilfrid Perruquetti,et al.  Finite-time stability and stabilization: State of the art , 2006 .

[8]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

[9]  Leonid M. Fridman,et al.  Design of a prescribed convergence time uniform Robust Exact Observer in the presence of measurement noise , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[10]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[11]  P.V. Kokotovic,et al.  The joy of feedback: nonlinear and adaptive , 1992, IEEE Control Systems.

[12]  V. Haimo.  Finite time controllers , 1986 .

[13]  Leonid M. Fridman,et al.  Stability notions and Lyapunov functions for sliding mode control systems , 2014, J. Frankl. Inst..

[14]  Alexander G. Loukianov,et al.  Non-Singular Predefined-Time Stable Manifolds , 2016 .

[15]  Alexander G. Loukianov,et al.  Predefined-time stability of dynamical systems with sliding modes , 2015, 2015 American Control Conference (ACC).