Linear Time Logic Control of Linear Systems

The control of complex hybrid systems poses new challenges that fall beyond the traditional approaches of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several modules in a network of interacting systems. The desired objectives are no longer captured by the usual control specifications, such as stabilization or output regulation. Instead, we consider specifications given by Linear Temporal Logic (LTL) formulas. We show that existence of controllers for discrete time controllable systems and LTL specifications can be decided and that such controllers can be effectively computed. The closed loop system is of hybrid nature combining the original continuous dynamics with the automatically synthesized switching logic required to enforce the specification.