An SDS modeling approach for simulation-based control

We initiate a study of mathematical models for specifying (discrete) simulation-based control systems. It is desirable to specify simulation-based control systems using a model that is intuitive, succinct, expressive, and whose state space properties are relatively easy computationally. We compare automata-based models for specifying control systems and find that all systems that are currently used (such as finite state machines, communicating hierarchical finite state machines (FSM), communicating finite state machines, and Turing machines) lack at least one of the abovementioned features. We propose using sequential dynamical systems (SDS) - a formalism for representing discrete simulations - to specify simulation-based control systems. We show how to adapt the standard SDS model to specify cell-level controllers for a generic cell. For reasonable flexible manufacturing cells, the SDS-based specification has size polynomial in the size of the cell, while in the worst case the FSM-based specification has size exponential in the size of the cell.