512 research outputs found
OBDD-Based Representation of Interval Graphs
A graph can be described by the characteristic function of the
edge set which maps a pair of binary encoded nodes to 1 iff the nodes
are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store
can lead to a (hopefully) compact representation. Given the OBDD as an
input, symbolic/implicit OBDD-based graph algorithms can solve optimization
problems by mainly using functional operations, e.g. quantification or binary
synthesis. While the OBDD representation size can not be small in general, it
can be provable small for special graph classes and then also lead to fast
algorithms. In this paper, we show that the OBDD size of unit interval graphs
is and the OBDD size of interval graphs is $O(\
| V \ | \log \ | V \ |)\Omega(\ | V \ | \log
\ | V \ |)O(\log \ | V \ |)O(\log^2 \ | V \ |)$ operations and
evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic
Concepts 201
Faster Approximate Multicommodity Flow Using Quadratically Coupled Flows
The maximum multicommodity flow problem is a natural generalization of the
maximum flow problem to route multiple distinct flows. Obtaining a
approximation to the multicommodity flow problem on graphs is a well-studied
problem. In this paper we present an adaptation of recent advances in
single-commodity flow algorithms to this problem. As the underlying linear
systems in the electrical problems of multicommodity flow problems are no
longer Laplacians, our approach is tailored to generate specialized systems
which can be preconditioned and solved efficiently using Laplacians. Given an
undirected graph with m edges and k commodities, we give algorithms that find
approximate solutions to the maximum concurrent flow problem and
the maximum weighted multicommodity flow problem in time
\tilde{O}(m^{4/3}\poly(k,\epsilon^{-1}))
Interest rate models with Markov chains
Imperial Users onl
Optimal control and robust estimation for ocean wave energy converters
This thesis deals with the optimal control of wave energy converters and some associated
observer design problems. The first part of the thesis will investigate model
predictive control of an ocean wave energy converter to maximize extracted power.
A generic heaving converter that can have both linear dampers and active elements
as a power take-off system is considered and an efficient optimal control algorithm
is developed for use within a receding horizon control framework. The optimal
control is also characterized analytically. A direct transcription of the optimal control
problem is also considered as a general nonlinear program. A variation of
the projected gradient optimization scheme is formulated and shown to be feasible
and computationally inexpensive compared to a standard nonlinear program solver.
Since the system model is bilinear and the cost function is not convex quadratic, the
resulting optimization problem is shown not to be a quadratic program. Results are
compared with other methods like optimal latching to demonstrate the improvement
in absorbed power under irregular sea condition simulations.
In the second part, robust estimation of the radiation forces and states inherent in
the optimal control of wave energy converters is considered. Motivated by this, low
order H∞ observer design for bilinear systems with input constraints is investigated
and numerically tractable methods for design are developed. A bilinear Luenberger
type observer is formulated and the resulting synthesis problem reformulated as that
for a linear parameter varying system. A bilinear matrix inequality problem is then
solved to find nominal and robust quadratically stable observers. The performance
of these observers is compared with that of an extended Kalman filter. The robustness
of the observers to parameter uncertainty and to variation in the radiation
subsystem model order is also investigated.
This thesis also explores the numerical integration of bilinear control systems with
zero-order hold on the control inputs. Making use of exponential integrators, exact
to high accuracy integration is proposed for such systems. New a priori bounds
are derived on the computational complexity of integrating bilinear systems with a
given error tolerance. Employing our new bounds on computational complexity, we
propose a direct exponential integrator to solve bilinear ODEs via the solution of
sparse linear systems of equations. Based on this, a novel sparse direct collocation
of bilinear systems for optimal control is proposed. These integration schemes are
also used within the indirect optimal control method discussed in the first part.Open Acces
On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm
The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed
A Deterministic Theory for Exact Non-Convex Phase Retrieval
In this paper, we analyze the non-convex framework of Wirtinger Flow (WF) for
phase retrieval and identify a novel sufficient condition for universal exact
recovery through the lens of low rank matrix recovery theory. Via a perspective
in the lifted domain, we show that the convergence of the WF iterates to a true
solution is attained geometrically under a single condition on the lifted
forward model. As a result, a deterministic relationship between the accuracy
of spectral initialization and the validity of {the regularity condition} is
derived. In particular, we determine that a certain concentration property on
the spectral matrix must hold uniformly with a sufficiently tight constant.
This culminates into a sufficient condition that is equivalent to a restricted
isometry-type property over rank-1, positive semi-definite matrices, and
amounts to a less stringent requirement on the lifted forward model than those
of prominent low-rank-matrix-recovery methods in the literature. We
characterize the performance limits of our framework in terms of the tightness
of the concentration property via novel bounds on the convergence rate and on
the signal-to-noise ratio such that the theoretical guarantees are valid using
the spectral initialization at the proper sample complexity.Comment: In Revision for IEEE Transactions on Signal Processin
- …