Computational approaches also play an essential role in the control of
complex organizations of systems, from fleets of autonomous aircrafts, to myriad of MEMS.To deal efficiently with complexity, these organizations often have
a hierarchical structure, where the lower levels are usually characterized by continuous-time dynamics
with localized performance objectives, while the higher hierarchical levels
have more supervisory roles and respond and act on discrete events to
achieve a global goal.In designing such Hybrid Systems, it is fundamental to understand what information about the lower level, in a quantized or compressed form, is necessary to the higher level to
complete its task.
Avoiding redundancy greatly reduces the complexity of handling the
information at the higher level.
At the same time, knowing in advance what is the minimum information necessary
reduces the computational burden of verification algorithms.An idealized problem I am considering is the design of a discrete event system that
stabilizes a continuous time system by using the minimum number of symbols.
This problem also arises when the controller is connected to
the plant by communication channels that might be shared among many other
feedback systems.So far have been able to obtain results for stability with quantized state information.
For a linear discrete-time system, the optimal quantizer is {\em logarithmic}.
The extension of the approach to sample-data systems provide a new criterion for optimal sampling and quantization which is related to the problem of minimum attention control recently formulated by Brockett. These results form a basis of a methodology for design of hybrid systems, which are implicitly verified.