Multi-agent product systems: Analysis, synthesis and control

This thesis presents new approach to the supervisory control of complex systems modelled as Multi-Agent (MA) products of finite deterministic automata.; First, the centralized supervisory control problem for the MA product is considered. This differs from the standard approach to supervisory control since (i) vector languages are under consideration and (ii) each supervisor can disable only one particular component of a vector event. The notion of MA controllability is introduced and is shown to essentially constitute a necessary and sufficient condition for the synthesis of an MA supervisor. In the case when a given vector language K fails to be MA controllable, an algorithm for finding the infimal MA controllable superlanguage of K is presented. It is also shown that there exists, with respect to the inclusion partial order, a maximal MA controllable sublanguage of K. The results constitute a natural extension of the central classical supervisory control results for scalar systems to the more general MA product system case.; Second, the controllability properties of component structures are investigated. It is proved that the property of MA controllability is preserved under iterative MA product construction. Moreover, it is proved that in this case the MA product of supervisors of subsystems ensures the desired behaviour of the MA product of specifications for the iterative MA product. Several examples illustrate that neither standard controllability nor the second property of MA controllability, so-called MAC2, are preserved under projection operation. However, a sufficient condition for the standard controllability of a component in terms of the original vector specification and the MA product is given. The equality of the vector specification projected on the set of some components of an original MA product and an MA product of the projections on the corresponding components is shown to be a necessary and sufficient condition for the projected specification having MAC2 property. Furthermore, a special class of specifications, namely, state trajectory specifications, for both scalar and vector automata is considered and conditions for the embedding of two specifications are presented.; Third, the notion of the Graph-Relation MA product is introduced. Through this construction, we modify the connection of supervisors and vector system under consideration, and prove that the property of MA controllably remains the necessary and sufficient condition for the existence of a solution to the supervisory control problem. Next, an initial investigation on the MA product under partial observation is presented. The notions of MA observability and MA co-observability are formulated and it is shown that they play a key role in the solution of decentralized supervisory control problems for the MA product. Furthermore, applications to hybrid systems are explored.; Finally, a line of further research on centralized and decentralized MA product is mapped out, as well as complexity studies and the generation of MA software.