相关论文: Relaxation enhancement by controlling incompressib…
This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…
In this paper, we investigate the controllability of the point vortex system by means of a single vortex. The point vortex system is a well-known simplied model for the incompressible Euler equation, where the vorticity is concentrated in a…
Classical discrete-time adaptive controllers provide asymptotic stabilization. While the original adaptive controllers did not handle noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however,…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
This paper presents a new formulation for model-free robust optimal regulation of continuous-time nonlinear systems. The proposed reinforcement learning based approach, referred to as incremental adaptive dynamic programming (IADP),…
In this paper, we investigate the exact controllability properties of an advection-diffusion equation on a bounded domain, using time- and space-dependent velocity fields as the control parameters. This partial differential equation (PDE)…
We study Brenier's variational models for incompressible Euler equations. These models give rise to a relaxation of the Arnold distance in the space of measure-preserving maps and, more generally, measure-preserving plans. We analyze the…
We introduce discontinuous solutions to nonlinear impulsive control systems with state time delays in the dynamics and derive necessary optimality conditions in the form of a Maximum Principle for associated optimal control problems. In the…
This paper is concerned with the design of an augmented state feedback controller for finite-dimensional linear systems with nonlinear observation dynamics. Most of the theoretical results in the area of (optimal) feedback design are based…
We show that the Euler system of gas dynamics in $\mathbb{R}^d$, $d=2,3$, with positive far field density and arbitrary far field entropy, admits infinitely many steady solutions with compactly supported velocity. The same proof yields a…
It has been demonstrated that the Euler equations of inviscid fluid are incomplete: according to the principle of release of constraints, absence of shear stresses must be compensated by additional degrees of freedom, and leads to…
In addition to the Riemannian metricization of the thermodynamic state space, local relaxation times offer a natural time scale, too. Generalizing existing proposals, we relate {\it thermodynamic} time scale to the standard kinetic…
We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of stiff stochastic differential equations (SDEs) where both the drift and diffusion are non-globally Lipschitz continuous. This stiffness may…
This paper presents the design and analysis of an extremum seeking (ES) controller for scalar static maps in the context of infinite-dimensional dynamics governed by the 1D Euler-Bernoulli (EB) beam Partial Differential Equation (PDE). The…
We study a sampled-data implementation of linear controllers that depend on the output and its derivatives. First, we consider an LTI system of relative degree $r\ge 2$ that can be stabilized using $r-1$ output derivatives. Then, we…
In this paper, we are concerned with the approximate controllability results for a class of impulsive functional differential control systems involving time dependent operators in Banach spaces. First, we show the existence of a mild…
In this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in…
In this paper, we derive general theorems for controlling (vector-valued) first order ordinary differential equations such that its solutions stop at a finite time $T>0$ and apply them to relaxation and dissipative oscillation processes. We…