Related papers: Solvability of Approximate Reach-Avoid Games
Objective: To obtain explainable guarantees in the online synthesis of optimal controllers for high-integrity cyber-physical systems, we re-investigate the use of exhaustive search as an alternative to reinforcement learning. Approach: We…
A new framework for formulating reachability problems with competing inputs, nonlinear dynamics and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems…
Hybrid dynamical systems with nonlinear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of nonlinear…
With the recent surge of interest in using robotics and automation for civil purposes, providing safety and performance guarantees has become extremely important. In the past, differential games have been successfully used for the analysis…
In this paper, we present a method for finding approximate Nash equilibria in a broad class of reachability games. These games are often used to formulate both collision avoidance and goal satisfaction. Our method is computationally…
We propose a hybrid approach that combines Hamilton-Jacobi (HJ) reachability and mixed-integer optimization for solving a reach-avoid game with multiple attackers and defenders. The reach-avoid game is an important problem with potential…
Hamilton-Jacobi (HJ) reachability analysis has been developed over the past decades into a widely-applicable tool for determining goal satisfaction and safety verification in nonlinear systems. While HJ reachability can be formulated very…
Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
We study the class of reach-avoid dynamic games in which multiple agents interact noncooperatively, and each wishes to satisfy a distinct target criterion while avoiding a failure criterion. Reach-avoid games are commonly used to express…
Hamilton-Jacobi (HJ) reachability analysis is a powerful framework for ensuring safety and performance in autonomous systems. However, existing methods typically rely on a white-box dynamics model of the system, limiting their applicability…
We propose a novel formulation for approximating reachable sets through a minimum discounted reward optimal control problem. The formulation yields a continuous solution that can be obtained by solving a Hamilton-Jacobi equation.…
In this article, we consider the infinite-horizon reach-avoid (RA) and stabilize-avoid (SA) zero-sum game problems for general nonlinear continuous-time systems, where the goal is to find the set of states that can be controlled to reach or…
In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of…
This letter presents a density function based safe control synthesis framework for the pursuit-evasion problem. We extend safety analysis to dynamic unsafe sets by formulating a reach-avoid type pursuit-evasion differential game as a robust…
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…
In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed…
Safety assurance is a critical yet challenging aspect when developing self-driving technologies. Hamilton-Jacobi backward-reachability analysis is a formal verification tool for verifying the safety of dynamic systems in the presence of…
In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…