Safe and Robust Observer-Controller Synthesis using Control Barrier Functions

TL;DR

This paper develops a method for designing safe, robust controllers for nonlinear systems with partial state information, using observer-controller co-design and control barrier functions to ensure safety under disturbances.

Contribution

It introduces two novel approaches for synthesizing observer-controller interconnections with safety guarantees, combining stability analysis and control barrier functions.

Findings

Successfully maintains safety in simulations and experiments on a quadrotor.

Ensures Lipschitz continuity of controllers for reliable implementation.

Provides a systematic way to co-design observers and controllers for safety.

Abstract

This paper addresses the synthesis of safety-critical controllers using estimate feedback. We propose an observer-controller interconnection to ensure that the nonlinear system remains safe despite bounded disturbances on the system dynamics and measurements that correspond to partial state information. The co-design of observers and controllers is critical, since even in undisturbed cases, observers and controllers designed independently may not render the system safe. We propose two approaches to synthesize observer-controller interconnections. The first approach utilizes Input-to-State Stable observers, and the second uses Bounded Error observers. Using these stability and boundedness properties of the observation error, we construct novel Control Barrier Functions that impose inequality constraints on the control inputs which, when satisfied, certifies safety. We propose quadratic program-based controllers to satisfy these constraints, and prove Lipschitz continuity of the derived controllers. Simulations and experiments on a quadrotor demonstrate the efficacy of the proposed methods.