65 research outputs found
Nehari problems and equalizing vectors for infinite-dimensional systems
For a class of infinite-dimensional systems we obtain a simple frequency domain solution for the suboptimal Nehari extension problem. The approach is via -spectral factorization, and it uses the concept of equalizing vectors. Moreover, the connection between the equalizing vectors and the Nehari extension problem is given. \u
J-spectral factorization and equalizing vectors
For the Wiener class of matrix-valued functions we provide necessary and sufficient conditions for the existence of a -spectral factorization. One of these conditions is in terms of equalizing vectors. A second one states that the existence of a -spectral factorization is equivalent to the invertibility of the Toeplitz operator associated to the matrix to be factorized. Our proofs are simple and only use standard results of general factorization theory. Note that we do not use a state space representation of the system. However, we make the connection with the known results for the Pritchard-Salamon class of systems where an equivalent condition with the solvability of an algebraic Riccati equation is given. For Riesz-spectral systems another necessary and sufficient conditions for the existence of a -spectral factorization in terms of the Hamiltonian is added
UMTS Network Planning - The Impact of User Mobility
The impact of user mobility on network planning is investigated. For a system of two base stations the stationary distribution of a Markov chain, including mobility, is computed
Tools for analysis of Dirac structures on Hilbert spaces
In this paper tools for the analysis of Dirac structures on Hilbert spaces are developed. Some properties are pointed out and two natural representations of Dirac structures on Hilbert spaces are presented. The theory is illustrated on the example of the ideal transmission line. \u
Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations
We consider integer-restricted optimal control of systems governed by
abstract semilinear evolution equations. This includes the problem of optimal
control design for certain distributed parameter systems endowed with multiple
actuators, where the task is to minimize costs associated with the dynamics of
the system by choosing, for each instant in time, one of the actuators together
with ordinary controls. We consider relaxation techniques that are already used
successfully for mixed-integer optimal control of ordinary differential
equations. Our analysis yields sufficient conditions such that the optimal
value and the optimal state of the relaxed problem can be approximated with
arbitrary precision by a control satisfying the integer restrictions. The
results are obtained by semigroup theory methods. The approach is constructive
and gives rise to a numerical method. We supplement the analysis with numerical
experiments
A comparison between LQR control for a long string of 2x2 MIMO systems and LQR control of the infinite spatially invariant version
We compare the LQR control for a long-but-finite string of 2 x 2 MIMO systems with the LQR control for the corresponding infinite-dimensional spatially invariant system. We provide analytical and numerical examples where these are different and we investigate the cause. We also provide sufficient conditions for the LQR solutions to be similar as the length of the string increases. This work extends to the 2 x 2 MIMO systems part of the analysis presented in recent papers for the scalar case
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