Robust model predictive control for discrete-time fractional-order systems

In this paper we propose a tube-based robust model predictive control scheme for fractional-order discretetime systems of the Grünwald-Letnikov type with state and input constraints. We first approximate the infinite-dimensional fractional-order system by a finite-dimensional linear system and we show that the actual dynamics can be approximated arbitrarily tight. We use the approximate dynamics to design a tube-based model predictive controller which endows to the controlled closed-loop system robust stability properties.

[1]  M. Bettayeb,et al.  A New Approach for Stability Analysis of Linear Discrete-Time Fractional-Order Systems , 2010 .

[2]  Tadeusz Kaczorek,et al.  Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems , 2009, Int. J. Appl. Math. Comput. Sci..

[3]  Pantelis Sopasakis,et al.  Controlled Drug Administration by a Fractional PID , 2014 .

[4]  Xi Li,et al.  Generalized predictive control for fractional order dynamic model of solid oxide fuel cell output power , 2010 .

[5]  Faouzi Bouani,et al.  Model Predictive Control of fractional systems using numerical approximation , 2014, 2014 World Symposium on Computer Applications & Research (WSCAR).

[6]  M. Bettayeb,et al.  Discrete-Time Fractional-Order Systems: Modeling and Stability Issues , 2012 .

[7]  Panos Macheras,et al.  Power law IVIVC: an application of fractional kinetics for drug release and absorption. , 2010, European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences.

[8]  A. Dokoumetzidis,et al.  IVIVC of controlled release formulations: physiological-dynamical reasons for their failure. , 2008, Journal of controlled release : official journal of the Controlled Release Society.

[9]  Moritz Diehl,et al.  Robust dynamic programming for min-max model predictive control of constrained uncertain systems , 2004, IEEE Transactions on Automatic Control.

[10]  Panos Macheras,et al.  The Changing Face of the Rate Concept in Biopharmaceutical Sciences: From Classical to Fractal and Finally to Fractional , 2011, Pharmaceutical Research.

[11]  Roberto Hernández Berlinches,et al.  Generalized Predictive Control of Arbitrary Real Order , 2010 .

[12]  James B. Rawlings,et al.  Postface to “ Model Predictive Control : Theory and Design ” , 2012 .

[13]  Djalil Boudjehem,et al.  The use of fractional order models in predictive control , 2010 .

[14]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[15]  Miguel Romero,et al.  Fractional-Order Generalized Predictive Control: Formulation and some properties , 2010, 2010 11th International Conference on Control Automation Robotics & Vision.

[16]  Miguel Romero,et al.  GPC strategies for the lateral control of a networked AGV , 2009, 2009 IEEE International Conference on Mechatronics.

[17]  Miguel Romero,et al.  Fractional-Order Generalized Predictive Control: Application for Low-Speed Control of Gasoline-Propelled Cars , 2013 .

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

[19]  R. Tyrrell Rockafellar,et al.  Variational Analysis , 1998, Grundlehren der mathematischen Wissenschaften.

[20]  Peter Gritzmann,et al.  Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Basis , 1993, SIAM J. Discret. Math..

[21]  Richard Magin,et al.  Fractional kinetics in multi-compartmental systems , 2010, Journal of Pharmacokinetics and Pharmacodynamics.

[22]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

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

[24]  Miguel Romero,et al.  A survey of Fractional-Order Generalized Predictive Control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[25]  Stefan Domek Fuzzy Predictive Control of Fractional-Order Nonlinear Discrete-Time Systems , 2011 .

[26]  A. Kurzhanski,et al.  Ellipsoidal Calculus for Estimation and Control , 1996 .

[27]  S. Domek Switched State Model Predictive Control of Fractional‐Order Nonlinear Discrete‐Time Systems , 2013 .

[28]  I. Podlubny Fractional differential equations , 1998 .

[29]  Pantelis Sopasakis,et al.  MPC for Sampled-Data Linear Systems: guaranteeing continuous-time positive invariance , 2014 .

[30]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .