Constrained model predictive control of high dimensional Jump Markov linear systems

This paper proposes a model predictive control (MPC) approach for discrete-time jump Markov linear systems (JMLS) considering constraints on the inputs as well as on the expectancy of the states. Prediction equations for the first moment of the states are formulated, in which the dependencies on the inputs, on the expected values of disturbances, and on the current states are directly considered. For the computation of the matrices needed for predicting the first moment of the states, a recursive algorithm is presented. Finally, the prediction equations are used to formulate the MPC problem as a quadratic program (QP). Due to the recursive structure of the prediction equations and the formulation as a QP, the computational effort is low compared to existing approaches. Simulation results demonstrate the properties of the presented MPC approach and its capabilities of controlling large-scale JMLS online.

[1]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

[2]  V. V. Dombrovskii,et al.  Predictive control of random-parameter systems with multiplicative noise. Application to investment portfolio optimization , 2005 .

[3]  Alessandro N. Vargas,et al.  Constrained model predictive control of jump linear systems with noise and non-observed Markov state , 2006, 2006 American Control Conference.

[4]  Zheng Yan,et al.  Stochastic model predictive control of Markov jump linear systems based on a two-layer recurrent neural network , 2013, 2013 IEEE International Conference on Information and Automation (ICIA).

[5]  Dewei Li,et al.  Probabilistic constrained stochastic model predictive control for Markovian jump linear systems with additive disturbance , 2014 .

[6]  Oswaldo Luiz do Valle Costa,et al.  Discrete-time constrained quadratic control of Markovian jump linear systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[7]  Tamer Basar,et al.  Receding horizon control of jump linear systems and a macroeconomic policy problem , 1999 .

[8]  H. Karimi,et al.  A Simplified Predictive Control of Constrained Markov Jump System with Mixed Uncertainties , 2014 .

[9]  Xi Yu-geng,et al.  Constrained MPC of uncertain discrete-time Markovian jump linear systems , 2012, Proceedings of the 31st Chinese Control Conference.

[10]  V. V. Dombrovskii,et al.  Predictive control of systems with Markovian jumps under constraints and its application to the investment portfolio optimization , 2011 .

[11]  Masahiro Ono,et al.  Robust, Optimal Predictive Control of Jump Markov Linear Systems Using Particles , 2007, HSCC.

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

[14]  Masahiro Ono,et al.  A Probabilistic Particle-Control Approximation of Chance-Constrained Stochastic Predictive Control , 2010, IEEE Transactions on Robotics.

[15]  D. Sworder,et al.  Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria , 1975 .

[17]  Alessandro N. Vargas,et al.  Receding horizon control of Markov jump linear systems subject to noise and unobserved state chain , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[18]  Oswaldo Luiz do Valle Costa,et al.  Constrained quadratic state feedback control of discrete-time Markovian jump linear systems , 1999, Autom..

[19]  Wook Hyun Kwon,et al.  Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems , 2002, Autom..

[20]  Wook Hyun Kwon,et al.  Robust Receding Horizon Control of Discrete-Time Markovian Jump Uncertain Systems , 2001 .

[21]  Alberto Bemporad,et al.  Stochastic model predictive control for constrained discrete-time Markovian switching systems , 2014, Autom..

[22]  Alessandro N. Vargas,et al.  Second moment constraints and the control problem of Markov jump linear systems , 2013, Numer. Linear Algebra Appl..

[23]  Vasile Dragan,et al.  On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach , 2014, Syst. Control. Lett..