Lebesgue-Approximation Model Predictive Control of Nonlinear Sampled-Data Systems

This article studies discrete-time implementation of model predictive control (MPC) algorithms in continuous-time nonlinear sampled-data systems. We present a discrete-time and aperiodic nonlinear MPC algorithm to stabilize continuous-time nonlinear dynamics, based on the Lebesgue approximation model (LAM). In this LAM-based MPC (LAMPC), the sampling instants are triggered by a self-triggered scheme, and the predicted states and transition time instants in the optimal control problem are calculated in an aperiodic manner subject to the LAM. Sufficient conditions are derived on feasibility and stability of the resulting closed-loop systems. According to these conditions, the parameters in LAMPC are designed with the guarantee of exclusion of Zeno behavior. Meanwhile, it is shown that the periodic task model is a special case in our framework with appropriate choice of the parameters in the LAM. Simulation results indicate that LAMPC can dynamically adjust the computation periods and has the potential to reduce the computational costs compared with periodic approaches.

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

[2]  B. Øksendal.  Stochastic Differential Equations , 1985 .

[3]  Xiaofeng Wang,et al.  Sporadic model predictive control using Lebesgue approximation , 2017, 2017 American Control Conference (ACC).

[4]  D. Limón,et al.  Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

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

[6]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[7]  Pantelis Sopasakis,et al.  MPC for Sampled-Data Linear Systems: Guaranteeing Constraint Satisfaction in Continuous-Time , 2014, IEEE Transactions on Automatic Control.

[8]  Moritz Diehl,et al.  An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range , 2011, Autom..

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

[10]  Biao Huang,et al.  Robust digital model predictive control for linear uncertain systems with saturations , 2004, IEEE Trans. Autom. Control..

[11]  W. P. M. H. Heemels,et al.  Resource-aware MPC for constrained nonlinear systems: A self-triggered control approach , 2015, Syst. Control. Lett..

[12]  Hongye Su,et al.  Sampled-data MPC for LPV systems with input saturation , 2014 .

[13]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[14]  W. P. M. H. Heemels,et al.  On integration of event-based estimation and robust MPC in a feedback loop , 2010, HSCC '10.

[15]  Xiaofeng Wang,et al.  Lebesgue approximation model of continuous-time nonlinear dynamic systems , 2016, Autom..

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

[17]  Marko Bacic,et al.  Model predictive control , 2003 .

[18]  Frank Allgöwer,et al.  Robust Event-Triggered MPC for Constrained Linear Discrete-Time Systems with Guaranteed Average Sampling Rate* , 2015 .

[19]  Frank Allgöwer,et al.  Model predictive control of uncertain continuous-time systems with piecewise constant control input: A convex approach , 2008, 2008 American Control Conference.

[20]  Xiaofeng Wang,et al.  Event-Triggering in Cyber-Physical Systems , 2009 .

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

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

[23]  Marcello Farina,et al.  Tube-based robust sampled-data MPC for linear continuous-time systems , 2012, Autom..

[24]  F. Allgöwer,et al.  MODEL PREDICTIVE CONTROL OF CONTINUOUS TIME NONLINEAR DIFFERENTIAL ALGEBRAIC SYSTEMS , 2007 .

[25]  Riccardo Scattolini,et al.  Model predictive control of continuous-time nonlinear systems with piecewise constant control , 2004, IEEE Transactions on Automatic Control.

[26]  F. Fontes.  A General Framework to Design Stabilizing Nonlinear Model Predictive Controllers , 2001 .

[27]  Antonella Ferrara,et al.  Model-based event-triggered robust MPC/ISM , 2014, 2014 European Control Conference (ECC).

[28]  Dimos V. Dimarogonas,et al.  Novel event-triggered strategies for Model Predictive Controllers , 2011, IEEE Conference on Decision and Control and European Control Conference.

[29]  W. P. M. H. Heemels,et al.  Robust self-triggered MPC for constrained linear systems , 2014, 2014 European Control Conference (ECC).

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

[31]  Dimos V. Dimarogonas,et al.  Event-Triggered Strategies for Decentralized Model Predictive Controllers , 2011 .

[32]  S. Shreve,et al.  Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[33]  Antonella Ferrara,et al.  Robust Model Predictive Control With Integral Sliding Mode in Continuous-Time Sampled-Data Nonlinear Systems , 2011, IEEE Transactions on Automatic Control.

[34]  Huiping Li,et al.  Event-triggered robust model predictive control of continuous-time nonlinear systems , 2014, Autom..