83 research outputs found
Example Setups of Navier-Stokes Equations with Control and Observation: Spatial Discretization and Representation via Linear-quadratic Matrix Coefficients
We provide spatial discretizations of nonlinear incompressible Navier-Stokes
equations with inputs and outputs in the form of matrices ready to use in any
numerical linear algebra package. We discuss the assembling of the system
operators and the realization of boundary conditions and inputs and outputs. We
describe the two benchmark problems - the driven cavity and the cylinder wake -
and provide the corresponding data. The use of the data is illustrated by
numerous example setups. The test cases are provided as plain PYTHON or
OCTAVE/MATLAB script files for immediate replication
Classical System Theory Revisited for Turnpike in Standard State Space Systems and Impulse Controllable Descriptor Systems
The concept of turnpike connects the solution of long but finite time horizon
optimal control problems with steady state optimal controls. A key ingredient
of the analysis of the turnpike is the linear quadratic regulator problem and
the convergence of the solution of the associated differential Riccati equation
as the terminal time approaches infinity. This convergence has been
investigated in linear systems theory in the 1980s. We extend classical system
theoretic results for the investigation of turnpike properties of standard
state space systems and descriptor systems. We present conditions for turnpike
in the nondetectable case and for impulse controllable descriptor systems. For
the latter, in line with the theory for standard linear systems, we establish
existence and convergence of solutions to a generalized differential Riccati
equation.Comment: 28 pages, 1 figur
Differential-algebraic Riccati Decoupling for Linear-quadratic Optimal Control Problems for Semi-explicit Index-2 DAEs
We investigate existence and structure of solutions to quadratic control problems with semi-explicit differential algebraic constraints. By means of an equivalent index-1 formulation we identify conditions for the unique existence of optimal solutions. Knowing of the existence of an optimal input, we provide a representation of the associated feedback-law via a Riccati-like decoupling that is formulated for the original index-2 equations
Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales
In this article, we investigate exponential lag synchronization results for
the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed
delays on an arbitrary time domain by applying feedback control. We formulate
the problem by using the time scales theory so that the results can be applied
to any uniform or non-uniform time domains. Also, we provide a comparison of
results that shows that obtained results are unified and generalize the
existing results. Mainly, we use the unified matrix-measure theory and Halanay
inequality to establish these results. In the last section, we provide two
simulated examples for different time domains to show the effectiveness and
generality of the obtained analytical results.Comment: 20 pages, 18 figure
A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems
Linear projection schemes like Proper Orthogonal Decomposition can
efficiently reduce the dimensions of dynamical systems but are naturally
limited, e.g., for convection-dominated problems. Nonlinear approaches have
shown to outperform linear methods in terms of dimension reduction versus
accuracy but, typically, come with a large computational overhead. In this
work, we consider a quadratic reduction scheme which induces nonlinear
structures that are well accessible to tensorized linear algebra routines. We
discuss that nonintrusive approaches can be used to simultaneously reduce the
complexity in the equations and propose an operator inference formulation that
respects dynamics on nonlinear manifolds
A low-rank solution method for Riccati equations with indefinite quadratic terms
Algebraic Riccati equations with indefinite quadratic terms play an important
role in applications related to robust controller design. While there are many
established approaches to solve these in case of small-scale dense
coefficients, there is no approach available to compute solutions in the
large-scale sparse setting. In this paper, we develop an iterative method to
compute low-rank approximations of stabilizing solutions of large-scale sparse
continuous-time algebraic Riccati equations with indefinite quadratic terms. We
test the developed approach for dense examples in comparison to other
established matrix equation solvers, and investigate the applicability and
performance in large-scale sparse examples.Comment: 19 pages, 2 figures, 5 table
Frequency-dependent Switching Control for Disturbance Attenuation of Linear Systems
The generalized Kalman-Yakubovich-Popov lemma as established by Iwasaki and
Hara in 2005 marks a milestone in the analysis and synthesis of linear systems
from a finite-frequency perspective. Given a pre-specified frequency band, it
allows us to produce passive controllers with excellent in-band disturbance
attenuation performance at the expense of some of the out-of-band performance.
This paper focuses on control design of linear systems in the presence of
disturbances with non-strictly or non-stationary limited frequency spectrum. We
first propose a class of frequency-dependent excited energy functions (FD-EEF)
as well as frequency-dependent excited power functions (FD-EPF), which possess
a desirable frequency-selectiveness property with regard to the in-band and
out-of-band excited energy as well as excited power of the system. Based upon a
group of frequency-selective passive controllers, we then develop a
frequency-dependent switching control (FDSC) scheme that selects the most
appropriate controller at runtime. We show that our FDSC scheme is capable to
approximate the solid in-band performance while maintaining acceptable
out-of-band performance with regard to global time horizons as well as
localized time horizons. The method is illustrated by a commonly used benchmark
model
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