1,438 research outputs found
Identification of Piecewise Linear Models of Complex Dynamical Systems
The paper addresses the realization and identification problem or a subclass
of piecewise-affine hybrid systems. The paper provides necessary and sufficient
conditions for existence of a realization, a characterization of minimality,
and an identification algorithm for this subclass of hybrid systems. The
considered system class and the identification problem are motivated by
applications in systems biology
Realization Theory for LPV State-Space Representations with Affine Dependence
In this paper we present a Kalman-style realization theory for linear
parameter-varying state-space representations whose matrices depend on the
scheduling variables in an affine way (abbreviated as LPV-SSA representations).
We deal both with the discrete-time and the continuous-time cases. We show that
such a LPV-SSA representation is a minimal (in the sense of having the least
number of state-variables) representation of its input-output function, if and
only if it is observable and span-reachable. We show that any two minimal
LPV-SSA representations of the same input-output function are related by a
linear isomorphism, and the isomorphism does not depend on the scheduling
variable.We show that an input-output function can be represented by a LPV-SSA
representation if and only if the Hankel-matrix of the input-output function
has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension
of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart
of partial realization theory for LPV-SSA representation and prove correctness
of the Kalman-Ho algorithm. These results thus represent the basis of systems
theory for LPV-SSA representation.Comment: The main difference with respect to the previous version is as
follows: typos have been fixe
Switching Control for Parameter Identifiability of Uncertain Systems
This paper considers the problem of identifying the parameters of an
uncertain linear system by means of feedback control. The problem is approached
by considering time-varying controllers. It is shown that even when the
uncertainty set is not finite, parameter identifiability can be generically
ensured by switching among a finite number of linear time-invariant
controllers. The results are shown to have several implications, ranging from
fault detection and isolation to adaptive and supervisory control. Practical
aspects of the problem are also discussed in details
Optimal Precoders for Tracking the AoD and AoA of a mm-Wave Path
In millimeter-wave channels, most of the received energy is carried by a few
paths. Traditional precoders sweep the angle-of-departure (AoD) and
angle-of-arrival (AoA) space with directional precoders to identify directions
with largest power. Such precoders are heuristic and lead to sub-optimal
AoD/AoA estimation. We derive optimal precoders, minimizing the Cram\'{e}r-Rao
bound (CRB) of the AoD/AoA, assuming a fully digital architecture at the
transmitter and spatial filtering of a single path. The precoders are found by
solving a suitable convex optimization problem. We demonstrate that the
accuracy can be improved by at least a factor of two over traditional
precoders, and show that there is an optimal number of distinct precoders
beyond which the CRB does not improve.Comment: Resubmission to IEEE Trans. on Signal Processing. 12 pages and 9
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