相关论文: The Convex Geometry of Integrator Reach Sets

This is the first of a two part paper investigating the geometry of the integrator reach sets, and the applications thereof. In this Part I, assuming box-valued input uncertainties, we establish that this compact convex reach set is…

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…

We present a semi-analytical method for exact computation of the boundary of the reach set of a single-input controllable linear time invariant (LTI) system with given bounds on its input range. In doing so, we deduce a parametric formula…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

In this paper, we tackle the long-standing challenges of ensemble control analysis and design using a convex-geometric approach in a Hilbert space setting. Specifically, we formulate the control of linear ensemble systems as a convex…

We study the integrality gap of convex mixed-integer programs, that is, the difference between the optimal value of such a problem and the optimal value of its continuous relaxation. We study classes of convex sets whose associated…

This paper considers the problem of finding maximum volume (axis-aligned) inscribed boxes in a compact convex set, defined by a finite number of convex inequalities, and presents optimization and geometric approaches for solving them.…

The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…

In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex…

To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…

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…

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…

Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expressed as the projection of a much simpler set in higher…

This paper focuses on investigating generalized relative interior notions for sets in locally convex topological vector spaces with particular attentions to graphs of set-valued mappings and epigraphs of extended-real-valued functions. We…

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

We discuss the notions of circumradius, inradius, diameter, and minimum width in generalized Minkowski spaces (that is, with respect to gauges), i.e., we measure the "size" of a given convex set in a finite-dimensional real vector space…

We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and…

The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…

In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…

Building sets were introduced in the study of wonderful compactifications of hyperplane arrangement complements and were later generalized to finite meet-semilattices. Convex geometries, the duals of antimatroids, offer a robust…