Related papers: Solvability of Approximate Reach-Avoid Games
This study focuses on reachability problems in differential games. An improved level set method for computing reachable tubes is proposed in this paper. The reachable tube is described as a sublevel set of a value function, which is the…
We investigate the problem of synthesizing distributionally robust control policies for stochastic systems under safety and reach-avoid specifications. Using a game-theoretical framework, we consider the setting where the probability…
Designing provably safe control is a core problem in trustworthy autonomy. However, most prior work in this regard assumes either that the system dynamics are known or deterministic, or that the state and action space are finite,…
We prove an n-EXPTIME lower bound for the problem of deciding the winner in a reachability game on Higher Order Pushdown Automata (HPDA) of level n. This bound matches the known upper bound for parity games on HPDA. As a consequence the…
As part of an effort to apply the rigorous guarantees of formal verification to multi-agent systems, the field of equilibrium analysis, also called rational verification, studies equilibria in multiplayer games to reason about system-level…
This paper considers the problem of reachability analysis of control systems with optimal controllers, as a first step towards verifying the safety and correctness of such systems. Despite their appeal in guaranteeing task satisfaction…
Hamilton-Jacobi Reachability (HJR) is a popular method for analyzing the liveness and safety of a dynamical system with bounded control and disturbance. The corresponding HJ value function offers a robust controller and characterizes the…
This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB)…
Reinforcement learning based adaptive/approximate dynamic programming (ADP) is a powerful technique to determine an approximate optimal controller for a dynamical system. These methods bypass the need to analytically solve the nonlinear…
This paper studies a class of approach-evasion differential games, in which one player aims to steer the state of a dynamic system to the given target set in minimum time, while avoiding some set of disallowed states, and the other player…
A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage…
This paper investigates a reach-avoid game between two players with damped double integrator dynamics. An optimal state-feedback strategy is derived using a differential game framework combined with geometric analysis. To facilitate the…
We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic…
Hamilton-Jacobi reachability (HJR) provides a value function that encodes the set of states from which a system with bounded control inputs can reach or avoid a target despite any bounded disturbance, and the corresponding robust, optimal…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…
The maximization of reach-avoid probabilities for stochastic systems is a central topic in the control literature. Yet, the available methods are either restricted to low-dimensional systems or suffer from conservative approximations. To…
Hamilton-Jacobi (HJ) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. However, the provided safety assurances are often predicated on the assumption that once deployed, the system or its environment…
This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
Approachability has become a standard tool in analyzing earning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in the obtained reward that belongs to a set,…