Feedback Stabilization and Output Tracking for Discrete-Time Lipschitz Nonlinear Systems via Iterative Convex Approximations

The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs for dynamic systems in which the nonlinearity belongs to Lipschitz functions have been proposed. However, most of them only focus on output feedback and consequently, state feedback design remains less developed. To that end, this paper is dedicated to the problem of full-state feedback controller design for discrete-time Lipschitz nonlinear systems. In addition, we present a simple iterative method for improving the convergence of the closed-loop performance. It is later demonstrated that our approach can be conveniently extended and utilized for output tracking.

[1]  Knud D. Andersen,et al.  The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algorithm , 2000 .

[2]  Nikolaos Gatsis,et al.  Robust Control for Renewable-Integrated Power Networks Considering Input Bound Constraints and Worst Case Uncertainty Measure , 2018, IEEE Transactions on Control of Network Systems.

[3]  P. Pagilla,et al.  Controller and observer design for Lipschitz nonlinear systems , 2004, Proceedings of the 2004 American Control Conference.

[4]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[5]  Qing Zhao,et al.  H/sub /spl infin// observer design for lipschitz nonlinear systems , 2006, IEEE Transactions on Automatic Control.

[6]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

[7]  Wim Michiels,et al.  Combining Convex–Concave Decompositions and Linearization Approaches for Solving BMIs, With Application to Static Output Feedback , 2011, IEEE Transactions on Automatic Control.

[8]  D. Siljak,et al.  Robust stability and stabilization of discrete-time non-linear systems: The LMI approach , 2001 .

[9]  Fucheng Liao,et al.  Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications , 2020 .

[10]  Masoud Abbaszadeh,et al.  Static Output Feedback Control for Nonlinear Systems subject to Parametric and Nonlinear Uncertainties , 2016, ArXiv.

[11]  Jianghai Hu,et al.  A sequential parametric convex approximation method for solving bilinear matrix inequalities , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[12]  Keum-Shik Hong,et al.  Stabilization and tracking control for a class of nonlinear systems , 2011 .

[13]  Hieu Minh Trinh,et al.  Robust observer and observer-based control designs for discrete one-sided Lipschitz systems subject to uncertainties and disturbances , 2019, Appl. Math. Comput..

[14]  Mohsen Ekramian,et al.  Observer-based controller for Lipschitz nonlinear systems , 2017, Int. J. Syst. Sci..

[15]  Muhammad Afzal Lashari,et al.  Stabilization and tracking control for a class of discrete-time nonlinear systems , 2015, 2015 12th International Bhurban Conference on Applied Sciences and Technology (IBCAST).

[16]  Chun-Yi Su,et al.  Observer-based control of discrete-time Lipschitzian non-linear systems: application to one-link flexible joint robot , 2005 .

[17]  Nikolaos Gatsis,et al.  Time-Varying Sensor and Actuator Selection for Uncertain Cyber-Physical Systems , 2017, IEEE Transactions on Control of Network Systems.

[18]  Ahmad Afshar,et al.  Observer-based tracking controller design for a class of Lipschitz nonlinear systems , 2018 .