Related papers: Low-order Linear Parameter Varying Approximations …
Nonlinear parameter-varying (NPV) systems are a class of nonlinear systems whose dynamics explicitly depend on time-varying external parameters, making them suitable for modeling real-world systems with dynamics variations. Traditional…
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…
We present two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
In this paper, an automated Linear Parameter-Varying (LPV) model conversion approach is proposed for nonlinear dynamical systems. The proposed method achieves global embedding of the original nonlinear behavior of the system by leveraging…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
The Linear Parameter-Varying (LPV) framework has been introduced with the intention to provide stability and performance guarantees for analysis and controller synthesis for Nonlinear (NL) systems via convex methods. By extending results of…
We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…
This paper describes the design process for developing a nonlinear model predictive controller for fault tolerant flight control. After examining and implementing a number of numerical techniques, this paper identifies pseudospectral…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional…
We are concerned with the simulation and control of a two phase flow model governed by a coupled Cahn-Hilliard Navier-Stokes system involving a nonsmooth energy potential. We establish the existence of optimal solutions and present two…
This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by…
The numerical simulation of incompressible flows is challenging due to the tight coupling of velocity and pressure. Projection methods offer an effective solution by decoupling these variables, making them suitable for large-scale…
This paper presents a robust controller using a Linear Parameter Varying (LPV) model of the lane-keeping system with parameter reduction. Both varying vehicle speed and roll motion on a curved road influence the lateral vehicle model…
We study the controllability of linearized shape-dependent operators for flow problems. The first operator is a mapping from the shape of the computational domain to the tangential wall velocity of the potential flow problem and the second…
In this paper we deal with distributed optimal control for nonlinear dynamical systems over graph, that is large-scale systems in which the dynamics of each subsystem depends on neighboring states only. Starting from a previous work in…
In this paper, we propose a model reduction technique for linear parameter varying (LPV) systems based on available tools for fixed-structure controller synthesis. We start by transforming a model reduction problem into an equivalent…
In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…