This paper presents a framework for constructing and analyzing enclosures of the reachable
set of nonlinear ordinary differential equations using continuous-time set-propagation …

Novel convex and concave relaxations are proposed for the solutions of parametric ordinary
differential equations (ODEs), to aid in furnishing bounding information for deterministic …

A new method is presented for enclosing the reachable sets of nonlinear ordinary differential
equations subject to a range of inputs. Reachable set enclosures are used for uncertainty …

In many automated motion planning systems, vehicles are tasked with tracking a reference
path or trajectory that is safe by design. However, due to various uncertainties, real vehicles …

This work presents a general theory for the construction of a polyhedral outer approximation
of the reachable set (“polyhedral bounds”) of a dynamic system subject to time-varying …

This paper is concerned with guaranteed parameter estimation of non-linear dynamic
systems in a context of bounded measurement error. The problem consists of finding—or …

This work presents a numerical method for evaluating affine relaxations of the solutions of
parametric ordinary differential equations. This method is derived from a general theory for …

This paper presents a novel algorithm for bounding the reachable set of parametric
nonlinear differential equations. This algorithm is based on a first-discretize-then-bound …

Many set-valued integration algorithms for parametric ordinary differential equations (ODEs)
implement a combination of Taylor series expansion with either interval arithmetic or Taylor …

For the performance of global optimization algorithms, the rate of convergence of convex
relaxations to the objective and constraint functions is critical. We extend results from …