Supervisory Control of Discrete Event Systems

PDSLAB has made many important contributions to supervisory control of discrete event systems. Some specific accomplishments include:

• Developed techniques to resolve uncertainty in models of discrete event systems. Earlier work concerning control of discrete event systems assume that a correct model of the system to be controlled is available. (SIAM Journal on Control and Optimization, Jan 95)
• Developed techniques to solve extremal supervisory control problems by posing them as solving inequations in lattices. Many formulas developed for supervisory control can be derived very simply by results from this theory. (Theoretical Computer Science, Nov 95)
• Introduced notion of control in the max-plus algebra for timed discrete event systems. It is shown that the conditions for controllability of a timed DES performance specification can be expressed as inequations on the lattice of sequences of event occurrence times. Optimal behaviors are then found as extremal solutions to inequations using fixed point results. (IEEE Trans. on Automatic Control, Feb 96).
• Introduced an algebra of probabilistic languages (p-languages). The set of p-languages is a complete partial order and the operators defined are continuous in it. That is, recursive equations may be defined in this algebra using fixpoints of continuous functions. It is also shown that the set of p-languages forms a complete metric space in which many useful operators are contractions. Again, Banach's fixed point theorem provides solutions to equations in p-languages. (IEEE Trans. on Automatic Control, 99, IEEE Trans. on Auto. Control 2001).
• Generalized Ramadge and Wonham's framework for optimal control. It is shown that network flow techniques can be used to solve optimal control problem under complete as well as partial observation. (SIAM J. on Control and Optimization, March 95)
• Introduced the notions of stable and dispatchable buffering units for input-output discrete event systems. Provided effectively computable necessary and sufficient conditions for checking existence of such units. This work has applications in manufacturing systems. (IEEE Trans. on Automatic Control, June 95).