Related papers: Low-order Linear Parameter Varying Approximations …
We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of…
Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each…
We consider the 3D Navier-Stokes system driven by an additive finite-dimensional control force. The purpose of this paper is to show how the approximate controllability of this system can be derived from the approximate controllability of…
We consider the optimal regulation problem for nonlinear control-affine dynamical systems. Whereas the linear-quadratic regulator (LQR) considers optimal control of a linear system with quadratic cost function, we study polynomial systems…
While convergence of polynomial chaos approximation for linear equations is relatively well understood, a lot less is known for non-linear equations. The paper investigates this convergence for a particular equation with quadratic…
Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…
Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational…
In this paper, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant…
Falling liquid films are complex physical processes modelled by infinite-dimensional dynamical systems. The interfacial behaviour is characterised by the Reynolds number, a nondimensional parameter, and above a critical value the uniform…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…
This paper investigates the control of nonlinear systems using a piecewise linear approximation framework. The proposed approach combines a PID controller with locally linearized models obtained by partitioning the nonlinear function into…
We propose a model reduction method for LPV systems. We consider LPV state-space representations with an affine dependence on the scheduling variables. The main idea behind the proposed method is to compute the reduced order model in such a…
Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…
One designs a linear stabilizable boundary feedback controller for the Navier-Stokes equations which is oblique to boundary.
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
This paper describes an adaptive preconditioner for numerical continuation of incompressible Navier--Stokes flows. The preconditioner maps the identity (no preconditioner) to the Stokes preconditioner (preconditioning by Laplacian) through…
This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical…
Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output…
We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced…