Inductive Certificate Synthesis for Control Design

TL;DR

This thesis presents a framework for synthesizing correct-by-construction controllers for nonlinear dynamical systems using control certificates, ensuring formal guarantees for stability, safety, and reach-while-stay specifications.

Contribution

It introduces a systematic approach to define and find control certificates via an inductive search, enabling automatic controller synthesis with formal correctness guarantees.

Findings

Control certificates can be effectively discovered using the proposed inductive search framework.

Automatically designed controllers demonstrate correctness through simulations and physical experiments.

The framework applies to nonlinear systems with multiple specifications, including stability, safety, and reach-while-stay.

Abstract

The focus of this thesis is developing a framework for designing correct-by-construction controllers using control certificates. We use nonlinear dynamical systems to model the physical environment (plants). The goal is to synthesize controllers for these plants while guaranteeing formal correctness w.r.t. given specifications. We consider different fundamental specifications including stability, safety, and reach-while-stay. Stability specification states that the execution traces of the system remain close to an equilibrium state and approach it asymptotically. Safety specification requires the execution traces to stay in a safe region. Finally, for reach-while-stay specification, safety is needed until a target set is reached. The design task consists of two phases. In the first phase, the control design problem is reduced to the question of finding a control certificate. More precisely, the goal of the first phase is to define a class of control certificates with a specific structure. This definition should guarantee the following: "Having a control certificate, one can systematically design a controller and prove its correctness at the same time." The goal in the second phase is to find such a control certificate. We define a potential control certificate space (hypothesis space) using parameterized functions. Next, we provide an inductive search framework to find proper parameters, which yield a control certificate. Finally, we evaluate our framework. We show that discovering control certificates is practically feasible and demonstrate the effectiveness of the automatically designed controllers through simulations and real physical systems experiments.