Control Óptimo-L2 Basado en Red Mediante Funcionales de Lyapunov-Krasovskii

En el presente trabajo se estudia el control optimo con rechazo de perturbaciones  L 2  para sistemas lineales controlados a traves de red. En estos sistemas el lazo de control se cierra utilizando una red de comunicaciones. Entre los problemas que introduce la red se encuentran posibles retrasos, en general aleatorios, asi como perdidas de paquetes. Desde un enfoque basado en funcionales de Lyapunov- Krasovskii (LKF) se aborda el diseno de controladores optimos que, dado un nivel deseado de atenuacion de perturbaciones, estabilicen el sistema minimizando a su vez un funcional de coste. En el articulo se desarrolla, en primer lugar, una formulacion y solucion general para el problema. Posteriormente, se resuelve para un funcional de Lyapunov-Krasovskii particular. El comportamiento de los controladores obtenidos se compara con el dado por un control clasico LQR en un escenario de control de distancia en carretera.

[1]  Sandro Zampieri,et al.  Trends in Networked Control Systems , 2008 .

[2]  James Lam,et al.  Network‐based H∞ control for stochastic systems , 2009 .

[3]  Yiannis S. Boutalis,et al.  A linear matrix inequality approach for guaranteed cost control of systems with state and input delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[4]  B. Azimi-Sadjadi,et al.  Stability of networked control systems in the presence of packet losses , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[5]  Anthony Tzes,et al.  Experimental controller tuning and QoS optimization of a wireless transmission scheme for real-time remote control applications , 2004 .

[6]  S. Sastry,et al.  An LQG Optimal Linear Controller for Control Systems with Packet Losses , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[7]  D. W. Ross,et al.  An Optimal Control Problem for Systems with Differential-Difference Equation Dynamics , 1969 .

[8]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

[9]  Qing-Long Han,et al.  A New $H_{{\bm \infty}}$ Stabilization Criterion for Networked Control Systems , 2008, IEEE Transactions on Automatic Control.

[10]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[11]  C. Calvo,et al.  Sistemas de control basados en red. Modelado y diseño de estructuras de control. , 2011 .

[12]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[13]  Sebastián Dormido,et al.  MUESTREO, CONTROL Y COMUNICACIÓN BASADOS EN EVENTOS , 2008 .

[14]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[15]  Qing-Long Han,et al.  New stability criteria for linear systems with interval time-varying delay , 2008, Autom..

[16]  Yue Dong,et al.  Network-based Robust H_∞ Control of Systems with State-delay and Uncertainty , 2007 .

[17]  Ian R. Petersen,et al.  LMI approach to suboptimal guaranteed cost control for uncertain time-delay systems , 1998 .

[18]  J.P. Hespanha,et al.  Designing an observer-based controller for a network control system , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[19]  C.T. Abdallah,et al.  Inherent issues in networked control systems: a survey , 2004, Proceedings of the 2004 American Control Conference.

[20]  Richard M. Murray,et al.  Optimal LQG control across packet-dropping links , 2007, Syst. Control. Lett..

[21]  Sekhar Tatikonda,et al.  Control under communication constraints , 2004, IEEE Transactions on Automatic Control.

[22]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .

[23]  Michel C. Delfour,et al.  Stability and the Infinite-Time Quadratic Cost Problem for Linear Hereditary Differential Systems , 1975 .

[24]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[25]  Shengyuan Xu,et al.  On Equivalence and Efficiency of Certain Stability Criteria for Time-Delay Systems , 2007, IEEE Transactions on Automatic Control.

[26]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[27]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1996, Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design.

[28]  Huanshui Zhang,et al.  Linear quadratic regulation for linear time-varying systems with multiple input delays part I: discrete-time case , 2005, 2005 International Conference on Control and Automation.

[29]  Dongmei Zhang,et al.  Equivalence of some stability criteria for linear time-delay systems , 2008, Appl. Math. Comput..

[30]  James Lam,et al.  Stabilization of linear systems over networks with bounded packet loss , 2007, Autom..

[31]  Bing Li,et al.  New stability criteria for linear systems with interval time-varying delay , 2013, Proceedings of 2013 2nd International Conference on Measurement, Information and Control.

[32]  V. G. Boltyanskiy.  The Maximum Principle in the Theory of Optimal Processes. , 1961 .

[33]  Hanyong Shao,et al.  New delay-dependent stability criteria for systems with interval delay , 2009, Autom..