MATHEMATICAL LOGIC IN THE MODELING OF CONTROL SYSTEMS

The design of a control strategy involves the consideration of a mathematical model of the corresponding process and includes the solution of a control problem. In particular, optimal control problems are viewed and solved as mathematical programming problems by optimizing an objective function over a feasible region defined by constraints. Clearly, the process model must be expressed in constraint form. However, consistency assumptions regarding the process behavior lead to the consideration of conditional piece-wise functions or logical sentences in the corresponding model that are not in constraint form. For this, two methodologies based on analogies from mathematical logic for the transformation of the aforementioned functions into mixed-integer linear constraints have been developed, and they are presented by applying them in a flow function that is met in the modeling of surface street signal systems.