A nonlinear optimization-based identification procedure for fully parameterized multivariable state-space models is presented. The method can be used to identify linear time-invariant, linear parameter-varying, compos...
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A nonlinear optimization-based identification procedure for fully parameterized multivariable state-space models is presented. The method can be used to identify linear time-invariant, linear parameter-varying, composite local linear, bilinear. Hammerstein and Wiener systems. The nonuniqueness of the full parameterization is dealt with by a projected gradient search to solve the nonlinear optimization problem. Both white and nonwhite measurement noise at the output can be dealt with in a maximum likelihood setting. It is proposed to use subspace identification methods to initialize the nonlinear optimization problem. A computationally efficient and numerically reliable implementation of the procedure is discussed in detail.
We present a method for the certification of algorithms that approximate the L ∞ - or H ∞ -norm of transfer functions of large-scale (descriptor) systems. This certification is needed because such algorithms depend ...
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We present a method for the certification of algorithms that approximate the L ∞ - or H ∞ -norm of transfer functions of large-scale (descriptor) systems. This certification is needed because such algorithms depend heavily on user input, and may converge to a local maximizer of the related singular value function leading to an incorrect value, much lower than the actual norm. Hence, we design an algorithm that determines whether a given value is less than the L ∞ -norm of the transfer function under consideration, and that does not require user input other than the system matrices. In the algorithm, we check whether a certain structured matrix pencil has any purely imaginary eigenvalues by repeatedly applying a structure-preserving shift-and-invert Arnoldi iteration combined with an appropriate shifting strategy. Our algorithm consists of two stages. First, an interval on the imaginary axis which may contain imaginary eigenvalues is determined. Then, in the second stage, a shift is chosen on this interval and the eigenvalues closest to this shift are computed. If none of these eigenvalues is purely imaginary, then an imaginary interval around the shift of appropriate length is removed such that two subintervals remain. This second stage is then repeated on the remaining two subintervals until either a purely imaginary eigenvalue is found or no critical subintervals are left. We show the effectiveness of our method by testing it without any parameter adaptation on a benchmark collection of large-scale systems.
An efficient algorithm for L ∞ -norm calculations, implemented in the SLICOT Library, is described and compared with other available algorithms. The algorithm exploits the Hamiltonian structure of the computational p...
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An efficient algorithm for L ∞ -norm calculations, implemented in the SLICOT Library, is described and compared with other available algorithms. The algorithm exploits the Hamiltonian structure of the computational problem and offers generality and flexibility. Continuous- and discrete-time, standard as well as generalized systems are addressed. Extensive comparisons with other L ∞ -norm solvers show that the generalpurpose SLICOT solver is the most efficient one, especially for standard continuous-time problems.
The paper investigates the use of an iterative procedure based on Broyden’s method for updating estimates of first-order derivatives used in algorithms for solving optimising and optimal control problems. Broyden’s ...
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The paper investigates the use of an iterative procedure based on Broyden’s method for updating estimates of first-order derivatives used in algorithms for solving optimising and optimal control problems. Broyden’s method is employed in two iterative algorithms, the first for use in on-line steady-state optimising control and the second for solving dynamic optimal control problems. Both algorithms are based on Integrated System Optimisation and Parameter Estimation (ISOPE) and require measurements or estimates of derivatives of real process measurements with respect to control variables. Simulation examples demonstrate that the Broyden approach provides an effective means for obtaining the required derivative estimates.
The present wok provides a comparative study on the numerical solution of the dynamic population balance equation (PBE) in batch particulate processes undergoing simultaneous particle aggregation, growth and nucleatio...
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The present wok provides a comparative study on the numerical solution of the dynamic population balance equation (PBE) in batch particulate processes undergoing simultaneous particle aggregation, growth and nucleation. The general PBE was numerically solved using three different techniques namely, the Galerkin on finite elements method (GFEM), the generalized method of moments (GMOM) and stochastic Monte Carlo simulations (MC). numerical simulations were carried out over a wide range of variation of particle aggregation and growth rate models.
作者：
You, J. W.Bongu, S. R.Bao, Q.Panoiu, N. C.UCL
Dept Elect & Elect Engn Torrington Pl London WC1E 7JE England Shenzhen Univ
Key Lab Optoelect Devices & Syst Minist Educ & Guangdong Prov Coll Elect Sci & Technol Shenzhen 518060 Peoples R China Monash Univ
Dept Mat Sci & Engn Clayton Vic 3800 Australia Monash Univ
ARC Ctr Excellence Future Low Energy Elect Techno Clayton Vic 3800 Australia
In this review, we survey the recent advances in nonlinear optics and the applications of two-dimensional (2D) materials. We briefly cover the key developments pertaining to research in the nonlinear optics of graphen...
