# Automated Formal Synthesis of Digital Controllers for State-Space Physical Plants

## TL;DR

This paper introduces an automated method for synthesizing safe digital controllers for linear time-invariant physical plants, combining CEGIS and reachability analysis to ensure stability and safety.

## Contribution

It presents a novel, sound, and automated approach that integrates counterexample guided synthesis with reachability analysis for controller synthesis.

## Key findings

- Successfully synthesizes controllers for complex physical models
- Ensures system safety and stability through formal verification
- Demonstrates effectiveness on digital control benchmarks

## Abstract

We present a sound and automated approach to synthesize safe digital feedback controllers for physical plants represented as linear, time invariant models. Models are given as dynamical equations with inputs, evolving over a continuous state space and accounting for errors due to the digitalization of signals by the controller. Our approach has two stages, leveraging counterexample guided inductive synthesis (CEGIS) and reachability analysis. CEGIS synthesizes a static feedback controller that stabilizes the system under restrictions given by the safety of the reach space. Safety is verified either via BMC or abstract acceleration; if the verification step fails, we refine the controller by generalizing the counterexample. We synthesize stable and safe controllers for intricate physical plant models from the digital control literature.