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A numerical-CALCULATION FOR SOME NONLINEAR OPTIMAL-CONTROL PROBLEMS WITH A TERMINAL CONSTRAINT USING SYNTHETIC RICCATI TRANSFORMATION AND ITS APPLICATIONS TO THE MANIPULATOR CONTROL PROBLEM

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 1994年第5期77卷 76-86页

作者： CAI, D YAMAURA, H SHIDAMA, Y SHINSHU UNIV FAC ENGNNAGANO 380JAPAN

This paper describes a new numerical calculation algorithm for the nonlinear quadratic optimal problem with nonlinear terminal constraint. Synthetic Riccati transformation proposed earlier by the authors is utilized to solve the forementioned problem. The state differential equation is changed into two differential equations with respect to the two substates vector selected from the state vector. Then, based on the maximum principle and Kronecker's product, two differential equations with respect to the adjoint variables can be derived. To solve the forementioned differential equations, synthetic Riccati transformation is introduced to obtain a Riccati differential equation and an accessory differential equation. Thus, we can calculate the initial values of the adjoint variables by solving Riccati equations backward in time. The convergence condition about this algorithm also is provided. As the application of this algorithm, an attempt is made to apply it to an optimal trajectory control problem for a two-link manipulator. As the result of the simulation, it is confirmed that the algorithm not only has a performance of both fast convergence and high computation accuracy but also is not subject to the selection of the normal parameter for computation.

关键词： NONLINEAR CONTROL OPTIMAL CONTROL numerical algorithm algorithm CONVERGENCE MANIPULATOR CONTROL

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A numerical Analysis of the M/G/1/N Queue with Vacations

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IFAC Proceedings Volumes 2014年第2期47卷 504-509页

作者： Sofiane Ouazine Karim Abbas Department of Mathematics Exact Sciences Faculty University of Bejaia Campus of Targua Ouzemour 06000 Bejaia Algeria LAMOS Laboratory Exact Sciences Faculty University of Bejaia Campus of Targua Ouzemour 06000 Bejaia Algeria

In this paper we discuss the applicability of a computational approach based on a Taylor series expansion for the numerical evaluation of the M/G/1/N queueing model with, so called, working vacations and vacation interruptions. Specifically, we develop the performance measures of the considered system into a Taylor series with respect to the vacation parameter. Our objective is to understand how the vacation rate affects the system performance. numerical results are carried out to illustrate the efficiency of our approach.

关键词： Taylor series expansion numerical algorithm Queues Vacations Performance measures Deviation matrix

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Calculation of supersonic gas flow over a ducted body in regimes with a detached shock wave

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Fluid Dynamics 1981年第3期16卷 460-464页

作者： Tillyaeva, N.I. Moscow

Calculations were made of the supersonic flow of an inviscid gas which does not conduct heat over two-dimensional and axisymmetric ducted bodies in regimes with a detached shock wave and completely subsonic gas velocity in the cylindrical duct. The investigated bodies have a pointed leading edge. The flow rate of the gas through the duct is assumed to be given. This corresponds to the presence in the exit section of the duct of a throttle or an impermeable barrier (in which case the flow rate is zero). The numerical algorithm used in the calculations is based on stabilization in time and Godunov's difference scheme [1] with separation of the shock wave. The integrated flow characteristics are given. The values of the wave resistance coefficient obtained in the calculations are compared with the values found using Taganov's approximate approach. © 1982 Plenum Publishing Corporation.

关键词： Shock Wave Difference Scheme Flow Characteristic numerical algorithm Supersonic Flow

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OPTIMAL INTERMEDIATED INVESTMENT IN A LIQUIDITY-DRIVEN BUSINESS CYCLE

OPTIMAL INTERMEDIATED INVESTMENT IN A LIQUIDITY-DRIVEN BUSIN...

