**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30521

##### Online Robust Model Predictive Control for Linear Fractional Transformation Systems Using Linear Matrix Inequalities

**Authors:**
Peyman Sindareh Esfahani,
Jeffery Kurt Pieper

**Abstract:**

In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the *l*_{2}-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

**Keywords:**
Robust Model Predictive Control,
linear matrix inequality,
state feedback control,
linear fractional transformation

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1130425

**References:**

[1] S. J. Qin, and T. A. Badgwell, “A survey of industrial model predictive control technology”. Control Engineering Practice, (2003). 11(7), 733–764.

[2] J. K. Gruber, C. Bordons, and A. Oliva. "Nonlinear MPC for the airflow in a PEM fuel cell using a Volterra series model." Control Engineering Practice 20.2 (2012): 205-217.

[3] A. Santucci, A. Sorniotti, and C. Lekakou. "Power split strategies for hybrid energy storage systems for vehicular applications." Journal of Power Sources 258 (2014): 395-407.

[4] D. Zhao, C. Liu, R. Stobart, J. Deng., Winward, E., & Dong, G. (2014). An explicit model predictive control framework for turbocharged diesel engines. IEEE Transactions on Industrial Electronics, 61(7), 3540-3552.

[5] V. Yaramasu, M. Rivera, M. Narimani, B. Wu, and J. Rodriguez. “Model Predictive Approach for a Simple and Effective Load Voltage Control of Four-Leg Inverter With an Output Filter.” IEEE Transactions on Industrial Electronics 61, no. 10 (2014): 5259-5270.

[6] P. Sindareh-Esfahani, S. S. Tabatabaei, J. K. Pieper, “Model Predictive Control of a Heat Recovery Steam Generator during Cold Startup Operation Using Piecewise Linear Models”. Applied Thermal Engineering, (2017) http://dx.doi.org/10.1016/j.applthermaleng.2017.03.041

[7] M. R. Amini, M. Shahbakhti, S. Pan, and J. K. Hedrick. "Bridging the gap between designed and implemented controllers via adaptive robust discrete sliding mode control." Control Engineering Practice 59 (2017): 1-15.

[8] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert. "Constrained model predictive control: Stability and optimality." Automatica 36, no. 6 (2000): 789-814.

[9] M.R. Amini, M. Razmara, and M. Shahbakhti, “Robust Model-Based Discrete Sliding Mode Control of an Automotive Electronic Throttle Body”. SAE International Journal of Commercial Vehicles, 10(2017-01-0598).

[10] M. V. Kothare, V. Balakrishnan, and M. Morari. "Robust constrained model predictive control using linear matrix inequalities." Automatica 32, no. 10 (1996): 1361-1379.

[11] F. A. Cuzzola, J. C. Geromel, and M. Morari. "An improved approach for constrained robust model predictive control." Automatica 38, no. 7 (2002): 1183-1189.

[12] D. Q. Mayne, S. V. Raković, R. Findeisen, and F. Allgöwer. "Robust output feedback model predictive control of constrained linear systems." Automatica 42, no. 7 (2006): 1217-1222.

[13] L. Zhang. "Automatic offline formulation of robust model predictive control based on linear matrix inequalities method." In Abstract and Applied Analysis, vol. 2013. Hindawi Publishing Corporation, 2013.

[14] J. Yang, Y. Chen, F. Zhu, K. Yu, and X. Bu. "Synchronous switching observer for nonlinear switched systems with minimum dwell time constraint." Journal of the Franklin Institute 352, no. 11 (2015): 4665-4681.

[15] P. J. Campo, M. Morari. “Robust model predictive control.” In Proceedings of the American control conference, (1987) pp. 1021–1026. Minneapolis, MN.

[16] Z. Q. Zheng, and M. Morari. "Robust stability of constrained model predictive control." In American Control Conference, 1993, pp. 379-383. IEEE, 1993.

[17] P. Sindareh-Esfahani, A. Ghaffari, P. Ahmadi. Thermodynamic modeling based optimization for thermal systems in heat recovery steam generator during cold start-up operation. Applied Thermal Engineering. 2014 Aug 31;69(1):286-96.

[18] P. Sindareh-Esfahani, E. Habibi-Siyahposh, M. Saffar-Avval, A. Ghaffari, F. Bakhtiari-Nejad. Cold start-up condition model for heat recovery steam generators. Applied Thermal Engineering. 2014 Apr 30;65(1):502-12.

[19] F. Borrelli, A. Bemporad, and M. Morari. "Predictive control for linear and hybrid systems." Cambridge February 20 (2011): 2011.

[20] G. R. Duan, and H. Yu. LMIs in Control Systems: Analysis, Design and Applications. CRC Press, 2013.

[21] G. V., Jeremy, and R. D. Braatz. "A tutorial on linear and bilinear matrix inequalities." Journal of process control 10, no. 4 (2000): 363-385.

[22] S. P. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan. “Linear matrix inequalities in system and control theory”. Vol. 15. Philadelphia: Society for industrial and applied mathematics, 1994.