Related papers: Approximate Computation of Reach Sets in Hybrid Sy…
We present a method of computing backward reachable sets for nonlinear discrete-time control systems possessing continuous symmetries. The starting point is a dynamic game formulation of reachability analysis where control inputs aim to…
Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear…
Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…
Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
This paper introduces robust differential dynamic logic (a fragment of differential dynamic logic) to specify and reason about robust hybrid systems. Practically meaningful syntactic restrictions naturally ensure that definable properties…
A fundamental question in systems biology is what combinations of mean and variance of the species present in a stochastic biochemical reaction network are attainable by perturbing the system with an external signal. To address this…
Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical control systems. Its advantages include compatibility with general nonlinear system…
Deploying autonomous systems in safety critical settings necessitates methods to verify their safety properties. This is challenging because real-world systems may be subject to disturbances that affect their performance, but are unknown a…
Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a large attention in the control and computer science communities. In this paper we study the fault diagnosis problem for hybrid…
This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…
In this work, we present a novel Koopman spectrum-based reachability verification method for nonlinear systems. Contrary to conventional methods that focus on characterizing all potential states of a dynamical system over a presupposed time…
Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded…
Backward reachability (also termed controllability) has been extensively studied in control theory, and tools for a wide class of systems have been developed. Nevertheless, assessing a backward reachability analysis or synthesis remains…
The hitting set problem is a well-known NP-hard optimization problem in which, given a set of elements and a collection of subsets, the goal is to find the smallest selection of elements, such that each subset contains at least one element…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
In this paper we consider the problem of finding an evolution of a dynamical system that originates and terminates in given sets of states. However, if such an evolution exists then it is usually not unique. We investigate this problem and…
Over-approximating the forward reach sets of controlled dynamical systems subject to set-valued uncertainties is a common practice in systems-control engineering for the purpose of performance verification. However, specific algebraic and…
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
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…