Differentially Flat Control Systems

Muruhan Rathinam, Department of Applied Mathematics, Caltech

A (non linear) control system is said to be differentially flat if one can find a set of outputs (equal in number to the number of inputs) such that given these outputs as functions of time the states and inputs of the system can be uniquely determined without any integration. Differentially flat systems are interesting because the problem of trajectory generation can be solved in a simple way. In this talk I shall explain the tools from Exterior Differential Systems and Prolongations (primarily due to Cartan) and their relevance to flatness. Also a brief summary of existing theory for single input systems will be given. Very little results are available for multi input systems and it is not easy to determine if a given system is flat or not. Latter part of the talk will describe interesting examples of simple mechanical systems (multi input) and our attempts to determine the flatness (or otherwise) of these systems.