Related papers: An Improved Level Set Method for Reachability Prob…
We present a causality-based algorithm for solving two-player reachability games represented by logical constraints. These games are a useful formalism to model a wide array of problems arising, e.g., in program synthesis. Our technique for…
The notion of approachability was introduced by Blackwell [1] in the context of vector-valued repeated games. The famous Blackwell's approachability theorem prescribes a strategy for approachability, i.e., for `steering' the average cost of…
Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…
Here we present a decomposition technique for a class of differential games. The technique consists in a decomposition of the target set which produces, for geometrical reasons, a decomposition in the dimensionality of the problem. Using…
This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the…
We design heat exchangers using level-set method based topology optimization. The heat exchange between two fluids in separate channels is maximized while constraining the pressure drop across each channel. The flow is modeled by an…
Hamilton-Jacobi (HJ) reachability-based filtering provides a powerful framework to co-optimize performance and safety (or liveness) for autonomous systems. Under this filtering scheme, a nominal controller is minimally modified to ensure…
We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…
The reachability problem for vector addition systems is a central problem of net theory. This problem is known to be decidable but the complexity is still unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds complexity…
This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…
This paper introduces a novel reachability problem for the scenario involving two agents, where one agent follows another agent using a feedback strategy. The geometry of the reachable set for an agent, termed \emph{dependent reachable…
We investigate Petri nets with data, an extension of plain Petri nets where tokens carry values from an infinite data domain, and executability of transitions is conditioned by equalities between data values. We provide a decision procedure…
Recent approaches to leveraging deep learning for computing reachable sets of continuous-time dynamical systems have gained popularity over traditional level-set methods, as they overcome the curse of dimensionality. However, as with…
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…
We introduce a new numerical method to approximate the solutions of a class of stationary Hamilton-Jacobi (HJ) partial differential equations arising from minimum time optimal control problems. We rely on nested grid approximations, and…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
Hamilton-Jacobi Reachability (HJR) analysis has been successfully used in many robotics and control tasks, and is especially effective in computing reach-avoid sets and control laws that enable an agent to reach a goal while satisfying…
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…