546 research outputs found
Coherent Quantum Filtering for Physically Realizable Linear Quantum Plants
The paper is concerned with a problem of coherent (measurement-free)
filtering for physically realizable (PR) linear quantum plants. The state
variables of such systems satisfy canonical commutation relations and are
governed by linear quantum stochastic differential equations, dynamically
equivalent to those of an open quantum harmonic oscillator. The problem is to
design another PR quantum system, connected unilaterally to the output of the
plant and playing the role of a quantum filter, so as to minimize a mean square
discrepancy between the dynamic variables of the plant and the output of the
filter. This coherent quantum filtering (CQF) formulation is a simplified
feedback-free version of the coherent quantum LQG control problem which remains
open despite recent studies. The CQF problem is transformed into a constrained
covariance control problem which is treated by using the Frechet
differentiation of an appropriate Lagrange function with respect to the
matrices of the filter.Comment: 14 pages, 1 figure, submitted to ECC 201
Solving the generalized Sylvester matrix equation AV+BW=EVF via a Kronecker map
AbstractThis note considers the solution to the generalized Sylvester matrix equation AV+BW=EVF with F being an arbitrary matrix, where V and W are the matrices to be determined. With the help of the Kronecker map, some properties of the Sylvester sum are first proposed. By applying the Sylvester sum as tools, an explicit parametric solution to this matrix equation is established. The proposed solution is expressed by the Sylvester sum, and allows the matrix F to be undetermined
Factorized solution of generalized stable Sylvester equations using many-core GPU accelerators
[EN] We investigate the factorized solution of generalized stable Sylvester equations such as those arising in model reduction, image restoration, and observer design. Our algorithms, based on the matrix sign function, take advantage of the current trend to integrate high performance graphics accelerators (also known as GPUs) in computer systems. As a result, our realisations provide a valuable tool to solve large-scale problems on a variety of platforms.We acknowledge support of the ANII - MPG Independent Research Group: "Efficient Hetergenous Computing" at UdelaR, a partner group of the Max Planck Institute in Magdeburg.Benner, P.; Dufrechou, E.; Ezzatti, P.; Gallardo, R.; Quintana-OrtĂ, ES. (2021). Factorized solution of generalized stable Sylvester equations using many-core GPU accelerators. The Journal of Supercomputing (Online). 77(9):10152-19164. https://doi.org/10.1007/s11227-021-03658-y101521916477
Guaranteed passive parameterized macromodeling by using Sylvester state-space realizations
A novel state-space realization for parameterized macromodeling is proposed in this paper. A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. This technique is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parameterized macromodels. The key points of the novel state-space realizations are the choice of a proper pivot matrix and a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester realization for parameterized macromodeling
New optimization methods in predictive control
This thesis is mainly concerned with the efficient solution of a linear discrete-time
finite horizon optimal control problem (FHOCP) with quadratic cost and linear constraints
on the states and inputs. In predictive control, such a FHOCP needs to be
solved online at each sampling instant. In order to solve such a FHOCP, it is necessary
to solve a quadratic programming (QP) problem. Interior point methods (IPMs) have
proven to be an efficient way of solving quadratic programming problems. A linear system
of equations needs to be solved in each iteration of an IPM. The ill-conditioning
of this linear system in the later iterations of the IPM prevents the use of an iterative
method in solving the linear system due to a very slow rate of convergence; in some cases
the solution never reaches the desired accuracy. A new well-conditioned IPM, which increases
the rate of convergence of the iterative method is proposed. The computational
advantage is obtained by the use of an inexact Newton method along with the use of
novel preconditioners.
A new warm-start strategy is also presented to solve a QP with an interior-point
method whose data is slightly perturbed from the previous QP. The effectiveness of
this warm-start strategy is demonstrated on a number of available online benchmark
problems. Numerical results indicate that the proposed technique depends upon the
size of perturbation and it leads to a reduction of 30-74% in floating point operations
compared to a cold-start interior point method.
Following the main theme of this thesis, which is to improve the computational efficiency
of an algorithm, an efficient algorithm for solving the coupled Sylvester equation
that arises in converting a system of linear differential-algebraic equations (DAEs) to
ordinary differential equations is also presented. A significant computational advantage
is obtained by exploiting the structure of the involved matrices. The proposed algorithm
removes the need to solve a standard Sylvester equation or to invert a matrix. The
improved performance of this new method over existing techniques is demonstrated by
comparing the number of floating-point operations and via numerical examples
Low computational complexity model reduction of power systems with preservation of physical characteristics
A data-driven algorithm recently proposed to solve the problem of model reduction by moment matching is extended to multi-input, multi-output systems. The algorithm is exploited for the model reduction of large-scale interconnected power systems and it offers, simultaneously, a low computational complexity approximation of the moments and the possibility to easily enforce constraints on the reduced order model. This advantage is used to preserve selected slow and poorly damped modes. The preservation of these modes has been shown to be important from a physical point of view and in obtaining an overall good approximation. The problem of the choice of the socalled tangential directions is also analyzed. The algorithm and the resulting reduced order model are validated with the study of the dynamic response of the NETS-NYPS benchmark system (68-Bus, 16-Machine, 5-Area) to multiple fault scenarios
Optimal Control of Two-Player Systems with Output Feedback
In this article, we consider a fundamental decentralized optimal control
problem, which we call the two-player problem. Two subsystems are
interconnected in a nested information pattern, and output feedback controllers
must be designed for each subsystem. Several special cases of this architecture
have previously been solved, such as the state-feedback case or the case where
the dynamics of both systems are decoupled. In this paper, we present a
detailed solution to the general case. The structure of the optimal
decentralized controller is reminiscent of that of the optimal centralized
controller; each player must estimate the state of the system given their
available information and apply static control policies to these estimates to
compute the optimal controller. The previously solved cases benefit from a
separation between estimation and control which allows one to compute the
control and estimation gains separately. This feature is not present in
general, and some of the gains must be solved for simultaneously. We show that
computing the required coupled estimation and control gains amounts to solving
a small system of linear equations
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