Modeling Hybrid Systems with MLD Approach and Analysis of the Model Size and Complexity
Recently, a great amount of interest has been shown
in the field of modeling and controlling hybrid systems. One of the
efficient and common methods in this area utilizes the mixed logicaldynamical
(MLD) systems in the modeling. In this method, the
system constraints are transformed into mixed-integer inequalities by
defining some logic statements. In this paper, a system containing
three tanks is modeled as a nonlinear switched system by using the
MLD framework. Comparing the model size of the three-tank system
with that of a two-tank system, it is deduced that the number of
binary variables, the size of the system and its complexity
tremendously increases with the number of tanks, which makes the
control of the system more difficult. Therefore, methods should be
found which result in fewer mixed-integer inequalities.
 A. Bemporad and M. Morari, "Control of systems integrating logic,
dynamic and constraints," Automatica, vol. 35, no. 3, Mar. 1999, pp.
 W. P. M. H. Heemels, J. M. Schumacher, "Linear Complementarity
systems," SIAM J. Appl. Math., vol. 60, no. 4, pp. 1234-1269,2000.
 B. D. Schutter and T. van den Boom, "Model predictive control for maxplus-
linear discrete event systems," Automatica, vol. 37, no. 7, pp. 1049-
 E. D. Sontag, "Nonlinear regulation: the piecewise linear approach,"
IEEE Trans. Automat. Contr., 26(2), pp. 346-358, Apr.1981.
 B. De Schutter and B. De Moor," The extended linear complementarity
problem and the modeling and analysis of hybrid systems," in Haybrid
Systems V, P. Antsaklis, W.Kohn, M. Lemmon, A. Nerode, and S.
Sastry, Eds. New York: Spring- verlag, vol. 1567, Lecture Notes in
Computer Science, pp. 70-85,1999.
 W. P. Maurice H. Heemles and Bart De Schutter and Alberto Bemporad,
"Equivalence of hybrid dynamical models," Automatica, vol. 37, no. 7,
pp. 1085-1091, July 2001.
 Domenico Mignone "Control and Estimation of Hybrid Systems with
mathematical Optimization", PhD Thesis, Swiss Federal Institute of
Technology, Zurich, 2002.
 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.
 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.
 M. Morari, Mato Baotic and Francesco Borrelli, "Hybrid system
modeling and control," Europian Journal of Control, 2003.
 J. Habibi, B. Moshiri and A. Khaki Seddigh, "Hybrid Modeling and
Predictive Control of a Multi-Tank System: A Mixed Logical Dynamical
Approach" in Proc. IAWTIC-2005, Vienna Austria, 2005.