Feedback Refinement Relations for the Synthesis of Symbolic Controllers

TL;DR

This paper introduces feedback refinement relations for automated symbolic controller synthesis, enabling robust control with quantized state information and practical implementation considerations.

Contribution

It proposes a novel feedback refinement relation concept, providing a systematic method for abstraction and refinement in symbolic controller synthesis.

Findings

Feedback refinement relations are introduced as a new theoretical tool.

The methodology allows for robust control under uncertainties and disturbances.

Practical examples demonstrate the effectiveness of the approach.

Abstract

We present an abstraction and refinement methodology for the automated controller synthesis to enforce general predefined specifications. The designed controllers require quantized (or symbolic) state information only and can be interfaced with the system via a static quantizer. Both features are particularly important with regard to any practical implementation of the designed controllers and, as we prove, are characterized by the existence of a feedback refinement relation between plant and abstraction. Feedback refinement relations are a novel concept introduced in this paper. Our work builds on a general notion of system with set-valued dynamics and possibly non-deterministic quantizers to permit the synthesis of controllers that robustly, and provably, enforce the specification in the presence of various types of uncertainties and disturbances. We identify a class of abstractions that is canonical in a well-defined sense, and provide a method to efficiently compute canonical abstractions. We demonstrate the practicality of our approach on two examples.