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The purpose of this paper is to probe the recursive identification of piecewise affine Hammerstein models directly by using input-output data. To explain the identification process of a parametric piecewise affine nonlinear function, the authors prove that the inverse function corresponding to the given piecewise affine nonlinear function is also an equivalent piecewise affine form. Based on this equivalent property, during the detailed identification process with respect to piecewise affine function and linear dynamical system, three recursive least squares methods are proposed to identify those unknown parameters under the probabilistic description or bounded property of noise.

First, the basic recursive least squares method is used to identify those unknown parameters under the probabilistic description of noise. Second, multi-innovation recursive least squares method is proposed to improve the efficiency lacked in basic recursive least squares method. Third, to relax the strict probabilistic description on noise, the authors provide a projection algorithm with a dead zone in the presence of bounded noise and analyze its two properties.

Based on complex mathematical derivation, the inverse function of a given piecewise affine nonlinear function is also an equivalent piecewise affine form. As the least squares method is suited under one condition that the considered noise may be a zero mean random signal, a projection algorithm with a dead zone in the presence of bounded noise can enhance the robustness in the parameter update equation.

To the best knowledge of the authors, this is the first attempt at identifying piecewise affine Hammerstein models, which combine a piecewise affine function and a linear dynamical system. In the presence of bounded noise, the modified recursive least squares methods are efficient in identifying two kinds of unknown parameters, so that the common set membership method can be replaced by the proposed methods.

The purpose of this paper is to derive the output predictor for a stationary normal process with rational spectral density and linear stochastic discrete-time state-space model, respectively, as the output predictor is very important in model predictive control. The derivations are only dependent on matrix operations. Based on the output predictor, one quadratic programming problem is constructed to achieve the goal of subspace predictive control. Then an improved ellipsoid optimization algorithm is proposed to solve the optimal control input and the complexity analysis of this improved ellipsoid optimization algorithm is also given to complete the previous work. Finally, by the example of the helicopter, the efficiency of the proposed control strategy can be easily realized.

First, a stationary normal process with rational spectral density and one stochastic discrete-time state-space model is described. Second, the output predictors for these two forms are derived, respectively, and the derivation processes are dependent on the Diophantine equation and some basic matrix operations. Third, after inserting these two output predictors into the cost function of predictive control, the control input can be solved by using the improved ellipsoid optimization algorithm and the complexity analysis corresponding to this improved ellipsoid optimization algorithm is also provided.

Subspace predictive control can not only enable automatically tune the parameters in predictive control but also avoids many steps in classical linear Gaussian control. It means that subspace predictive control is independent of any prior knowledge of the controller. An improved ellipsoid optimization algorithm is used to solve the optimal control input and the complexity analysis of this algorithm is also given.

To the best knowledge of the authors, this is the first attempt at deriving the output predictors for stationary normal processes with rational spectral density and one stochastic discrete-time state-space model. Then, the derivation processes are dependent on the Diophantine equation and some basic matrix operations. The complexity analysis corresponding to this improved ellipsoid optimization algorithm is analyzed.

Many important electronic systems are modelled by discrete‐time equations with nonlinearities that are discontinuous and piecewise‐linear, often arising as a result of quantization. Approximations based on linearization – the standard engineering response to nonlinearity – are often quite unhelpful in these systems, because of the form of the nonlinearity. Certain methods and results have been developed over a number of years for the analysis of discontinuous piecewise‐linear discrete‐time dynamics. The aim of this tutorial paper is to review that body of knowledge, and to show how it can be applied to representative electronic systems.

The paper uses an important electronic circuit – the ΣΔ modulator – as a central example, and considers the dynamical behaviour exhibited by this circuit and related circuits.

The circuits under investigation exhibit complex forms of behaviour that can be explained by the application of methods of nonlinear discrete‐time dynamics.

This paper is intended to provide a brief introduction to the body of research that exists into the behaviour of nonlinear discrete‐time circuits and systems with discontinuous piecewise‐linear nonlinearities.

Mesh Parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus area distortion. This study aims to present an assessment of the sensitivity of the minimized distortion with respect to weighed area and angle distortions.

A Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg–Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: α with 0 ≤ α ≤ 1) and angle distortion (weight: 1 − α).

The present study parameterization algorithm has linear complexity [𝒪(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets.

The devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones.

The Reduced Basis Method (RBM) generates low-order models of parametrized PDEs to allow for efficient evaluation of parametrized models in many-query and real-time contexts. The purpose of this paper is to investigate the performance of the RBM in microwave semiconductor devices, governed by Maxwell's equations.

The paper shows the theoretical framework in which the RBM is applied to Maxwell's equations and present numerical results for model reduction under geometry variation.

The RBM reduces model order by a factor of $1,000 and more with guaranteed error bounds.

Exponential convergence speed can be observed by numerical experiments, which makes the RBM a suitable method for parametric model reduction (PMOR).

By using complementarity (solving for both potentials, scalar and vector), one often can provide bilateral bounds for some quantities of interest, like for instance the reluctance of a circuit. However, the vector potential method is expensive, and does not make use of information acquired in the first phase of solving for the scalar potetential. We show how to improve on this by a “local correction” process which, starting from h = grad φ, yields a divergence‐free b, close to μh, by a series of local and independent (parallel) problems.

