Representing Hybrid Transition Systems in an Action Language Modulo ODEs

Several physical systems exist in the real world that involve continuous as well as discrete changes. These range from natural dynamic systems like the system of a bouncing ball to robotic dynamic systems such as planning the motion of a robot across obstacles. The key aspects of effectively describing such dynamic systems is to be able to plan and verify the evolution of the continuous components of the system while simultaneously maintaining critical constraints. Developing a framework that can effectively represent and find solutions to such physical systems prove to be highly advantageous. Both hybrid automata and action languages are formal models for describing the evolution of dynamic systems. The action language C+ is a rich and expressive language framework to formalize physical systems, but can be used only with physical systems in the discrete domain and is limited in its support of continuous domain components of such systems. Hybrid Automata is a well established formalism used to represent such complex physical systems at a theoretical level, however it is not expressive enough to capture the complex relations between the components of the system the way C+ does.

This thesis will focus on establishing a formal relationship between these two formalisms by showing how to succinctly represent Hybrid Automata in an action language which in turn is defined as a high-level notation for answer set programming modulo theories (ASPMT) --- an extension of answer set programs in the first-order level. Furthermore, this encoding framework is shown to be more effective and expressive than Hybrid Automata by highlighting its ability in allowing states of a hybrid transition system to be defined by complex relations among components that would otherwise be abstracted away in Hybrid Automata. The framework is further realized in the implementation of the system CPLUS2ASPMT, which takes advantage of state of the art ODE(Ordinary Differential Equations) based SMT solver dReal to provide support for ODE based evolution of continuous components of a dynamic system.