# An Iterative Abstraction Algorithm for Reactive Correct-by-Construction Controller Synthesis

### Robert Mattila, Yilin Mo and Richard M. Murray

Submitted, 2015 International Conference on Hybrid Systems: Computation and Control (HSCC)

In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a finite transition system (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) (GR1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are underand over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the e�ciency of the new abstraction algorithm is illustrated by numerical examples.

- Conference Paper: http://www.cds.caltech.edu/~murray/preprints/mmm15-hscc_s.pdf
- Project(s): iCyPhy