LMI-Based Control Design for Output Regulation Problem of Linear Systems in the Presence of Limited Measurement Streams

This paper deals with the output regulation problem of a linear time-invariant system in the presence of sporadically available measurement streams. A regulator with a continuous intersample injection term is proposed, where the intersample injection is provided by a linear dynamical system and the state of which is reset with the arrival of every new measurement updates. The resulting system is augmented with a timer triggering an instantaneous update of the new measurement and the overall system is then analyzed in a hybrid system framework. With the Lyapunov based stability analysis, we offer sufficient conditions to ensure the objectives of the output regulation problem are achieved under intermittency of the measurement streams. Then, from the solution to linear matrix inequalities, a numerically tractable regulator design procedure is presented. Finally, with the help of an illustrative example, the effectiveness of the theoretical results are validated.

[1]  Ricardo G. Sanfelice,et al.  L2 State Estimation with Guaranteed Convergence Speed in the Presence of Sporadic Measurements , 2018, ArXiv.

[2]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[3]  Ricardo G. Sanfelice,et al.  Hybrid Dynamical Systems: Modeling, Stability, and Robustness , 2012 .

[4]  D. Lawrence,et al.  Output regulation for linear systems with sampled measurements , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[5]  Daniele Astolfi,et al.  Emulation-based semiglobal output regulation of minimum phase nonlinear systems with sampled measurements , 2018, 2018 European Control Conference (ECC).

[6]  Nathan van de Wouw,et al.  Emulation-based output regulation of linear networked control systems subject to scheduling and uncertain transmission intervals , 2019, IFAC-PapersOnLine.

[7]  Ricardo G. Sanfelice,et al.  State estimation of linear systems in the presence of sporadic measurements , 2016, Autom..

[8]  Jie Huang,et al.  Nonlinear Output Regulation: Theory and Applications , 2004 .

[9]  Dragan Nesic,et al.  A Framework for the Observer Design for Networked Control Systems , 2012, IEEE Transactions on Automatic Control.

[10]  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).

[11]  João P. Hespanha,et al.  Output regulation for non‐square linear multi‐rate systems , 2014 .

[12]  Ricardo G. Sanfelice,et al.  LMI-Based Output Feedback Control Design in the Presence of Sporadic Measurements , 2020, 2020 American Control Conference (ACC).

[13]  Lorenzo Marconi,et al.  About a Post-processing Design of Regression-like Nonlinear Internal Models , 2017 .

[14]  S. Hara,et al.  Output Regulation for Sampled-Data Feedback Systems: Internal Model Principle and H∞ Servo Controller Synthesis , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[15]  Kim-Chuan Toh,et al.  Solving semidefinite-quadratic-linear programs using SDPT3 , 2003, Math. Program..