Complexity and Size Analysis of Hybrid System Modeling with Mixed Logical Dynamical Approach

Recently, a great amount of interest has been shown in the field of modeling and control of hybrid systems. One of the efficient methods in this area utilizes the mixed logical-dynamical (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 using the MLD framework. Regarding this three-tank modeling, an n-tank system is modeled and number of binary and continuous auxiliary variables and also number of mixed-integer inequalities are obtained in terms of n. Then, the system size and complexity due to increase in number of tanks are considered. It is concluded that as the number of tanks increases, the system size and complexity increase exponentially which hampers control of the system. Therefore, methods should be found which result in fewer variables