Optimal solutions of modular supervisory control problems with indecomposable specification languages

This paper concerns supervisory control of large-scale modular discrete event systems (DES) with partial observations and general (indecomposable) specification languages. We have found new methods for computing supremal controllable sublanguages and supremal normal sublanguages independently. Unfortunately, these methods are difficult to put simply together for computation of supremal controllable and normal sublanguages. Therefore, we propose first a new method for computation of supremal controllable sublanguages that can be viewed as a complete observation counterpart of a method we have developed for supremal normal sublanguages. These can be put together in a procedure for computing optimal sublanguages, which avoids building of the global plant. Unlike our previous results, we present both necessary and sufficient structural conditions for modular control synthesis to equal global control synthesis for partially observed modules and general (indecomposable) specification languages