12,775 research outputs found
Enlarging the domain of attraction of MPC controller using invariant sets
2002 IFAC15th Triennial World Congress, Barcelona, SpainThis paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The useful way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost in the optimization problem. The terminal constraint is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the prediction horizon. By increasing the prediction horizon, the domain of attraction is enlarged but at expense of a greater computational burden. A strategy to enlarge the domain of attraction of MPC without increasing the prediction horizon is presented. The terminal constraint is replaced by a contractive terminal constraint which is given by a sequence of control invariant sets for the system. This strategy guarantees closed loop stability under the same assumptions
Practical Evaluation of Lempel-Ziv-78 and Lempel-Ziv-Welch Tries
We present the first thorough practical study of the Lempel-Ziv-78 and the
Lempel-Ziv-Welch computation based on trie data structures. With a careful
selection of trie representations we can beat well-tuned popular trie data
structures like Judy, m-Bonsai or Cedar
Can local single-pass methods solve any stationary Hamilton-Jacobi-Bellman equation?
The use of local single-pass methods (like, e.g., the Fast Marching method)
has become popular in the solution of some Hamilton-Jacobi equations. The
prototype of these equations is the eikonal equation, for which the methods can
be applied saving CPU time and possibly memory allocation. Then, some natural
questions arise: can local single-pass methods solve any Hamilton-Jacobi
equation? If not, where the limit should be set? This paper tries to answer
these questions. In order to give a complete picture, we present an overview of
some fast methods available in literature and we briefly analyze their main
features. We also introduce some numerical tools and provide several numerical
tests which are intended to exhibit the limitations of the methods. We show
that the construction of a local single-pass method for general Hamilton-Jacobi
equations is very hard, if not impossible. Nevertheless, some special classes
of problems can be actually solved, making local single-pass methods very
useful from the practical point of view.Comment: 19 page
A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries
In order to achieve a better understanding of degradation processes in
lithium-ion batteries, the modelling of cell dynamics at the mircometer scale
is an important focus of current mathematical research. These models lead to
large-dimensional, highly nonlinear finite volume discretizations which, due to
their complexity, cannot be solved at cell scale on current hardware. Model
order reduction strategies are therefore necessary to reduce the computational
complexity while retaining the features of the model. The application of such
strategies to specialized high performance solvers asks for new software
designs allowing flexible control of the solvers by the reduction algorithms.
In this contribution we discuss the reduction of microscale battery models with
the reduced basis method and report on our new software approach on integrating
the model order reduction software pyMOR with third-party solvers. Finally, we
present numerical results for the reduction of a 3D microscale battery model
with porous electrode geometry.Comment: 7 pages, 2 figures, 2 table
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