A symbolic approach to controlling piecewise affine systems

Abstract-- We present a computational framework for automatic synthesis of a feedback control strategy for a piecewise affine (PWA) system from a specification given as a Linear Temporal Logic (LTL) formula over an arbitrary set of linear predicates in its state variables. Our approach consists of two main steps. First, by defining appropriate partitions for its state t spaces, we construct a finite abstraction of the PWA system in the form of a control transition system. Second, by leveraging ideas and techniques from Rabin games and LTL model checking, we develop an algorithm to generate a control for the finite abstraction. While provably correct and robust to small perturbations in both state measurements and applied inputs, the overall procedure is conservative and expensive. The proposed algorithms have been implemented and are available for download. Illustrative examples are included.

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Jana Tumova, Boyan Yordanov, Calin Belta, Ivana Cerna, Jiri Barnat
• Keywords: CDC 2010, Control Systems, Feedback Control Strategy, Finite Abstraction, Linear Temporal Logic