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An algorithm for numerical integration of nonlinear Lagrange equations is presented. Formulas for approximate solutions are derived using the Taylor Series Method. Radius of convergence of estimates and error bounds are given.
This paper describes the resolution of the optimal reactive dispatch (ORD) problem with respect to voltage magnitudes and taps of on-load tap changing (OLTC) transformers. Although the ORD consists in a large-scale mixed integer nonlinear programming (MINLP) problem due to the discrete nature of some system controls, most papers in technical journals disregard the discrete modeling of such variables...
We explore several options to introduce a pseudo-spectral expansion along the longitudinal direction in a spectral-domain integral equation for scattering by periodic dielectric structures. To this end we first simplify the integral equation to the formulation for a one-dimensional dielectric slab and consider the computational efficiency, convergence, and conditioning of several schemes. One scheme...
In this paper the method for optimisation of PDα controllers for linear systems was investigated. A new method for approximation of performance index with infinite horizon was presented and used. Optimisation was undertaken on approximated performance index with satisfactory results for multiple test systems. Results are promising, convergence of approximant and performance index was observed and...
This paper proposes a new efficient multi-antenna expansion method for Vandermonde-subspace frequency division multiplexing (VFDM). VFDM is a technique for interference cancellation in overlay networks that allows a secondary network to operate simultaneously with a primary network on the same frequency band; however, conventional VFDM is not applicable to multi-antenna systems in general, such as...
Traditional techniques like Monte-Carlo (MC) methods have been widely used to quantify the effect of uncertainties in numerical models. However, MC solution statistics converge slowly requiring many simulations. In this paper, the Polynomial Chaos Expansion (PCE) and Control Variate (CV) method, which display faster rates of convergence are investigated. A non-intrusive formulation of a third order...
We describe a new algorithm for trajectory optimization of mechanical systems. Our method combines pseudo-spectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical quantities such as momentum. We thus obtain a global discretization of the Lagrange-d'Alembert variational principle using pseudo-spectral methods. Our proposed scheme...
In this paper, stabilization of a class of power converters with discrete-time bilinear averaged dynamic model is investigated by using Sum of Squares (SOS) programming and quadratic Lyapunov functions. A general bilinear mathematical discrete model is derived for a class of DC/DC power converters and the coordinates of the developed model are transformed to the origin. A controller design methodology...
Several well-known algorithms in the field of combinatorial optimization can be interpreted in terms of the primal-dual method for solving linear programs. For example, Dijkstra's algorithm, the Ford-Fulkerson algorithm, and the Hungarian algorithm can all be viewed as the primal-dual method applied to the linear programming formulations of their respective optimization problems. Roughly speaking,...
This work proposes a policy iteration procedure for the synthesis of optimal and globally stabilizing control policies for Linear Time Invariant (LTI) Asymptotically Null-controllable with Bounded Inputs (ANCBI) systems. This class includes systems with eigenvalues on the imaginary axis (possibly repeated) but no pole with positive real part. The proposed policy iteration relies on a class of piecewise...
Unlike traditional methods that aim to approximate a function over a large compact set, a function approximation method is developed in this paper that aims to approximate a function in a small neighborhood of a state that travels within a compact set. The development is based on universal reproducing kernel Hilbert spaces over the n..dimensional Euclidean space. Three theorems are introduced that...
We formulate a method for designing dynamic average consensus estimators with optimal worst-case asymptotic convergence rate over a large set of undirected graphs. The estimators achieve average consensus for constant inputs and are robust to both initialization errors and changes in network topology. The structure of a general class of polynomial linear protocols is characterized and used to find...
Volume estimates of metric balls in manifolds find diverse applications in communications and information theory. In this paper, we derive some new results for the volume of a metric ball in unitary group under Frobenius norm topological metric. Our first result is an integral representation of the exact volume, which involves a Toeplitz determinant of Bessel functions. The connection to matrix-variate...
The Maximum Likelihood Estimator (MLE) is widely used in estimating information measures, and involves “plugging-in” the empirical distribution of the data to estimate a given functional of the unknown distribution. In this work we propose a general framework and procedure to analyze the nonasymptotic performance of the MLE in estimating functionals of discrete distributions, under the worst-case...
Growth conditions are given on the samples f(n), n = 0, ±1, ±2, …, of an entire function f(z) of exponential type less than π that imply that the corresponding cardinal sine series converges. These conditions are the least restrictive of their kind that are possible. Furthermore, an example is provided of an entire function f(z) of exponential type π that is bounded on the real axis and whose corresponding...
The selection of a suitable set of visual features for an optimal performance of closed-loop visual control or Structure from Motion (SfM) schemes is still an open problem in the visual servoing community. For instance, when considering integral region-based features such as image moments, only heuristic, partial, or local results are currently available for guiding the selection of an appropriate...
In this paper we consider the periodic Riccati differential equation (PRDE) X = A∗(t)X − XA(t) − Q(t) + XS(t)X (PRDE) where A, Q and S are n×n piecewise continuous, bounded matrix functions of period ω. Furthermore Q(t) = Q∗(t), S(t) = S∗(t) for all t ∊ R.
In this paper, model sets for continuous-time linear time invariant systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalise the well known Laguerre and Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces Hp(Π), 1 ≤ p < ∞ and the right half plane algebra Α(Π) provided that a mild condition on the choice of basis...
An algorithm for the numerical solution of an important algebraic matrix equation in control system design is developed. It is based on ideas arising from probability-1 homotopy methods, for the solution of algebraic systems of equations. The specialisation of this matrix equation into the algebraic Riccati matrix equation for continuous time systems is discussed. The proposed algorithm can be used...
By factorizing the A- and B-polynomials in an ARMAX model and filtering the input/output data with the appropriate factors, the parameters of the model are estimated in a decoupled fashion. This may improve the robustness of some estimators significantly, e.g., when applied to very stiff systems. Earlier work on these techniques has established both local and global convergence properties of some...
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