Safe and Robust Observer-Controller Synthesis Using Control Barrier Functions

Abstract

This paper addresses the synthesis of safety-critical controllers using\nestimate feedback. We propose an observer-controller interconnection to ensure\nthat the nonlinear system remains safe despite bounded disturbances on the\nsystem dynamics and measurements that correspond to partial state information.\nThe co-design of observers and controllers is critical, since even in\nundisturbed cases, observers and controllers designed independently may not\nrender the system safe. We propose two approaches to synthesize\nobserver-controller interconnections. The first approach utilizes\nInput-to-State Stable observers, and the second uses Bounded Error observers.\nUsing these stability and boundedness properties of the observation error, we\nconstruct novel Control Barrier Functions that impose inequality constraints on\nthe control inputs which, when satisfied, certifies safety. We propose\nquadratic program-based controllers to satisfy these constraints, and prove\nLipschitz continuity of the derived controllers. Simulations and experiments on\na quadrotor demonstrate the efficacy of the proposed methods.\n