4,307 research outputs found
Infinite horizon control and minimax observer design for linear DAEs
In this paper we construct an infinite horizon minimax state observer for a
linear stationary differential-algebraic equation (DAE) with uncertain but
bounded input and noisy output. We do not assume regularity or existence of a
(unique) solution for any initial state of the DAE. Our approach is based on a
generalization of Kalman's duality principle. The latter allows us to transform
minimax state estimation problem into a dual control problem for the adjoint
DAE: the state estimate in the original problem becomes the control input for
the dual problem and the cost function of the latter is, in fact, the
worst-case estimation error. Using geometric control theory, we construct an
optimal control in the feed-back form and represent it as an output of a stable
LTI system. The latter gives the minimax state estimator. In addition, we
obtain a solution of infinite-horizon linear quadratic optimal control problem
for DAEs.Comment: This is an extended version of the paper which is to appear in the
proceedings of the 52nd IEEE Conference on Decision and Control, Florence,
Italy, December 10-13, 201
A Pseudospectral Approach to High Index DAE Optimal Control Problems
Historically, solving optimal control problems with high index differential
algebraic equations (DAEs) has been considered extremely hard. Computational
experience with Runge-Kutta (RK) methods confirms the difficulties. High index
DAE problems occur quite naturally in many practical engineering applications.
Over the last two decades, a vast number of real-world problems have been
solved routinely using pseudospectral (PS) optimal control techniques. In view
of this, we solve a "provably hard," index-three problem using the PS method
implemented in DIDO, a state-of-the-art MATLAB optimal control toolbox. In
contrast to RK-type solution techniques, no laborious index-reduction process
was used to generate the PS solution. The PS solution is independently verified
and validated using standard industry practices. It turns out that proper PS
methods can indeed be used to "directly" solve high index DAE optimal control
problems. In view of this, it is proposed that a new theory of difficulty for
DAEs be put forth.Comment: 14 pages, 9 figure
Diseño para operabilidad: Una revisión de enfoques y estrategias de solución
In the last decades the chemical engineering scientific research community has largely addressed the design-foroperability problem. Such an interest responds to the fact that the operability quality of a process is determined by design, becoming evident the convenience of considering operability issues in early design stages rather than later when the impact of modifications is less effective and more expensive. The necessity of integrating design and operability is dictated by the increasing complexity of the processes as result of progressively stringent economic, quality, safety and environmental constraints. Although the design-for-operability problem concerns to practically every technical discipline, it has achieved a particular identity within the chemical engineering field due to the economic magnitude of the involved processes. The work on design and analysis for operability in chemical engineering is really vast and a complete review in terms of papers is beyond the scope of this contribution. Instead, two major approaches will be addressed and those papers that in our belief had the most significance to the development of the field will be described in some detail.En las últimas décadas, la comunidad cientÃfica de ingenierÃa quÃmica ha abordado intensamente el problema de diseño-para-operabilidad. Tal interés responde al hecho de que la calidad operativa de un proceso esta determinada por diseño, resultando evidente la conveniencia de considerar aspectos operativos en las etapas tempranas del diseño y no luego, cuando el impacto de las modificaciones es menos efectivo y más costoso. La necesidad de integrar diseño y operabilidad esta dictada por la creciente complejidad de los procesos como resultado de las cada vez mayores restricciones económicas, de calidad de seguridad y medioambientales. Aunque el problema de diseño para operabilidad concierne a prácticamente toda disciplina, ha adquirido una identidad particular dentro de la ingenierÃa quÃmica debido a la magnitud económica de los procesos involucrados. El trabajo sobre diseño y análisis para operabilidad es realmente vasto y una revisión completa en términos de artÃculos supera los alcances de este trabajo. En su lugar, se discutirán los dos enfoques principales y aquellos artÃculos que en nuestra opinión han tenido mayor impacto para el desarrollo de la disciplina serán descriptos con cierto detalle.Fil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Planta Piloto de IngenierÃa QuÃmica. Universidad Nacional del Sur. Planta Piloto de IngenierÃa QuÃmica; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Planta Piloto de IngenierÃa QuÃmica. Universidad Nacional del Sur. Planta Piloto de IngenierÃa QuÃmica; Argentin
Gather-and-broadcast frequency control in power systems
We propose a novel frequency control approach in between centralized and
distributed architectures, that is a continuous-time feedback control version
of the dual decomposition optimization method. Specifically, a convex
combination of the frequency measurements is centrally aggregated, followed by
an integral control and a broadcast signal, which is then optimally allocated
at local generation units. We show that our gather-and-broadcast control
architecture comprises many previously proposed strategies as special cases. We
prove local asymptotic stability of the closed-loop equilibria of the
considered power system model, which is a nonlinear differential-algebraic
system that includes traditional generators, frequency-responsive devices, as
well as passive loads, where the sources are already equipped with primary
droop control. Our feedback control is designed such that the closed-loop
equilibria of the power system solve the optimal economic dispatch problem
Efficient Solution of Large-Scale Algebraic Riccati Equations Associated with Index-2 DAEs via the Inexact Low-Rank Newton-ADI Method
This paper extends the algorithm of Benner, Heinkenschloss, Saak, and
Weichelt: An inexact low-rank Newton-ADI method for large-scale algebraic
Riccati equations, Applied Numerical Mathematics Vol.~108 (2016), pp.~125--142,
doi:10.1016/j.apnum.2016.05.006 to Riccati equations associated with Hessenberg
index-2 Differential Algebratic Equation (DAE) systems. Such DAE systems arise,
e.g., from semi-discretized, linearized (around steady state) Navier-Stokes
equations. The solution of the associated Riccati equation is important, e.g.,
to compute feedback laws that stabilize the Navier-Stokes equations. Challenges
in the numerical solution of the Riccati equation arise from the large-scale of
the underlying systems and the algebraic constraint in the DAE system. These
challenges are met by a careful extension of the inexact low-rank Newton-ADI
method to the case of DAE systems. A main ingredient in the extension to the
DAE case is the projection onto the manifold described by the algebraic
constraints. In the algorithm, the equations are never explicitly projected,
but the projection is only applied as needed. Numerical experience indicates
that the algorithmic choices for the control of inexactness and line-search can
help avoid subproblems with matrices that are only marginally stable. The
performance of the algorithm is illustrated on a large-scale Riccati equation
associated with the stabilization of Navier-Stokes flow around a cylinder.Comment: 21 pages, 2 figures, 4 table
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