相关论文: Non-convex sweeping processes in the space of regu…
The purpose of this article is twofold. First, we prove that the squeezing function approaches 1 near strongly pseudoconvex boundary points of bounded domains in $\mathbb{C}^{n+1}$. Second, we show that the squeezing function approaches 1…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity…
Recent advances in the study of conformally invariant discrete random processes have lead to increasing interest in the study of discrete analogues to holomorphic functions. Of particular interest are results which provide conditions under…
In this paper, we consider a finite-dimensional optimization problem minimizing a continuous objective on a compact domain subject to a multi-dimensional constraint function. For the latter, we assume the availability of a global Lipschitz…
Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known…
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of…
This paper introduces a novel closed-form strategy that dynamically modifies the reference of a pre-compensated nonlinear system to ensure the satisfaction of a set of convex constraints. The main idea consists of translating constraints in…
This paper presents an approach to externally influencing a team of robots by means of time-varying density functions. These density functions represent rough references for where the robots should be located. To this end, a continuous-time…
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\epsilon$-covering number of $\C([a, b]^d, B)$, in the $L_p$-metric, $1…
We study tracking control for uncertain nonlinear multi-input, multi-output systems modelled by $r$-th order functional differential equations (encompassing systems with arbitrary strict relative degree) in the presence of input…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
This paper addresses some fundamental issues in nonconvex analysis. By using pure complementary energy principle proposed by the author, a class of fully nonlinear partial diforerential equations in nonlinear elasticity is able to converted…
We define and study a class of subshifts of finite type (SFTs) defined by a family of allowed patterns of the same shape where, for any contents of the shape minus a corner, the number of ways to fill in the corner is the same. The main…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…