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The Model of Nonlinear Filtration Optimal Control for the Problem of Areas Underflooding

JOURNAL OF AUTOMATION AND INFORMATION SCIENCES 2010年第8期42卷 65-82页

作者： Akimenko, V. V. Mitrokhin, S. A. Kiev Natl Taras Shevchenko Univ Kiev Ukraine

A model of optimal control of underflooding of restricted areas by groundwater on the basis of the initial boundary value problem for a parabolic type quasilinear equation is considered. For the initial boundary value problem the maximum principle is proved, sufficient conditions of the existence and uniqueness of a generalized solution, sufficient conditions of the existence of optimal control of this system are obtained. The numerical algorithm for solving the optimal control problem is constructed and the numerical calculations for a model example are given.

关键词： underflooding of restricted areas model of optimal control initial boundary value problem for a parabolic type quasilinear equation the maximum principle numerical algorithm

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Simultaneous solution algorithms for Eulerian-Eulerian gas-solid flow models: Stability analysis and convergence behaviour of a point and a plane solver

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JOURNAL OF COMPUTATIONAL PHYSICS 2005年第1期207卷 309-353页

作者： De Wilde, J Vierendeels, J Heynderickx, GJ Marin, GB State Univ Ghent Petrochem Tech Lab B-9000 Ghent Belgium State Univ Ghent Dept Fluid Heat & Combust Mech Fluid Mech Lab B-9000 Ghent Belgium

Simultaneous solution algorithms for Eulerian-Eulerian gas-solid flow models are presented and their stability analyzed. The integration algorithms are based on dual-time stepping with fourth-order Runge-Kutta in pseudo-time. The domain is solved point or plane wise. The discretization of the inviscid terms is based on a low-Mach limit of the multi-phase preconditioned advection upstream splitting method (MP-AUSMP). The numerical stability of the simultaneous solution algorithms is analyzed in 2D with the Fourier method. Stability results are compared with the convergence behaviour of 3D riser simulations. The impact of the grid aspect ratio, preconditioning, artificial dissipation, and the treatment of the source terms is investigated. A particular advantage of the simultaneous solution algorithms is that they allow a fully implicit treatment of the source terms which are of crucial importance for the Eulerian-Eulerian gas-solid flow models and their solution. The numerical stability of the optimal simultaneous solution algorithm is analyzed for different solids volume fractions and gas-solid slip velocities. Furthermore, the effect of the grid resolution on the convergence behaviour and the simulation results is investigated. Finally, simulations of the bottom zone of a pilot-scale riser with a side solids inlet are experimentally validated. (c) 2005 Elsevier Inc. All rights reserved.

关键词： gas-solid flow Eulerian-Eulerian approach numerical algorithm simultaneous solution algorithm stability analysis point solver plane solver preconditioning advection upstream splitting method riser

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Methods of variational data assimilation with application to problems of hydrothermodynamics of marine water areas

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RUSSIAN JOURNAL OF numerical ANALYSIS AND MATHEMATICAL MODELLING 2020年第4期35卷 189-202页

作者： Agoshkov, Valery I. Lezina, Natalia R. Parmuzin, Eugene I. Sheloput, Tatiana O. Shutyaev, Victor P. Zakharova, Natalia B. RAS Marchuk Inst Numer Math Moscow 119333 Russia Moscow Inst Phys & Technol Dolgoprudnyi 141701 Moscow Region Russia

A series of problems related to the class of inverse problems of ocean hydrothermodynamics and problems of variational data assimilation are formulated in the present paper. We propose methods for solving the problems... 详细信息

关键词： Variational assimilation numerical algorithm determination of heat fluxes sea surface temperature liquid boundaries sea level domain decomposition data processing

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Combined state and least squares parameter estimation algorithms for dynamic systems

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APPLIED MATHEMATICAL MODELLING 2014年第1期38卷 403-412页

作者： Ding, Feng Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China Jiangnan Univ Control Sci & Engn Res Ctr Wuxi 214122 Peoples R China

The control theory and automation technology cast the glory of our era. Highly integrated computer chip and automation products are changing our lives. Mathematical models and parameter estimation are basic for automatic control. This paper discusses the parameter estimation algorithm of establishing the mathematical models for dynamic systems and presents an estimated states based recursive least squares algorithm, and the states of the system are computed through the Kalman filter using the estimated parameters. A numerical example is provided to confirm the effectiveness of the proposed algorithm. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Dynamic system numerical algorithm Least squares Parameter estimation Recursive identification State space model

