Symbolic control of incrementally stable systems

Antoine Girard


Advances in control systems technology demand that we make constant progresses in the design of controllers achieving always more complex specifications such as safety and reachability requirements, sequencing of tasks, fault-tolerance, etc... Symbolic control approaches offer the possibility to deal with such specifications by abstracting the continuous dynamics of the control system under consideration. In this talk, we will present an approach based on the notion of approximate bisimulation, that applies to incrementally stable systems. More precisely, we will show that under the assumption of incremental stability, it is possible to compute discrete dynamic systems, called symbolic models, that are accurate descriptions of the original control system. These symbolic models can be used for controller synthesis and enable to leverage all the control techniques of discrete dynamic systems theory. Refinements of these discrete controllers can then be used to control the original system. Moreover, by carefully handling the discrete synthesis, these refined controllers can be certified correct by design. We will also briefly present the most recent advances for improving scalability of this approach.

Presentation Slides