Modelling and optimisation of general hybrid systems in the continuous time domain

Abstract This paper presents a mathematical formulation for the dynamic optimisation of hybrid processes described by general state-transition networks. In each state, the system behaviour is described by a set of differential and algebraic equations (DAEs). Transitions occur from one state to another whenever certain logical conditions are satisfied. The time horizon of interest is divided into a number of periods of variable duration, with the system potentially being in a different state in each period. Neither the initial nor the final state of the system, nor indeed any of its intermediate states, need to be known a priori. The resulting dynamic optimisation problem involves both continuous and discrete variables and is solved using a complete discretisation approach. Two examples of the application of the proposed methodology are presented.