Hybrid Modeling and Optimal Control of a Two-Tank System as a Switched System

Authors: H. Mahboubi, B. Moshiri, A. Khaki Seddigh

Abstract:

In the past decade, because of wide applications of hybrid systems, many researchers have considered modeling and control of these systems. Since switching systems constitute an important class of hybrid systems, in this paper a method for optimal control of linear switching systems is described. The method is also applied on the two-tank system which is a much appropriate system to analyze different modeling and control techniques of hybrid systems. Simulation results show that, in this method, the goals of control and also problem constraints can be satisfied by an appropriate selection of cost function.

Keywords: Hybrid systems, optimal control, switched systems, two-tank system

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1327451

References:

[1] X. Xu and P. J. Antsaklis, "Optimal control of switched systems based on parameterization of the switching instants," IEEE Trans. Automat. Contr., vol. 49, no. 1, pp. 2-16, 2004.
[2] A. Bemporad, F. Borrelli, and M. Morari. Optimal controllers for hybrid systems: stability and piecewise linear explicit form. In Proceedings of the 39th IEEE Conference on Decision and Control, pages 1810-1815, 2000.
[3] A. Giua, C. Seatzu, and C. Van Der Mee. Optimal control of switched autonomous linear systems. In Proceedings of the 40th IEEE Conference on Decision and Control, pages 2472-2477, 2001.
[4] A. Giua, C. Seatzu, and C. Van Der Mee. Optimal control of autonomous linear systems switched with a pre-assigned finite sequence. In Proceedings of the 2001 IEEE International Symposium on Intelligent Control, pages 144-149, 2001.
[5] S. Hedlund and A. Rantzer. Optimal control of hybrid system. In Proceedings of the 38th IEEE Conference on Decision and Control, pages 3972-3977, 1999.
[6] M.S. Branicky, V.S. Borkar, and S.K. Mitter. A unified framework for hybrid control: model and optimal control theory. IEEE Transactions on Automatic Control, 43(1):31-45, January 1998.
[7] B. Piccoli. Hybrid systems and optimal control. In Proceedings of the 37th IEEE Conference on Decision and Control, pages 13-18, 1998.
[8] X. Xu and P.J. Antsaklis. An approach for solving general switched linear quadratic optimal control problems. In Proceedings of the 40th IEEE Conference on Decision and Control, pages 2478-2483, 2001.
[9] X. Xu and P.J. Antsaklis. Optimal control of switched systems: new results and open problems. In Proceedings of the 2000 American ControlConference, pages 2683-2687, 2000
[10] X. Xu and P.J. Antsaklis. Optimal control of switched systems via nonlinear optimization based on direct differentiations of value functions. International Journal of Control, 75(16/17):1406-1426, 2002.
[11] X. Xu and P.J. Antsaklis. Results and perspectives on computational methods for optimal control of switched systems. In Hybrid Systems: Computation and Control (HSCC 2003), LNCS 2623, pages 540-555, Springer, 2003.
[12] X. Xu. Analysis and design of switched systems. PhD thesis, University of Notre Dame, August 2001. Also available at: http://ece.bd.psu.edu/_xu/
[13] T. Bas┬©ar and G.J. Olsder. Dynamic Noncooperative Game Theory, Second Edition. SIAM, 1999.
[14] O. Stursberg and S. Engell, "Optimal Control of Switched Continues Systems using Mixed-Integer Programing," in Proc. 42nd IEEE Conference on Decision and Control, Hawaii USA, 2003, pp. 640-645
[15] Domenico Mignone "Control and Estimation of Hybrid Systems with mathematical Optimization", PhD Thesis, Swiss Federal Institute of Technology Zurich, 2002
[16] J. Till, S. Engell, S. Panek and Olaf Stursberg , "Applied hybrid system optimization: an empirical investigation of complexity," Control Engineering Practice, vol. 12, pp. 1291-1303,2004.