• Smart Structures and Systems
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• v.5 no.1
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• pp.69-79
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• 2009

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.

• East Asian mathematical journal
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• v.28 no.3
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• pp.293-303
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• 2012

Sequential quadratic programming (SQP) has been one of the most important methods for solving nonlinear constrained optimization problems. Recently, filter method, proposed by Fletcher and Leyffer, has been extensively applied for its promising numerical results. In this paper, we present and study an active set SQP-filter algorithm for inequality constrained optimization. The active set technique reduces the size of quadratic programming (QP) subproblem. While by the filter method, there is no penalty parameter estimate. Moreover, Maratos effect can be overcome by filter technique. Global convergence property of the proposed algorithm are established under suitable conditions. Some numerical results are reported in this paper.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.899-902
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• 1993

A neural model predictive control strategy combining a neural network for plant identification and a nonlinear programming algorithm for solving nonlinear control problems is proposed. A constrained nonlinear optimization approach using successive quadratic programming combined with neural identification network is used to generate the optimum control law for complex continuous chemical reactor systems that have inherent nonlinear dynamics. The neural model predictive controller (MNPC) shows good performances and robustness. To whom all correspondence should be addressed.

• Journal of Astronomy and Space Sciences
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• v.25 no.4
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• pp.361-374
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• 2008

Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.137-142
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• 2003

We discuss why sample design by mathematical programming can be beneficial to practical surveys. We illustrate some developments of software for sample design using mathematical programming in several statistical organizations. Also, we present certain restrictions on the use of mathematical programming.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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• pp.39-54
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• 1997

This paper presents four process models for machining processes : 1) an economical mathematical model of machining process, 2) a prediction model for surface roughness, 3) a decision model for fuzzy cutting conditions, and 4) a judgment model of machinability with automatic selection of cutting conditions. Each model was developed the economic machining, and these models were applied to theories widely studied in industrial engineering which are nonlinear programming, computer simulation, fuzzy theory, and neural networks. The results of this paper emphasize the human oriented domain of a nonlinear programming problem. From a viewpoint of the decision maker, fuzzy nonlinear programming modeling seems to be apparently more flexible, more acceptable, and more reliable for uncertain, ill-defined, and vague problem situations.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.399-409
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• 2007

In this paper we use iterative dynamic programming in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. In using iterative dynamic programming to solve optimal control problems up to now, we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. Suppose that the performance index can not be expressed in terms of the variables at the last stage only. In other words, suppose the performance index is also a function of controls and variables at the other stages. Then we have a nonseparable optimal control problem. Furthermore, we obtain the path from the initial point up to the approximate solution.

• Progress in Superconductivity and Cryogenics
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• v.18 no.1
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• pp.50-54
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• 2016

In this paper, a hybrid method is proposed to design an air-core superconducting solenoid system for 6 T axial uniform magnetic field using Niobium Titanium (NbTi) superconducting wire. In order to minimize the volume of conductor, the hybrid optimization method including a linear programming and a nonlinear programming was adopted. The feasible space of solenoid is divided by several grids and the magnetic field at target point is approximated by the sum of magnetic field generated by an ideal current loop at the center of each grid. Using the linear programming, a global optimal current distribution in the feasible space can be indicated by non-zero current grids. Furthermore the clusters of the non-zero current grids also give the information of probable solenoids in the feasible space, such as the number, the shape, and so on. Applying these probable solenoids as the initial model, the final practical configuration of solenoids with integer layers can be obtained by the nonlinear programming. The design result illustrates the efficiency and the flexibility of the hybrid method. And this method can also be used for the magnet design which is required the high homogeneity within several ppm (parts per million).

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.12
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• pp.1748-1755
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• 2015

A linear regression is widely used for prediction problem, but it is hard to manage an irregular nature of nonlinear system. Although nonlinear regression methods have been adopted, most of them are only fit to low and limited structure problem with small number of independent variables. However, real-world problem, such as weather prediction required complex nonlinear regression with large number of variables. GP(Genetic Programming) based evolutionary nonlinear regression method is an efficient approach to attach the challenging problem. This paper introduces the improvement of an GP based nonlinear regression method using ADF(Automatically Defined Function). It is believed ADFs allow the evolution of modular solutions and, consequently, improve the performance of the GP technique. The suggested ADF based GP nonlinear regression methods are compared with UM, MLR, and previous GP method for 3 days prediction of wind speed using MOS(Model Output Statistics) for partial South Korean regions. The UM and KLAPS data of 2007-2009, 2011-2013 years are used for experimentation.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.231-244
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• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.