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Eleven-Point Gradient-Zhang Dynamics algorithm for Time-Dependent Nonlinear Equality-Constraint Programming and Manipulator Application

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2024年第4期21卷 7242-7256页

作者： Wu, Dongqing Zhang, Yunong Zhongkai Univ Agr & Engn Dept Informat & Computat Sci Guangzhou 510220 Peoples R China Sun Yat sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Sun Yat sen Univ Shenzhen Res Inst Shenzhen 518057 Guangdong Peoples R China

The problem of time-dependent nonlinear equality-constraint programming (TDNECP) is a hot topic in various scientific and engineering fields. In this paper, the problem-solving of TDNECP is investigated thoroughly. Combining the gradient dynamics (GD) and the Zhang dynamics (ZD), this study proposes the continuous-time gradient-ZD (GZD) model for the problem-solving of TDNECP by constructing the integrated feedback term from GD and ZD. In addition, a novel eleven-point Zhang time discretization (ZTD-XI) formula is proposed. The convergenceness and order of truncation errors of the proposed ZTD-XI formula are rigorously proven through mathematical derivation. On the basis of the proposed ZTD-XI formula and the continuous-time GZD model, a novel eleven-point discrete-time GZD-based (DTGZD-XI) algorithm is proposed and generalized to obtain the optimal solution of TDNECP. Alongside this, the two-, five-, and eight-point discrete-time GZD-based and GD-based algorithms for the problem-solving of TDNECP are prepared for comparison purpose. Finally, challenging numerical experiments and UR5 manipulator-based computer simulations are carried out. The results further substantiate the effectiveness and superiority of the proposed DTGZD-XI algorithm. Note to Practitioners-This paper is motivated by the need for a high-precision and online dynamics-based algorithm to solve time-dependent nonlinear equality-constraint programming. While existing dynamics-based approaches can be applied to this problem, they often suffer from lagging error and accuracy issues. To address these problems, we propose an integrated dynamics approach, namely the gradient-Zhang dynamics (GZD), along with a novel eleven-point Zhang time discretization (ZTD-XI) formula that achieves order-6 precision. On the basis of the proposed ZTD-XI formula and the continuous-time GZD model, a novel eleven-point discrete-time GZD-based (DTGZD-XI) algorithm is proposed and generalized to obtain the optimal solution of

关键词： Time-dependent nonlinear equality-constraint programming gradient-Zhang dynamics Zhang time discretization numerical algorithm

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ELASTIC WAVE-PROPAGATION USING CYLINDRICAL COORDINATES

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GEOPHYSICS 1991年第12期56卷 2080-2089页

作者： KESSLER, D KOSLOFF, D GEOPHYS DEV CORP HOUSTONTX 77063

A pseudo-spectral method for a solution of the equations of dynamic elasticity in cylindrical coordinates is based on the Chebychev expansion in the radial direction and the Fourier expansion in the angular direction and is suitable for simulating wave propagation in the vicinity of cylindrical objects. The numerical grid consists of a series of concentric rings, each one with a separate Chebychev-Fourier mesh. One numerical grid is defined for the cylindrical cavity and another grid for the medium around the cavity. Combining these two numerical grids allows reduction of the number of grid points in the angular direction in the interior grid and thus increases the time step. This makes the use of polar coordinates much more economic. The numerical algorithm is applicable to any arbitrary heterogeneous medium.

关键词： .number of grid cartesian cylindrical cavity elastic wave numerical algorithm Chebychev angular direction numerical grid

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Monotone Finite-Difference Schemes With Second Order Approximation Based on Regularization Approach for the Dirichlet Boundary Problem of the Gamma Equation

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IEEE ACCESS 2020年 8卷 45119-45132页

作者： Hieu, Le Minh Hanh, Truong Thi Hieu Thanh, Dang Ngoc Hoang Univ Econ Univ Danang Dept Econ Da Nang 550000 Vietnam Univ Econ Univ Danang Dept Ecommerce Da Nang 550000 Vietnam Univ Econ Ho Chi Minh City Sch Business Informat Technol Dept Informat Technol Ho Chi Minh City 700000 Vietnam

We investigate the initial boundary value problem for the Gamma equation transformed from the nonlinear Black-Scholes equation for pricing option to a quasilinear parabolic equation of second derivative. Furthermore, two-side estimates for the exact solution are also provided. By using regularization principle, the unconditionally monotone second order approximation finite-difference scheme on uniform and nonuniform grids is generalized, in that the maximum principle is satisfied without depending on relations of the coefficients and grid parameters. By using the difference maximum principle, we acquired two-side estimates for difference solution for the arbitrary non-sign-constant input data. Finally, we also provide a proof for a priori estimate. It can be confirmed that the two-side estimates for difference solution are completely consistent with the differential problem. Otherwise, the maximal and minimal values of the difference solution is independent from the diffusion and convection coefficients.

