Convergent Under-Approximations of Reachable Sets and Tubes for Linear Uncertain Systems

by   Mohamed Serry, et al.

In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable time-varying system matrices and uncertain initial and input values belonging to known convex compact sets. The proposed method depends upon the iterative use of constant-input reachable sets which results in convergent under-approximations in the sense of Hausdorff distance. We illustrate our approach through two numerical examples.


page 1

page 2

page 3

page 4


Under-Approximate Reachability Analysis for a Class of Linear Uncertain Systems

Under-approximations of reachable sets and tubes have received recent re...

An Adaptive Observer for Uncertain Linear Time-Varying Systems with Unknown Additive Perturbations

In this paper we are interested in the problem of adaptive state observa...

Higher Order Method for Differential Inclusions

Uncertainty is unavoidable in modeling dynamical systems and it may be r...

Approximations and asymptotics of continuous-time locally stationary processes

We introduce a general theory on stationary approximations for locally s...

Beurling-type density criteria for system identification

This paper addresses the problem of identifying a linear time-varying (L...

Finite-Time Analysis and Restarting Scheme for Linear Two-Time-Scale Stochastic Approximation

Motivated by their broad applications in reinforcement learning, we stud...

Rank Conditions for Observability and Controllability for Time-varying Nonlinear Systems

This paper provides the extension of the observability rank condition an...