A formal proof in Coq of a control function for the inverted pendulum

Abstract

Control theory provides techniques to design controllers, or control functions, for dynamical systems with inputs, so as to grant a particular behaviour of such a system. The inverted pendulum is a classic system in control theory: it is used as a benchmark for nonlinear control techniques and is a model for several other systems with various applications. We formalized in the Coq proof assistant the proof of soundness of a control function for the inverted pendulum. This is a first step towards the formal verification of more complex systems for which safety may be critical. CCS Concepts • Mathematics of computing → Ordinary differential equations; Topology; • Computer systems organization → Robotic control; • Software and its engineering → Software verification;