5 citations · 15 across the 17 of their papers we have counts for
14 papers · 1 filter
Differentiable Invariant Sets for Hybrid Limit Cycles with Application to Legged Robots
Varun Madabushi, Akash Harapanahalli, Samuel Coogan +1
For hybrid systems exhibiting periodic behavior, analyzing the invariant set containing the limit cycle is a natural way to study the robustness of the closed-loop system. However,…
Learning Certified Neural Network Controllers Using Contraction and Interval Analysis
Akash Harapanahalli, Samuel Coogan, Alexander Davydov
We present a novel framework that jointly trains a neural network controller and a neural Riemannian metric with rigorous closed-loop contraction guarantees using formal bound prop…
Automatic and Scalable Safety Verification using Interval Reachability with Subspace Sampling
Brendan Gould, Akash Harapanahalli, Samuel Coogan
Interval refinement is a technique for reducing the conservatism of traditional interval based reachability methods by lifting the system to a higher dimension using new auxiliary…
linrax: A JAX Compatible, Simplex Method Linear Program Solver
Brendan Gould, Akash Harapanahalli, Samuel Coogan
We present linrax, the first simplex based linear program (LP) solver compatible with the JAX ecosystem. In many control algorithms, LPs are often automatically generated and frequ…
A Linear Differential Inclusion for Contraction Analysis to Known Trajectories
Akash Harapanahalli, Samuel Coogan
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially…
A Global Coordinate-Free Approach to Invariant Contraction on Homogeneous Manifolds
Akash Harapanahalli, Samuel Coogan
In this work, we provide a global condition for contraction with respect to an invariant Riemannian metric on reductive homogeneous spaces. Using left-invariant frames, vector fiel…
Efficient Reachable Sets on Lie Groups Using Lie Algebra Monotonicity and Tangent Intervals
Akash Harapanahalli, Samuel Coogan
In this paper, we efficiently compute overapproximating reachable sets for control systems evolving on Lie groups, building off results from monotone systems theory and geometric i…
: A Parallelizable and Differentiable Toolbox for Interval Analysis and Mixed Monotone Reachability in JAX
Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
We present an implementation of interval analysis and mixed monotone interval reachability analysis as function transforms in Python, fully composable with the computational framew…
Interval Signal Temporal Logic from Natural Inclusion Functions
Luke Baird, Akash Harapanahalli, Samuel Coogan
We propose an interval extension of Signal Temporal Logic (STL) called Interval Signal Temporal Logic (\ISTL). Given an STL formula, we consider an interval inclusion function for…
Forward Invariance in Neural Network Controlled Systems
Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
We present a framework based on interval analysis and monotone systems theory to certify and search for forward invariant sets in nonlinear systems with neural network controllers.…
Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loops
Saber Jafarpour, Akash Harapanahalli, Samuel Coogan
In this paper, we propose a computationally efficient framework for interval reachability of systems with neural network controllers. Our approach leverages inclusion functions for…
A Toolbox for Fast Interval Arithmetic in numpy with an Application to Formal Verification of Neural Network Controlled Systems
Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
In this paper, we present a toolbox for interval analysis in numpy, with an application to formal verification of neural network controlled systems. Using the notion of natural inc…
Contraction-Guided Adaptive Partitioning for Reachability Analysis of Neural Network Controlled Systems
Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neur…
Interval Reachability of Nonlinear Dynamical Systems with Neural Network Controllers
Saber Jafarpour, Akash Harapanahalli, Samuel Coogan
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network…