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作者： Pan, Jia PennState University Libraries

学位级别：Doctor of Philosophy

The ﬁrst essay of this dissertation presents a general equilibrium model of a ﬁnan- cial intermediary that extends the model ﬁrst introduced by D. Diamond and P. Dybvig (JPE, 1983) to an inﬁnite-horizon environment. This extension enables the relationship between the real business cycle and the composition of assets held in the banking sector to be studied. As in the D-D model, the bank is modeled as an optimal ﬁnancial in- termediary coalition here. Moreover, the bank’s optimal policy involves decisions about liquidity that vary systematically over the business cycle. The second essay studies a version of the model in the ﬁrst essay with a broader set of contracts–the direct mecha- nisms. We design an efficient allocation of the direct mechanism such that truth telling reporting strategy is an Perfect Bayesian Nash equilibrium of the mechanism. Further analysis show that there may still exist other equilibrium. The third essay describes the numerical algorithm we use to solve the model and provides an estimate for the approx- imation error.

关键词： dynamical programming general equilibrium infinite horizon liquidity risk banking numerical algorithm

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numerical study of the process of unsteady flow in a three-layer porous medium

MAGAZINE OF CIVIL ENGINEERING

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MAGAZINE OF CIVIL ENGINEERING 2023年第3期119卷

作者： Ravshanov, R. Abdullaev, Z. S. Kotov, E. V. Turkmanova, Sh. N. Res Inst Dev Digital Technol & Artificial Intellig Tashkent Uzbekistan Tashkent Inst Irrigat & Agr Mechanizat Engineers Tashkent Uzbekistan Peter Great St Petersburg Polytech Univ St Petersburg Russia

The unsteady fluid flow in a three-layer porous medium is numerically investigated and is an important and topical problem. An analytical solution of the equation for the pressure fluid layer is obtained on the basis of the theory of elastic regime, taking into account the overflow from the coating and the low -permeability layer into the low-permeability bulkhead and external sources that greatly affect the liquid level change. In the main bounded aquifer only horizontal liquid migrations prevail, and in the cover and low -conductive layers only vertical migrations prevail, allowing for horizontal components of the flow rate to be omitted here. Evaporation from the surface of a liquid in a porous medium is considered. Evaporation from the surface of a liquid in a porous medium significantly affects the distribution of overflows in the layers and the distribution of the liquid level in a porous medium. Therefore, when designing vertical drains for enhanced oil recovery in multilayer reservoirs and designing fluid flows in reservoirs, evaporation must be taken into account. The computational experiments have established that the dynamics of changes in the liquid level in a porous medium depends significantly on the evaporation parameter. With an increase in its value, the liquid level in a porous medium decreases proportionally over time. The accuracy of the numerical solution using the balance equation showed that the error does not exceed 1.3%.

关键词： mathematical model groundwater filtration analytical solution numerical algorithm

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On a class of differential games without saddle-point solutions

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Journal of Optimization Theory and Applications 1971年第6期8卷 413-430页

作者： Medanić, J. Andjelić, M. Mihailo Pupin Institute Belgrade Yugoslavia

The minimax solution of a linear regulator problem is considered. A model representing a game situation in which the first player controls the dynamic system and selects a suitable, minimax control strategy, while the second player selects the aim of the game, is formulated. In general, the resulting differential game does not possess a saddle-point solution. Hence, the minimax solution for the player controlling the dynamic system is sought and obtained by modifying the performance criterion in such a way that (a) the minimax strategy remains unchanged and (b) the modified game possesses a saddle-point solution. The modification is achieved by introducing a regularization procedure which is a generalization of the method used in an earlier paper on the quadratic minimax problem. A numerical algorithm for determining the nonlinear minimax strategy in feedback form, in which Pagurek's result on open-loop and closed-loop sensitivity is used to nontrivially simplify the computational aspects of the problem, is presented and applied on a simple example. © 1971 Plenum Publishing Corporation.

关键词： Dynamic System Performance Criterion Early Paper numerical algorithm Linear Regulator

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On the Simultaneous Identification of the Volumetric Heat Capacity and the Thermal Conductivity of a Substance 13th

On the Simultaneous Identification of the Volumetric Heat Ca...

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13th International Conference on Optimization and Applications (OPTIMA)

作者： Albu, Alla Gorchakov, Andrei Zubov, Vladimir Russian Acad Sci Fed Res Ctr Comp Sci & Control Moscow Russia

ISBN: (纸本)9783031225420;9783031225437

The study of nonlinear problems associated with heat transfer in the substance is very important for practice. Previously, we proposed an efficient algorithm for identifying the thermal conductivity of a substance based on the results of experimental observation of the dynamics of the temperature field in an object. In this paper, we investigate the possibility of extending the application of the proposed algorithm to obtain a numerical solution to the problem of simultaneous identification of the temperature-dependent the thermal conductivity and the volumetric heat capacity of the substance under study. The consideration is carried out on the basis of the first initial-boundary value problem for the one-dimensional non-stationary heat equation. The considered inverse coefficient problem is reduced to a variational problem, which is solved by gradient methods based on the application of the Fast Automatic Differentiation technique.

