2,045 research outputs found
A fractional representation approach to the robust regulation problem for MIMO systems
The aim of this paper is in developing unifying frequency domain theory for
robust regulation of MIMO systems. The main theoretical results achieved are a
new formulation of the internal model principle, solvability conditions for the
robust regulation problem, and a parametrization of all robustly regulating
controllers. The main results are formulated with minimal assumptions and
without using coprime factorizations thus guaranteeing applicability with a
very general class of systems. In addition to theoretical results, the design
of robust controllers is addressed. The results are illustrated by two examples
involving a delay and a heat equation.Comment: 23 pages, 3 figures, submitted to International Journal of Robust and
Nonlinear Contro
Geometric characterization on the solvability of regulator equations
The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained
A fractional representation approach to the robust regulation problem for SISO systems
The purpose of this article is to develop a new approach to the robust
regulation problem for plants which do not necessarily admit coprime
factorizations. The approach is purely algebraic and allows us dealing with a
very general class of systems in a unique simple framework. We formulate the
famous internal model principle in a form suitable for plants defined by
fractional representations which are not necessarily coprime factorizations. By
using the internal model principle, we are able to give necessary and
sufficient solvability conditions for the robust regulation problem and to
parameterize all robustly regulating controllers.Comment: 13 pages, 1 figure, to appear in Systems & Control Letter
A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems
A state-space approach to Youla-parametrization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as (linear/nonlinear) fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parametrized output feedback controllers have separation structures. A separation principle follows from the construction. This machinery allows the parametrization of stabilizing controllers to be conducted directly in state space without using coprime-factorization
On the Minimization of Maximum Transient Energy Growth.
The problem of minimizing the maximum transient energy growth is considered.
This problem has importance in some fluid flow control problems and other
classes of nonlinear systems. Conditions for the existence of static controllers
that ensure strict dissipativity of the transient energy are established and an
explicit parametrization of all such controllers is provided. It also is shown
that by means of a Q-parametrization, the problem of minimizing the maximum
transient energy growth can be posed as a convex optimization problem that can
be solved by means of a Ritz approximation of the free parameter. By considering
the transient energy growth at an appropriate sequence of discrete time points,
the minimal maximum transient energy growth problem can be posed as a
semidefinite program. The theoretical developments are demonstrated on a
numerical example
Linear Control Theory with an ℋ∞ Optimality Criterion
This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods
Stochastic focusing coupled with negative feedback enables robust regulation in biochemical reaction networks
Nature presents multiple intriguing examples of processes which proceed at
high precision and regularity. This remarkable stability is frequently counter
to modelers' experience with the inherent stochasticity of chemical reactions
in the regime of low copy numbers. Moreover, the effects of noise and
nonlinearities can lead to "counter-intuitive" behavior, as demonstrated for a
basic enzymatic reaction scheme that can display stochastic focusing (SF).
Under the assumption of rapid signal fluctuations, SF has been shown to convert
a graded response into a threshold mechanism, thus attenuating the detrimental
effects of signal noise. However, when the rapid fluctuation assumption is
violated, this gain in sensitivity is generally obtained at the cost of very
large product variance, and this unpredictable behavior may be one possible
explanation of why, more than a decade after its introduction, SF has still not
been observed in real biochemical systems.
In this work we explore the noise properties of a simple enzymatic reaction
mechanism with a small and fluctuating number of active enzymes that behaves as
a high-gain, noisy amplifier due to SF caused by slow enzyme fluctuations. We
then show that the inclusion of a plausible negative feedback mechanism turns
the system from a noisy signal detector to a strong homeostatic mechanism by
exchanging high gain with strong attenuation in output noise and robustness to
parameter variations. Moreover, we observe that the discrepancy between
deterministic and stochastic descriptions of stochastically focused systems in
the evolution of the means almost completely disappears, despite very low
molecule counts and the additional nonlinearity due to feedback.
The reaction mechanism considered here can provide a possible resolution to
the apparent conflict between intrinsic noise and high precision in critical
intracellular processes
- …