相关论文: A geometric approach to convex processes: from rea…

This paper studies reachability and null-controllability for difference inclusions involving convex processes. Such difference inclusions arise, for instance, in the study of linear discrete-time systems whose inputs and/or states are…

Spectral analysis of convex processes has led to many results in the analysis of differential inclusions with a convex process. In particular the characterization of eigenvalues with eigenvectors in a given cone has led to results on…

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…

Motivated by applications requiring sparse or nonnegative controls, we investigate reachability properties of linear infinite-dimensional control problems under conic constraints. Relaxing the problem to convex constraints if the initial…

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…

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…

Some properties of solutions of convex sweeping processes with velocity constraints are studied in this paper. Namely, the solution sensitivity with respect to the initial value, the boundedness, the closedness, and the convexity of the…

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…

Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have…

An invex function generalizes a convex function in the sense that every stationary point is a global minimizer. Recently, invex functions and their subclasses have attracted attention in signal processing and machine learning. However,…

The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition…

This paper studies the informativity problem for reachability and null-controllability of constrained systems. To be precise, we will focus on an unknown linear systems with convex conic constraints from which we measure data consisting of…

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…

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation…

In this note we provide a simple proof of some properties enjoyed by convex functions having the engulfing property. In particular, making use only of results peculiar to convex analysis, we prove that differentiability and strict convexity…

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…

Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…

We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that…

In discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimodularity. These concepts of discrete convex functions are…