Stochastic Model Predictive Control for Constrained Networked Control Systems with Random Time Delay

Abstract In this paper the continuous time stochastic constrained optimal control problem is formulated for the class of networked control systems assuming that time delays follow a discrete-time, finite Markov chain. Polytopic overapproximations of the system's trajectories are employed to produce a polyhedral inner approximation of the non-convex constraint set resulting from imposing the constraints in continuous time. The problem is cast in a Markov jump linear systems (MJLS) framework and a stochastic MPC controller is calculated explicitly, offline, coupling dynamic programming with parametric piecewise quadratic (PWQ) optimization. The calculated control law leads to stochastic stability of the closed loop system, in the mean square sense and respects the state and input constraints in continuous time.

[1]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[2]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[3]  Nathan van de Wouw,et al.  On polytopic inclusions as a modeling framework for systems with time-varying delays , 2010, Autom..

[4]  Panos J. Antsaklis,et al.  Stability of model-based networked control systems with time-varying transmission times , 2004, IEEE Transactions on Automatic Control.

[5]  Alberto Bemporad,et al.  Stability analysis of stochastic Networked Control Systems , 2010, Proceedings of the 2010 American Control Conference.

[6]  Panos J. Antsaklis,et al.  Guest Editorial Special Issue on Networked Control Systems , 2004, IEEE Trans. Autom. Control..

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

[8]  Laurentiu Hetel,et al.  LMI control design for a class of exponential uncertain systems with application to network controlled switched systems , 2007, 2007 American Control Conference.

[9]  Panos J. Antsaklis,et al.  Control and Communication Challenges in Networked Real-Time Systems , 2007, Proceedings of the IEEE.

[10]  Wpmh Maurice Heemels,et al.  Stability and stabilization of networked control systems , 2010 .

[11]  Nathan van de Wouw,et al.  Robust Stability of Networked Control Systems with Time-varying Network-induced Delays , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[12]  S. Hirche,et al.  Stability, stabilization and experiments for networked control systems with random time delay , 2008, 2008 American Control Conference.

[13]  Nathan van de Wouw,et al.  Comparison of overapproximation methods for stability analysis of networked control systems , 2010, HSCC '10.

[14]  Carlos Silvestre,et al.  Control of impulsive renewal systems: Application to direct design in networked control , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[15]  Panagiotis Patrinos,et al.  Convex parametric piecewise quadratic optimization: Theory and algorithms , 2011, Autom..

[16]  Nathan van de Wouw,et al.  Stabilization of Networked Control Systems with large delays and packet dropouts , 2008, 2008 American Control Conference.

[17]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[18]  Nathan van de Wouw,et al.  Stability of Networked Control Systems With Uncertain Time-Varying Delays , 2009, IEEE Transactions on Automatic Control.

[19]  Y. Tipsuwan,et al.  Control methodologies in networked control systems , 2003 .

[20]  Mircea Lazar,et al.  On Polytopic Approximations of Systems with Time-Varying Input Delays , 2009 .

[21]  Yang Shi,et al.  Output Feedback Stabilization of Networked Control Systems With Random Delays Modeled by Markov Chains , 2009, IEEE Transactions on Automatic Control.

[22]  Johan Nilsson,et al.  Stochastic Analysis and Control of Real-Time Systems with Random Time Delays , 1996 .

[23]  R. P. Marques,et al.  Markov Jump Linear Systems , 2005 .

[24]  Raja Sengupta,et al.  An H/sub /spl infin// approach to networked control , 2005, IEEE Transactions on Automatic Control.

[25]  Biao Huang,et al.  A new method for stabilization of networked control systems with random delays , 2005, Proceedings of the 2005, American Control Conference, 2005..

[26]  Jamal Daafouz,et al.  Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays , 2006, IEEE Transactions on Automatic Control.

[27]  Sandra Hirche,et al.  Sampled-data Networked Control Systems with Random Time Delay , 2008 .