Nonlinear Robust and Optimal Control via Proper Orthogonal Decomposition

Nonlinear Robust and Optimal Control Via Proper Orthogonal Decomposition

In this paper, a methodology based on proper orthogonal decomposition (POD) for computing approximate closed-loop optimal or robust control laws for finite-dimensional nonlinear systems is proposed. The solution can be obtained on any arbitrary domain of the state space represented by a multidimensional grid. The method only requires the computation of a limited number of well-conditioned two-p...

Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control

Optimal control problems for partial differential equation are often hard to tackle numerically because their discretization leads to very large scale optimization problems. Therefore, different techniques of model reduction were developed to approximate these problems by smaller ones that are tractable with less effort. Balanced truncation [2, 66, 81] is one well studied model reduction techni...

Proper Orthogonal Decomposition in Optimal Control of Fluids

In this article, we present a reduced order modeling approach suitable for active control of uid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady ows. We examine the possibility of obtaining reduced o...

Model Reduction via Proper Orthogonal Decomposition

Proper Orthogonal Decomposition for Model Updating of Nonlinear Mechanical Systems

Proper Orthogonal Decomposition (POD), also known as Karhunen-Loeve decomposition, is emerging as a useful experimental tool in dynamics and vibrations. The POD is a means of extracting spatial information from a set of time series data available on a domain. The use of Karhunen-Loeve (K-L) transform is of great help in nonlinear settings where traditional linear techniques such as modal testin...