Full stability of locally optimal solutions in second-order cone programs

The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to second-order cone programs (SOCPs) expressed entirely in terms of their initial data. These characterizations are obtained via appropriate versions of the quadratic growth and strong second-order sufficient conditions under the corresponding constraint qualifications. We also establish close relationships between full stability of local minimizers for SOCPs and strong regularity of the associated generalized equations at nondegenerate points. Our approach is mainly based on advanced tools of second-order variational analysis and generalized differentiation

Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions

Modern nonlinear control theory seeks to develop feedback controllers that endow systems with properties such as safety and stability. The guarantees ensured by these controllers often rely on accurate estimates of the system state for determining control actions. In practice, measurement model uncertainty can lead to error in state estimates that degrades these guarantees. In this paper, we seek to unify techniques from control theory and machine learning to synthesize controllers that achieve safety in the presence of measurement model uncertainty. We define the notion of a Measurement-Robust Control Barrier Function (MR-CBF) as a tool for determining safe control inputs when facing measurement model uncertainty. Furthermore, MR-CBFs are used to inform sampling methodologies for learning-based perception systems and quantify tolerable error in the resulting learned models. We demonstrate the efficacy of MR-CBFs in achieving safety with measurement model uncertainty on a simulated Segway system