Self-Triggered Model Predictive Control for Network Scheduling and Control

We present an algorithm for controlling and scheduling multiple linear time-invariant processes on a shared bandwidth-limited communication network using adaptive sampling intervals. The controller is centralized and not only computes at every sampling instant the new control command for a process but also decides the time interval to wait until taking the next sample. The approach relies on model predictive control ideas, where the cost function penalizes the state and control effort as well as the time interval until the next sample is taken. The latter is introduced to generate an adaptive sampling scheme for the overall system such that the sampling time increases as the norm of the system state goes to zero. This paper presents a method for synthesizing such a predictive controller and gives explicit sufficient conditions for when it is stabilizing. Further explicit conditions are given that guarantee conflict free transmissions on the network. It is shown that the optimization problem may be solved offline and that the controller can be implemented as a lookup table of state feedback gains. The simulation studies which compare the proposed algorithm to periodic sampling illustrate potential performance gains.

[1]  Panos J. Antsaklis,et al.  Special Issue on Technology of Networked Control Systems , 2007 .

[2]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[3]  Paulo Tabuada,et al.  Dynamic programming formulation of periodic event-triggered control: Performance Guarantees and co-design , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[4]  Karl Henrik Johansson,et al.  Event-triggered model predictive control of discrete-time linear systems subject to disturbances , 2013, 2013 European Control Conference (ECC).

[5]  Alberto Bemporad,et al.  Energy-aware robust model predictive control based on noisy wireless sensors , 2012, Autom..

[6]  Paulo Tabuada,et al.  Periodic event-triggered control for nonlinear systems , 2013, 52nd IEEE Conference on Decision and Control.

[7]  Guo-Ping Liu,et al.  Improved predictive control approach to networked control systems , 2008 .

[8]  Carlos Silvestre,et al.  Scheduling measurements and controls over networks — Part II: Rollout strategies for simultaneous protocol and controller design , 2012, 2012 American Control Conference (ACC).

[9]  Karl-Erik Årzén,et al.  A simple event-based PID controller , 1999 .

[10]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[11]  K. Åström,et al.  Comparison of Periodic and Event Based Sampling for First-Order Stochastic Systems , 1999 .

[12]  Panagiotis D. Christofides,et al.  Distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements , 2010, Autom..

[13]  W. P. M. H. Heemels,et al.  Model-based periodic event-triggered control for linear systems , 2013, Autom..

[14]  David K. Smith,et al.  Dynamic Programming and Optimal Control. Volume 1 , 1996 .

[15]  W. P. M. H. Heemels,et al.  Periodic Event-Triggered Control for Linear Systems , 2013, IEEE Trans. Autom. Control..

[16]  Manuel Mazo,et al.  An ISS self-triggered implementation of linear controllers , 2009, Autom..

[17]  Patrizio Colaneri,et al.  Regulation of multirate sampled-data systems , 1991 .

[18]  Daniel E. Quevedo,et al.  Robust stability of packetized predictive control of nonlinear systems with disturbances and Markovian packet losses , 2012, Autom..

[19]  Sandra Hirche,et al.  On LQG joint optimal scheduling and control under communication constraints , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[20]  W. P. M. H. Heemels,et al.  Analysis of event-driven controllers for linear systems , 2008, Int. J. Control.

[21]  D.E. Quevedo,et al.  Minimizing down-link traffic in networked control systems via optimal control techniques , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[22]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[23]  Xiaofeng Wang,et al.  Self-Triggered Feedback Control Systems With Finite-Gain ${\cal L}_{2}$ Stability , 2009, IEEE Transactions on Automatic Control.

[24]  Clarence W. de Silva,et al.  Compensation for transmission delays in an ethernet-based control network using variable-horizon predictive control , 2006, IEEE Transactions on Control Systems Technology.

[25]  Olaf Stursberg,et al.  Distributed Predictive Control for a Class of Hybrid Systems with Event-Based Communication* , 2013 .

[26]  Wpmh Maurice Heemels,et al.  Self-triggered MPC for constrained linear systems and quadratic costs , 2012 .

[27]  M. Velasco,et al.  The Self Triggered Task Model for Real-Time Control Systems , 2003 .

[28]  Alberto Bemporad,et al.  Event-Based Model Predictive Control and Verification of Integral Continuous-Time Hybrid Automata , 2006, HSCC.

[29]  Dimos V. Dimarogonas,et al.  Event-triggered control for discrete-time systems , 2010, Proceedings of the 2010 American Control Conference.

[30]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[31]  Rolf Findeisen,et al.  Event-based model predictive control for Networked Control Systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[32]  Paulo Tabuada,et al.  To Sample or not to Sample: Self-Triggered Control for Nonlinear Systems , 2008, IEEE Transactions on Automatic Control.

[33]  Frank Allgöwer,et al.  On time-triggered and event-based control of integrator systems over a shared communication system , 2013, Math. Control. Signals Syst..

[34]  Senchun Chai,et al.  Design and stability analysis of networked control systems with random communication time delay using the modified MPC , 2006 .

[35]  Daniel E. Quevedo,et al.  Self-Triggered Model Predictive Control for Network Scheduling and Control , 2012 .

[36]  Sandra Hirche,et al.  A bi-level approach for the design of event-triggered control systems over a shared network , 2014, Discret. Event Dyn. Syst..

[37]  Daniel E. Quevedo,et al.  Packetized MPC with dynamic scheduling constraints and bounded packet dropouts , 2014, Autom..

[38]  Andreas Willig,et al.  Recent and Emerging Topics in Wireless Industrial Communications: A Selection , 2008, IEEE Transactions on Industrial Informatics.

[39]  Dimos V. Dimarogonas,et al.  Self-triggered Model Predictive Control for nonholonomic systems , 2013, 2013 European Control Conference (ECC).

[40]  Edoardo Mosca,et al.  Predictive teleoperation of constrained dynamic systems via Internet-like channels , 2006, IEEE Transactions on Control Systems Technology.

[41]  Paulo Tabuada,et al.  Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks , 2007, IEEE Transactions on Automatic Control.