关键词： Nonlinear problems Inverse coefficient problems Heat equation numerical algorithm Fast Automatic Differentiation

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The Problem of the Optimal Packing of the Equal Circles for Special Non-Euclidean Metric 5th

The Problem of the Optimal Packing of the Equal Circles for ...

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5th International Conference on Analysis of Images, Social Networks, and Texts (AIST)

作者： Kazakov, Alexander L. Lempert, Anna A. Nguyen, Huy L. Matrosov Inst Syst Dynam & Control Theory SB RAS Irkutsk Russia Irkutsk Natl Res Tech Univ Irkutsk Russia

ISBN: (纸本)9783319529202;9783319529196

The optimal packing problem of equal circles (2-D spheres) in a bounded set P in a two-dimensional metric space is considered. The sphere packing problem is to find an arrangement in which the spheres fill as large proportion of the space as possible. In the case where the space is Euclidean this problem is well known, but the case of non-Euclidean metrics is studied much worse. However there are some applied problems, which lead us to use other special non-Euclidean metrics. For instance such statements appear in the logistics when we need to locate a given number of commercial facilities and to maximize the overall service area. Notice, that we consider the optimal packing problem in the case, where P is a multiply-connected domain. The special algorithm based on optical-geometric approach is suggested and implemented. The results of numerical experiment are presented and discussed.

关键词： Optimal packing problem Equal circles Non-Euclidean space Multiply-connected domain numerical algorithm Computational experiment

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Discrete State Event-Driven Approach for High-Power Converter Simulations 11

Discrete State Event-Driven Approach for High-Power Converte...

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11th Annual IEEE Energy Conversion Congress and Exposition (ECCE)

作者： Shi, Bochen Zhao, Zhengming Zhu, Yicheng Yu, Zhujun Ju, Jiahe Yuan, Liqiang Chen, Kainan Tsinghua Univ Dept Elect Engn State Key Lab Control & Simulat Power Syst & Gene Beijing Peoples R China

ISBN: (纸本)9781728103952

Demands for high-power converters are increasing rapidly. Nevertheless, due to their complex structures and multi-time-scale features, accurate and efficient simulation of such systems has long been a huge obstacle. Aiming at improving the unacceptably slow simulation speed of high-power converters, this paper improves Discrete State Event-Driven (DSED) approach by implementing a decoupling method. Taking a 10kV 1MW electric energy router as an example, this paper evaluates the effectiveness of DSED with the proposed decoupling method in high-power applications. In the studied case, compared with commercially available tool for power electronics simulation, PLECS (R), DSED can achieve an up to 1000-fold improvement in simulation speed under the same accuracy: PLECS (R) takes 6 hours while DSED only takes 18 seconds. DSED provides a powerful simulation tool for analysis, design and control of high-power converters.

关键词： event-driven simulation numerical algorithm circuit partitioning high-power converter electric energy router solid-state transformer

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Computing Contraction Metrics: Comparison of Different Implementations 24

Computing Contraction Metrics: Comparison of Different Imple...

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24th International Symposium on Mathematical Theory of Networks and Systems (MTNS)

作者： Giesl, P. Hafstein, S. Mehrabinezhad, I Univ Sussex Dept Math Falmer BN1 9QH England Univ Iceland Fac Phys Sci Dunhagi 5 IS-107 Reykjavik Iceland

We discuss the implementation of a novel demanding algorithm to compute contraction metrics for nonlinear systems. We compare MATLAB- and C++-implementations and study the effect of parallelizing the code. Further, we explore the use of different low-level math-libraries for the C++ -implementation and the use of an undocumented code-path that considerably speeds up MATLAB code on AMD's Ryzen processors. Copyright (C) 2021 The Authors.

关键词： Contraction metric Riemannian metric Lyapunov function numerical algorithm Mesh-free collocation

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