On Generalized Homogenization of Linear Quadrotor Controller

A novel scheme for an "upgrade" of a linear control algorithm to a non-linear one is developed based on the concepts of a generalized homogeneity and an implicit homogeneous feedback design. Some tuning rules for a guaranteed improvement of a regulation quality are proposed. Theoretical results are confirmed by real experiments with the quadrotor QDrone of Quanser™.

[1]  L. S. Husch,et al.  Topological characterization of the dilation and the translation in Frechet spaces , 1970 .

[2]  J. Coron,et al.  Adding an integrator for the stabilization problem , 1991 .

[3]  Roland Siegwart,et al.  Full control of a quadrotor , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

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

[5]  Andrey Polyakov,et al.  Sliding mode control design using canonical homogeneous norm , 2019 .

[6]  Denis V. Efimov,et al.  Finite-time and fixed-time observer design: Implicit Lyapunov function approach , 2018, Autom..

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

[8]  Igor Boiko Non-parametric Tuning of PID Controllers , 2012 .

[9]  A. Bacciotti,et al.  Liapunov functions and stability in control theory , 2001 .

[10]  J. Pearson Linear multivariable control, a geometric approach , 1977 .

[11]  M. Kawski GEOMETRIC HOMOGENEITY AND STABILIZATION , 1995 .

[12]  Konstantin Zimenko,et al.  Robust Feedback Stabilization of Linear MIMO Systems Using Generalized Homogenization , 2020, IEEE Transactions on Automatic Control.

[13]  Eduardo Sontag Input to State Stability: Basic Concepts and Results , 2008 .

[14]  Willie L. Roberts,et al.  On systems of ordinary differential equations , 1961 .

[15]  Denis Efimov,et al.  Integral Control Design using the Implicit Lyapunov Function Approach , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[16]  Andrey Polyakov,et al.  On homogeneity and its application in sliding mode control , 2014, Journal of the Franklin Institute.

[17]  Andrey Polyakov,et al.  Generalized Homogeneity in Systems and Control , 2020 .

[18]  Hisakazu Nakamura,et al.  Smooth Lyapunov functions for homogeneous differential inclusions , 2002, Proceedings of the 41st SICE Annual Conference. SICE 2002..

[19]  Andrey Polyakov,et al.  On Homogeneous Finite-Time Control for Linear Evolution Equation in Hilbert Space , 2018, IEEE Transactions on Automatic Control.

[20]  Y. ORLOV,et al.  Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems , 2004, SIAM J. Control. Optim..

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