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Motivated by a vaccination coverage problem, we consider here a zero-sum differential game governed by a differential system consisting of a hyperbolic partial differential equation (PDE) and an ordinary differential equation (ODE). Two…

Analysis of PDEs · Mathematics 2024-12-18 Mauro Garavello , Elena Rossi , Abraham Sylla

We develop a game-theoretic framework for adversarially robust optimal safe predefined-time stabilization of parameter-dependent nonlinear dynamical systems with nonquadratic cost functionals. Our approach ensures that all system…

Optimization and Control · Mathematics 2025-11-20 Nick-Marios T. Kokolakis , Shanqing Liu , Jerome Darbon , Rahul Mangharam , George Em Karniadakis

Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions that prevent future failures. While in theory, HJ reachability can synthesize safe…

Robotics · Computer Science 2025-12-16 Kensuke Nakamura , Lasse Peters , Andrea Bajcsy

Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…

Computer Science and Game Theory · Computer Science 2021-02-02 Pranav Ashok , Krishnendu Chatterjee , Jan Kretinsky , Maximilian Weininger , Tobias Winkler

Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can…

Robotics · Computer Science 2023-06-13 Albert Lin , Somil Bansal

We study zero-sum stochastic differential games with player dynamics governed by a nondegenerate controlled diffusion process. Under the assumption of uniform stability, we establish the existence of a solution to the Isaac's equation for…

Optimization and Control · Mathematics 2019-03-20 Ari Arapostathis , Vivek S. Borkar , K. Suresh Kumar

Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and…

Systems and Control · Electrical Eng. & Systems 2024-08-23 Milan Ganai , Sicun Gao , Sylvia Herbert

We propose a new reachability learning framework for high-dimensional nonlinear systems, focusing on reach-avoid problems. These problems require computing the reach-avoid set, which ensures that all its elements can safely reach a target…

Systems and Control · Electrical Eng. & Systems 2025-02-18 Jingqi Li , Donggun Lee , Jaewon Lee , Kris Shengjun Dong , Somayeh Sojoudi , Claire Tomlin

A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the…

Optimization and Control · Mathematics 2009-09-29 A J Shaiju , Sheetal Dharmatti

This paper studies a variant of multi-player reach-avoid game played between intruders and defenders. The intruder team tries to score by sending as many intruders as possible to the target area, while the defender team tries to minimize…

Systems and Control · Electrical Eng. & Systems 2021-05-04 Daigo Shishika , Vijay Kumar

We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…

Analysis of PDEs · Mathematics 2020-02-25 Manh-Khang Dao , Boualem Djehiche

Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…

Optimization and Control · Mathematics 2025-02-25 Vincent Liu , Chris Manzie , Peter M. Dower

This paper investigates an infinite-horizon problems in the one-dimensional calculus of variations, arising from the Ramsey model of endogeneous economic growth. Following Chichilnisky, we introduce an additional term, which models concern…

Economics · Quantitative Finance 2015-11-03 Ivar Ekeland , Yiming Long , Qinglong Zhou

Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations. As a result, unmanned aerial systems traffic management is needed to ensure the safety and goal satisfaction of potentially…

Multiagent Systems · Computer Science 2017-02-01 Mo Chen , Qie Hu , Jaime Fisac , Kene Akametalu , Casey Mackin , Claire Tomlin

Westudy how a planner can design dynamic interventions to overcome status-quo inertia in living temporal games, where strategic agents control their state (active, sleep, partially dead) on a temporal network. Building on the…

Theoretical Economics · Economics 2026-05-20 Madjid Eshaghi Gordji , Ali Jabbari , Mohammad Ali Berahman , Esmaiel Abounoori

We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…

Systems and Control · Electrical Eng. & Systems 2024-09-04 Saber Jafarpour , Zishun Liu , Yongxin Chen

Hamilton-Jacobi (HJ) reachability is a method that provides rigorous analyses of the safety properties of dynamical systems. This method has been successfully applied to many low-dimensional dynamical system models such as coarse models of…

Optimization and Control · Mathematics 2016-09-20 Mo Chen , Sylvia Herbert , Claire J. Tomlin

In this paper, we establish a zero-sum, hybrid state stochastic game model for designing defense policies for cyber-physical systems against different types of attacks. With the increasingly integrated properties of cyber-physical systems…

Computer Science and Game Theory · Computer Science 2017-10-03 Fei Miao , Quanyan Zhu , Miroslav Pajic , George J. Pappas

With the continuous advancement in autonomous systems, it becomes crucial to provide robust safety guarantees for safety-critical systems. Hamilton-Jacobi Reachability Analysis is a formal verification method that guarantees performance and…

Systems and Control · Electrical Eng. & Systems 2024-01-01 Qian Wang , Tianhao Wu

We study a zero-sum stochastic differential switching game in infinite horizon. We prove the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities…

Optimization and Control · Mathematics 2018-05-04 Brahim El Asri , Sehail Mazid