关键词： Gamma equation Black-Scholes equation financial engineering stock price prediction numerical solution numerical algorithm maximum principle two-side estimates finite-difference scheme regularization principle

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Explicit integration of a thermo-mechanical model for clays

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COMPUTERS AND GEOTECHNICS 2012年 46卷 13-25页

作者： Hong, P. Y. Pereira, J. M. Cui, Y. J. Tang, A. M. Univ Paris Est Lab Navier Ecole Ponts ParisTech Paris France Tongji Univ Dept Geotechn Engn Shanghai Peoples R China

This paper considers the numerical implementation of an existing constitutive model that was developed to simulate the thermo-mechanical behavior of clays. The model, which combines two plastic mechanisms, has been reformulated using generalized stress and strain variables accounting for the presence of temperature as an additional variable. Mixed control conditions are introduced to simulate standard thermo-mechanical laboratory tests. An explicit integration scheme is used with an adaptive time-stepping scheme specifically designed for the considered thermo-mechanical model. This sub-stepping procedure enables the constitutive model to be integrated accurately and efficiently by automatically adjusting the size of sub-steps to maintain the local integration error below a specified tolerance. Special attention is paid to the cases where the two yield surfaces are activated simultaneously. The correction of the drift of the stress point from the yield surface is also accounted for. This thermo-elastoplastic model has been implemented in a constitutive driver aiming at simulating thermo-mechanical tests in the triaxial stress space. The efficiency of this integration algorithm is discussed and the clear advantage of using the adaptive sub-stepping procedure is shown. The constitutive model is finally used to simulate thermo-mechanical tests. The results are compared to available experimental data and show the good capabilities of the constitutive model. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： Thermo-mechanical behavior Constitutive model Stress integration Time integration numerical algorithm

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A constrained optimal PID-like controller design for spacecraft attitude stabilization

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ACTA ASTRONAUTICA 2012年 74卷 131-140页

作者： Li, Chuanjiang Teo, Kok Lay Li, Bin Ma, Guangfu Harbin Inst Technol Dept Control Sci & Engn Harbin 150001 Peoples R China Curtin Univ Dept Math & Stat Perth WA 6845 Australia Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China

In this paper, an optimal PID-like controller is proposed for a spacecraft attitude stabilization problem subject to continuous inequality constraints on the spacecraft angular velocity and control, as well as terminal constraints on the spacecraft attitude and angular velocity. The closed-loop stability is established using the Lyapunov stability theory. The constraint transcription method and a local smoothing technique are used to construct a smooth approximate function for each of the continuous inequality constraints on the angular velocity and control. Then, by using the concept of the penalty function, these approximate smooth functions are appended to the quadratic performance criterion forming an augmented cost function. Consequently, the constrained optimal control problem under the PID-like controller is approximated by a sequence of optimal parameter selection problems subject to only terminal constraints on the spacecraft attitudes. A reliable computational algorithm is derived for the tuning of the optimal PID-like control parameters. Finally, numerical simulations are carried out to illustrate the effectiveness of the methodology proposed. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Spacecraft attitude stabilization Closed-loop stability Optimal PID-like controller Optimal parameter selection problem numerical algorithm

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Simple algorithm for temperature distribution calculations

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APPLIED MATHEMATICAL MODELLING 2004年第2期28卷 173-182页

作者： Gembarovic, J Löffler, M Gembarovic, J TPRL Inc W Lafayette IN 47906 USA

Dumped heat wave algorithm is used to approximately calculate temperature distribution in a finite, one-dimensional medium and the results are compared to known analytical solutions and finite difference numerical algorithm. The proposed algorithm can serve as a rapid, easy to understand and easy to implement alternative to existing numerical and analytical procedures for calculating the temperature distribution in solids. (C) 2003 Elsevier Inc. All rights reserved.

关键词： numerical algorithm heat conduction temperature distribution

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