Related papers: Efficient Reachable Sets on Lie Groups Using Lie A…
This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a…
Tangencies correspond to singularities of impact systems, separating between impacting and non-impacting trajectory segments. The closure of their orbits constitute the singularity set, which, even in the simpler billiard limit, is known to…
We quantitatively study the speed of convergence of geodesic Lie groups to their metric limits. For nilpotent geodesic Lie groups, we give estimates on the difference of the original metrics and the asymptotic metrics, while for general…
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…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…
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…
Precisely characterizing and controlling realistic open quantum systems is one of the most challenging and exciting frontiers in quantum sciences and technologies. In this Letter, we present methods of approximately computing reachable sets…
Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between…
In this article, a unified approach to obtain symplectic integrators on T*G from Lie group integrators on a Lie group G is presented. The approach is worked out in detail for symplectic integrators based on Runge--Kutta--Munthe-Kaas methods…
This work presents the first application of the state-of-the-art Koenig-D'Amico reachable set theory solver to cislunar, chaotic relative motion in the Circular-Restricted Three-Body Problem (CR3BP). The relative motion dynamics of two…
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the…
We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We begin our investigation with the observation that agnostic…
In this work, we study controllability in the set of all density matrices for a two-level open quantum system driven by coherent and incoherent controls. In [A. Pechen, Phys. Rev. A 84, 042106 (2011)] an approximate controllability, i.e.,…
In this work, we present a numerical optimal control framework for reachable set computation using \emph{normotopes}, a new set representation as a norm ball with a shaping matrix. In reachable set computations, we expect to continuously…
This paper considers output reachability analysis for linear time-invariant systems with unknown state-space matrices and unknown observation map, given only noisy input-output measurements. The Cayley--Hamilton theorem is applied to…
A sensitivity-based approach for computing over-approximations of reachable sets, in the presence of constant parameter uncertainties and a single initial state, is used to analyze a three-link planar robot modeling a Powered Lower Limb…
The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous…