Constrained Model Predictive Control of Processes with Uncertain Structure Modeled by Jump Markov Linear Systems

Linear systems with abrupt changes in its structure, e.g. caused by component failures of a production system, can be modelled by the use of jump Markov linear systems (JMLS). This chapter proposes a finite horizon model predictive control (MPC) approach for discrete-time JMLS considering input constraints as well as constraints for the expectancy of the state trajectory. For the expected value of the state as well as a quadratic cost criterion, recursive prediction schemes are formulated, which consider dependencies on the input trajectory explicitly. Due to the proposed prediction scheme, the MPC problem can be formulated as a quadratic program (QP) exhibiting low computational effort compared to existing approaches. The resulting properties concerning stability as well as computational complexity are investigated and demonstrated by illustrative simulation studies.

[1]  Olaf Stursberg,et al.  Constrained model predictive control of high dimensional Jump Markov linear systems , 2015, 2015 American Control Conference (ACC).

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

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

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

[5]  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.

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

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

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

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

[11]  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.

[12]  Alan J. Lee,et al.  Linear Regression Analysis: Seber/Linear , 2003 .

[13]  Shuai Liu,et al.  Constrained robust distributed model predictive control for uncertain discrete-time Markovian jump linear system , 2015, J. Frankl. Inst..

[14]  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).

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

[16]  Alberto Bemporad,et al.  Stabilizing Model Predictive Control of Stochastic Constrained Linear Systems , 2012, IEEE Transactions on Automatic Control.

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

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

[19]  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..

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

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

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

[23]  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).

[24]  Eric C. Kerrigan,et al.  A condensed and sparse QP formulation for predictive control , 2011, IEEE Conference on Decision and Control and European Control Conference.