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In this review, we survey the recent advances in nonlinear optics and the applications of two-dimensional (2D) materials. We briefly cover the key developments pertaining to research in the nonlinear optics of graphene, the quintessential 2D material. Subsequently, we discuss the linear and nonlinear optical properties of several other 2D layered materials, including transition metal chalcogenides, black phosphorus, hexagonal boron nitride, perovskites, and topological insulators, as well as the recent progress in hybrid nanostructures containing 2D materials, such as composites with dyes, plasmonic particles, 2D crystals, and silicon integrated structures. Finally, we highlight a few representative current applications of 2D materials to photonic and optoelectronic devices.
For analyzing distribution functions of relativistic plasma, we propose a mixture model composed of relativistic Maxwellian distributions. We first summarize the basic properties of the relativistic Maxwellian distrib...
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For analyzing distribution functions of relativistic plasma, we propose a mixture model composed of relativistic Maxwellian distributions. We first summarize the basic properties of the relativistic Maxwellian distribution, including the derivation of the normalization constant when there is a bulk velocity. We also examine the maximum likelihood estimation of the relativistic Maxwellian distribution. We then introduce a relativistic Maxwellian mixture model (R-MMM), which is a weighted sum of relativistic Maxwellian distributions. We develop an expectation-maximization algorithm for estimating the parameters of R-MMM, namely, the mixing proportion, the bulk velocity, and the temperature of each component. We apply a two-component R-MMM to a distribution function by a particle-in-cell (PIC) simulation of relativistic pair plasma and separate the simulated distribution function into two components. We find that one component has a large bulk velocity while the other is almost stagnant, and that the two components have almost the same temperatures, which is also consistent with the initial temperature of PIC simulation. (c) 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:// ***/licenses/by/4.0/). https://***/10.1063/5.0059126
This paper concerns an optimal control problem defined on a class of switched mode hybrid dynamical systems. Such systems change modes whenever the state intersects certain surfaces that are defined in the state space...
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This paper concerns an optimal control problem defined on a class of switched mode hybrid dynamical systems. Such systems change modes whenever the state intersects certain surfaces that are defined in the state space. These switching surfaces are parameterized by a finite dimensional vector called the switching parameter. The optimization problem we consider is to minimize a given cost-functional with respect to the switching parameter under the assumption that the initial state of the system is not completely known. Instead, we assume that the initial state can be anywhere in a given set. We will approach this problem by minimizing the worst possible cost over the given set of initial states using results from minimax optimization. The results are then applied in order to solve a navigation problem in mobile robotics.
The paper deals with analysis of optimal control problems arising in models of economic growth. The Pontryagin maximum principle is applied for analysis of the optimal investment problem. Specifically, the research is...
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The paper deals with analysis of optimal control problems arising in models of economic growth. The Pontryagin maximum principle is applied for analysis of the optimal investment problem. Specifically, the research is based on existence results and necessary conditions of optimality in problems with infinite horizon. Properties of Hamiltonian systems are examined for different regimes of optimal control. The existence and uniqueness result is proved for a steady state of the Hamiltonian system. Analysis of properties of eigenvalues and eigenvectors is completed for the linearized system in a neighborhood of the steady state. Description of behavior of the nonlinear Hamiltonian system is provided on the basis of results of the qualitative theory of differential equations. This analysis allows us to outline proportions of the main economic factors and trends of optimal growth in the model. A numerical algorithm for construction of optimal trajectories of economic growth is elaborated on the basis of constructions of backward procedures and conjugation of an approximation linear dynamics with the nonlinear Hamiltonian dynamics. High order precision estimates are obtained for the proposed algorithm. These estimates establish connection between precision parameters in the phase space and precision parameters for functional indices.
Some upwind schemes on stretched meshes are introduced. Our concept for numerical schemes is based on two relations: 1) a polynomial and the derivatives, and 2) a polynomial and the integrations. In this paper, the Ta...
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Some upwind schemes on stretched meshes are introduced. Our concept for numerical schemes is based on two relations: 1) a polynomial and the derivatives, and 2) a polynomial and the integrations. In this paper, the Taylor series expansion of a function q about a certain point and the Lagrangian interpolation formula are utilized to construct the upwind scheme on a physical space. Three results in two dimensions are shown: a motion of viscous vortex with a uniform background flow, a driven cavity flow, and a flow past a circular cylinder. The method presented produces smooth and realistic results for computations with stretched meshes.
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