The use of the prominent finite difference time‐domain (FDTD) method for the time‐domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to unmanageable computational time and storage. The purpose of this paper is to extend the analysis of a discontinuous Galerkin time‐domain (DGTD) method (able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids) and investigate the use of perfectly matched layer regions and the coupling with a fictitious domain approach. The use of a DGTD method with a locally refined, non‐conforming mesh can help focusing on these small details. In this paper, the adaptation to the DGTD method of the fictitious domain approach initially developed for the FDTD is considered, in order to avoid the use of a volume mesh fitting the geometry near the details.

Based on a DGTD method, a fictitious domain approach is developed to deal with complex and small geometrical details.

The fictitious domain approach is a very interesting complement to the FDTD method, since it makes it possible to handle complex geometries. However, the fictitious domain approach requires small volume elements, thus making the use of the FDTD on wide, regular, fine grids often unmanageable. The DGTD method has the ability to handle easily locally refined grids and the paper shows it can be coupled to a fictitious domain approach.

Although the stability and dispersion analysis of the DGTD method is complete, the theoretical analysis of the fictitious domain approach in the DGTD context is not. It is a subject of further investigation (which could provide important insights for potential improvements).

This is believed to be the first time a DGTD method is coupled with a fictitious domain approach.

To model a bargaining environment where the tactic of qualitative commitment (staking a principle) can have a demonstrably strong effect.

Amend the two‐person alternating offers model due to Rubinstein to include simultaneously pre‐announced stakes, and a mechanism for altering agents' utilities by reference to substantial costs of “surrendering a principle” (capitulation costs). Identify all stationary, pure strategy equilibria. Isolate subgame perfect Nash equilibria (SPNE).

SPNE is unique and offers efficient re‐allocation. For high enough capitulation costs, gains at equilibrium (relative to the bench‐mark game without commitment) result to the first‐mover. The shift in the equilibrium allocation is linear in cost.

Symmetric fixed capitulation costs were assumed. Surrender of principle required introduction of discontinuities in the cost function (zero or fixed cost). No gradation of the cost was considered. Future directions could involve discovering what distortions are created by asymmetric costs, by gradations and from smoothing out of the discontinuity.

Practical implications at best point to the potential rewards available from identifying and introducing a high‐cost commitment tactics in a bargaining context.

The innovation is in the use of an explicit bargaining apparatus to examine the commitment tactic (previous research used an axiomatic treatment of bargaining), and in offering a model for the notion of a qualitative commitment. The result about the qualitative shift in the equilibrium is also new. The paper is thus a contribution to the understanding of how an agent may seek to influence the outcome of a game such as “divide the pie (the resource)” through the manufacture/introduction of a factor outside the original game.

This paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on a class of semi-analytical solutions of spatially symmetric Stefan problems in an arbitrary spatial dimension. Via a public repository this study provides a finite element numerical code based on the FEniCS computational platform, which can be used to test and compare any method of choice with the (semi-)analytical solutions. As a particular demonstration, this paper uses the benchmark to test several standard temperature-based implementations of the enthalpy method and assesses their accuracy and stability with respect to the discretization parameters.

The class of spatially symmetric semi-analytical self-similar solutions to the Stefan problem is found for an arbitrary spatial dimension, connecting some of the known results in a unified manner, while providing the solutions’ existence and uniqueness. For two chosen standard semi-implicit temperature-based enthalpy methods, the numerical error assessment of the implementations is carried out in the finite element formulation of the problem. This paper compares the numerical approximations to the semi-analytical solutions and analyzes the influence of discretization parameters, as well as their interdependence. This study also compares accuracy of these methods with other traditional approach based on time-explicit treatment of the effective heat capacity with and without iterative correction.

This study shows that the quantitative comparison between the semi-analytical and numerical solutions of the symmetric Stefan problems can serve as a robust tool for identifying the optimal values of discretization parameters, both in terms of accuracy and stability. Moreover, this study concludes that, from the performance point of view, both of the semi-implicit implementations studied are equivalent, for optimal choice of discretization parameters, they outperform the effective heat capacity method with iterative correction in terms of accuracy, but, by contrast, they lose stability for subcritical thickness of the mushy region.

The proposed benchmark provides a versatile, accessible test bed for computational methods approximating multidimensional phase change problems. The supplemented numerical code can be directly used to test any method of choice against the semi-analytical solutions.

While the solutions of the symmetric Stefan problems for individual spatial dimensions can be found scattered across the literature, the unifying perspective on their derivation presented here has, to the best of the authors’ knowledge, been missing. The unified formulation in a general dimension can be used for the systematic construction of well-posed, reliable and genuinely multidimensional benchmark experiments.

The v×B term in eddy current equations for conducting fluids is an instance of contraction of a differential form by a vector field. We search for a natural way to discretize such contractions. Looking at the operation of extrusion of a manifold, which is dual to contraction, provides the main clue. Two example applications, Carpenter's gauge and Eulerian computations in MHD problems, are suggested.