Other Articles by Authors

Roberd Saragih

Authors and WSEAS

Roberd Saragih

WSEAS Transactions on Mathematics

Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018

Bilinear Control based on Linear Matrix Inequalities

AUTHORS: Roberd Saragih

Download as PDF

In this paper we consider the bilinear model in the cell cycle specific cancer chemotherapy. The realistic control schemes have to deal with parametric uncertainties, hence, we apply the robust control to maximize both the bone marrow mass and the dose over the treatment interval. The robust control for bilinear system requires a solution to the state dependent algebraic Riccati equation. The bilinear system is described as polytopic parameter varying systems where state vector as parameter varying. The formulation of controller synthesis is done with reformulated the bilinear matrix inequalities in linear matrix inequalities for each subsystem on a polytope. Feasible solution which satisfies the linear matrix inequalities for design the controller is found. From the numerical calculations, we obtain the optimal treatment that prevent excessive destruction of the bone marrow based on the specific weights in our objective functional.

KEYWORDS: Robust control, bilinear system, cell-cycle-specific, LPV system


[1] Beom-Soo Kim and Myo-Taeg Lim, “Robust 𝐻𝐻∞ control method for bilinear systems”, International Journal of Control, Automation and Systems, Vol.1, No.2, pp. 171-177, 2003.

[2] G.H. Yang, J. Lam and J. Wang, “Robust control of uncertain nonlinear systems”, Proc. of the 35th Conference on Decision and Control, pp. 823-828, 1996.

[3] I. Masubuchi, A. Ohara and N. Suda, “LMI- based controller synthesis: a unified formulation and solution,” International Journal of Robust and Nonlinear Control, vol 8, pp. 669-686, 1998.

[4] K. Renee Fister and John Carl Panetta, “Optimal control applied to cell-cycle-specific cancer chemotherapy,” SIAM J. Math., Vol. 60, No. 3, pp. 1059-1072, 2000.

[5] R. Saragih and Widowati, “Coprime factor reduction of parameter varying controller,” International Journal of Control, Automation, and Systems, vol. 6, no. 6, pp. 836-844, December 2008.

[6] S. Boyd, Ghaoui, L.E. Feron, and V. Balakrishnan, “LMI in system and control theory”, SIAM, Philadelphia, 1994.

[7] Solikhatun, Saragih, R., Joelianto, E., Naiborhu, J., “Robust 𝐻𝐻∞ control for bilinear systems using the dynamic takagi-sugeno fuzzy models based on linear matrix inequalities”, International Journal of Control and Automation, 9(7), pp. 7-22, 2016.

[8] W. M. Lu and J. C. Doyle, “𝐻𝐻∞ control of nonlinear systems: A convex characterization”, IEEE Trans. Automatic Control, vol 40, pp. 1668-1675, 1995.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #43, pp. 352-358

Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

Bulletin Board


The editorial board is accepting papers.

WSEAS Main Site