Related papers: Reachability Analysis Using Constrained Polynomial…
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…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
This paper investigates the application of zonotope-based reachability analysis to low-thrust spacecraft in both two-body and cislunar environments. Reachable sets are generated under two-body and circular restricted three-body (CR3BP)…
Sapo is a C++ tool for the formal analysis of polynomial dynamical systems. Its main features are: 1) Reachability computation, i.e., the calculation of the set of states reachable from a set of initial conditions, and 2) Parameter…
Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
In this paper, we propose a novel approach for computing robust backward reachable sets from noisy data for unknown constrained linear systems subject to bounded disturbances. In particular, we develop an algorithm for obtaining zonotopic…
In this paper, we introduce a hybrid zonotope-based approach for formally verifying the behavior of autonomous systems operating under Linear Temporal Logic (LTL) specifications. In particular, we formally verify the LTL formula by…
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical…
We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show…
This paper proposes a method for set-valued state estimation of nonlinear, discrete-time systems. This is achieved by combining graphs of functions representing system dynamics and measurements with the hybrid zonotope set representation…
This paper studies deterministic data-driven reachability analysis for dynamical systems with unknown dynamics and nonconvex reachable sets. Existing deterministic data-driven approaches typically employ zonotopic set representations, for…
This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly…
Exploiting tools from algebraic geometry, the problem of finiteness of determination of accessibility/strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems. The…
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 proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). Unlike intervals, ellipsoids, and zonotopes, constrained zonotopes (CZs) can directly incorporate linear…
This paper presents identities for calculating over-approximated successor sets of discrete-time nonlinear systems using hybrid zonotopes. The proposed technique extends the state-update set construct, previously developed for linear hybrid…
Partially-Observable Markov Decision Processes (POMDPs) are a well-known stochastic model for sequential decision making under limited information. We consider the EXPTIME-hard problem of synthesising policies that almost-surely reach some…
The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped…
This paper investigates the application of reachability analysis to the re-entry problem faced by vehicles entering Earth's atmosphere. The study delves into the time evolution of reachable sets for the system, particularly when subject to…