Variables and Equations in Hybrid Systems with Structural Changes

In many models of physical systems, structural changes are common. Such structural changes may cause a variable to change from a differential variable to an algebraic variable, or to a variable that is not defined by an equation at all. Most hybrid modelling languages either restrict the kind of structural changes that may be modelled, or they require several different language elements to model the different kinds of structural changes. This paper proposes a new language element that can be used in combination with conditional equations to model structural changes. The language element is used to declare unknowns in equations, and thus makes a distinction between variables that are unknown in the equations and variables that are not determined by the equations. Examples are given in which unknown declarations are used for modelling steady state initialization, multi-body collision, and higher index systems. Unknown declarations can also be used to clarify the structure of the system of equations, and they can help the modeller detect structurally singular systems of equations.