Related papers: A non-classical class of variational problems
The purpose of this article is to obtain a better understanding of the extended variational principle (EVP). The EVP is a formula for the thermodynamic pressure of a statistical mechanical system as a limit of a sequence of minimization…
In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
In this thesis we deal with two different classes of variational problems: 1) the problem of closed curves with prescribed curvature, or $H$-loop problem; 2) the study of the nodal solutions of the fractional Brezis-Nirenberg problem. In…
We consider an optimal control problem for piecewise deterministic Markov processes (PDMPs) on a bounded state space. The control problem under study is very general: a pair of controls acts continuously on the deterministic flow and on the…
This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…
Integrable PDEs on the line can be analyzed by the so-called Inverse Scattering Transform (IST) method. A particularly powerful aspect of the IST is its ability to predict the large $t$ behavior of the solution. Namely, starting with…
The popularity of Conditional Value-at-Risk (CVaR), a risk functional from finance, has been growing in the control systems community due to its intuitive interpretation and axiomatic foundation. We consider a nonstandard optimal control…
The study of undersea cables and mooring lines statics remains an unavoidable subject of simulation in offshore field for either steady-state analysis or dynamic simulation initialization. Whether the study concerns mooring systems pinned…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…
The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…
The Variation Evolving Method (VEM), which seeks the optimal solutions with the variation evolution principle, is further developed to be more flexible in solving the Optimal Control Problems (OCPs) with terminal constraint. With the…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic…
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…
The paper deals with the problem of output regulation in a "non-equilibrium" context for a special class of multivariable nonlinear systems stabilizable by high-gain feedback. A post-processing internal model design suitable for the…
We consider a nonlinear control system depending on two controls u and v, with dynamics affine in the (unbounded) derivative of u, and v appearing initially only in the drift term. Recently, motivated by applications to optimization…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…