8 papers
Data-to-Certificates (D2C): Koopman Supereigenfunctions for Stability, Safety, and Control
Umesh Vaidya
Traditional dynamical system models, including Koopman operator representations, are fundamentally equality-based, whereas many analysis and control tools rely on inequalities. Thi…
Spectral Koopman-Hopf Formula for Reachability with Adversary
Sarang Sutavani, Umesh Vaidya
This paper develops a spectral Koopman-Hopf framework for adversarial reachability analysis of nonlinear systems. By lifting the nonlinear drift dynamics into Koopman eigenfunction…
Discovering the Kalman-Bucy-Koopman Filter
Umesh Vaidya
This paper introduces the Kalman-Bucy-Koopman (KBK) filter, a novel framework for nonlinear state estimation grounded in Koopman operator spectral theory. The nonlinear estimation…
RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments
Sriram S. K. S. Narayanan, Umesh Vaidya
This paper presents Residual Koopman MPC (RK-MPC), a Koopman-based, data-driven model predictive control framework for quadruped locomotion that improves prediction fidelity while…
When Koopman Meets Hamilton and Jacobi
Umesh Vaidya
In this paper, we establish a connection between the spectral theory of the Koopman operator and the solution of the Hamilton Jacobi (HJ) equation. The HJ equation occupies a centr…
Dynamical System Approach for Time-Varying Constrained Convex Optimization Problems
Rejitha Raveendran, Arun D. Mahindrakar, Umesh Vaidya
Optimization problems emerging in most of the real-world applications are dynamic, where either the objective function or the constraints change continuously over time. This paper…
Safe Motion Planning for Quadruped Robots Using Density Functions
Sriram S. K. S Narayanan, Andrew Zheng, Umesh Vaidya
This paper presents a motion planning algorithm for quadruped locomotion based on density functions. We decompose the locomotion problem into a high-level density planner and a mod…
Spectral Koopman Method for Identifying Stability Boundary
Bhagyashree Umathe, Umesh Vaidya
The paper is about characterizing the stability boundary of an autonomous dynamical system using the Koopman spectrum. For a dynamical system with an asymptotically stable equilibr…