Automated Formal Synthesis of Provably Safe Digital Controllers for Continuous Plants

We present a sound and automated approach to synthesizing safe,
digital controllers for physical plants represented as time-invariant models.
Models are linear differential equations with inputs, evolving over a continuous
state space. The synthesis precisely accounts for the effects of finite-precision
arithmetic introduced by the controller. The approach uses counterexampleguided inductive synthesis (CEGIS): an inductive generalization phase produces a controller that is known to stabilize the model but that may not be
safe for all initial conditions of the model. Safety is then verified via Bounded
Model Checking: if the verification step fails, a counterexample is provided
to the inductive generalization, and the process further iterates until a safe
controller is obtained. We demonstrate the practical value of this approach by
automatically synthesizing safe controllers for physical plant models from the
digital control literature.