• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.620-626
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• 2004

For general nonlinear processes, it is difficult to control with a linear model-based control method and nonlinear controls are considered. Among the numerous approaches suggested, the most rigorous approach is to use dynamic optimization. Many general engineering problems like control, scheduling, planning etc. are expressed by functional optimization problem and most of them can be changed into dynamic programming (DP) problems. However the DP problems are used in just few cases because as the size of the problem grows, the dynamic programming approach is suffered from the burden of calculation which is called as 'curse of dimensionality'. In order to avoid this problem, the Neuro-Dynamic Programming (NDP) approach is proposed by Bertsekas and Tsitsiklis (1996). To get the solution of seriously nonlinear process control, the interest in NDP approach is enlarged and NDP algorithm is applied to diverse areas such as retailing, finance, inventory management, communication networks, etc. and it has been extended to chemical engineering parts. In the NDP approach, we select the optimal control input policy to minimize the value of cost which is calculated by the sum of current stage cost and future stages cost starting from the next state. The cost value is related with a weight square sum of error and input movement. During the calculation of optimal input policy, if the approximate cost function by using simulation data is utilized with Bellman iteration, the burden of calculation can be relieved and the curse of dimensionality problem of DP can be overcome. It is very important issue how to construct the cost-to-go function which has a good approximate performance. The neural network is one of the eager learning methods and it works as a global approximator to cost-to-go function. In this algorithm, the training of neural network is important and difficult part, and it gives significant effect on the performance of control. To avoid the difficulty in neural network training, the lazy learning method like k-nearest neighbor method can be exploited. The training is unnecessary for this method but requires more computation time and greater data storage. The pH neutralization process has long been taken as a representative benchmark problem of nonlin ar chemical process control due to its nonlinearity and time-varying nature. In this study, the NDP algorithm was applied to pH neutralization process. At first, the pH neutralization process control to use NDP algorithm was performed through simulations with various approximators. The global and local approximators are used for NDP calculation. After that, the verification of NDP in real system was made by pH neutralization experiment. The control results by NDP algorithm was compared with those by the PI controller which is traditionally used, in both simulations and experiments. From the comparison of results, the control by NDP algorithm showed faster and better control performance than PI controller. In addition to that, the control by NDP algorithm showed the good results when it applied to the cases with disturbances and multiple set point changes.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.11
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• pp.1682-1688
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• 2012

This paper introduces a GP(Genetic Programming) based robust technique for temperature compensation in short-range prediction. Development of an efficient MOS(Model Output Statistics) is necessary to correct systematic errors of the model, because forecast models do not reliably determine weather conditions. Most of MOS use a linear regression to compensate a prediction model, therefore it is hard to manage an irregular nature of prediction. In order to solve the problem, a nonlinear and symbolic regression method using GP is suggested. The purpose of this study is to evaluate the accuracy of the estimation by a GP based nonlinear MOS for 3 days temperatures in Korean regions. This method is then compared to the UM model and has shown superior results. The training period of 2007-2009 summer is used, and the data of 2010 summer is adopted for verification.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.10a
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• pp.419-424
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• 1999

In this paper, the comparison of the first order approximation schemes such as SLP (sequential linear programming), CONLIN(convex linearization), MMA(method of moving asymptotes) and the second order approximation scheme, SQP(sequential quadratic programming) was accomplished for optimization of and nonlinear structures. It was found that MMA and SQP(sequential quadratic programming) was accomplished for optimization of and nonlinear structures. It was found that MMA and SQP are the most efficient methods for optimization. But the number of function call of SQP is much more than that of MMA. Therefore, when it is considered with the expense of computation, MMA is more efficient than SQP. In order to examine the efficiency of MMA for complex optimization problem, it was applied to the helicopter tail boom considering column buckling and local wall buckling constraints. It is concluded that MMA can be a very efficient approximation scheme from simple problems to complex problems.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.1-23
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• 2005

The decentralized static output feedback design problem is considered. A constrained trust region method is developed that solves this optimal control problem when a complete set of state variables is not available. The considered problem is interpreted as a non-linear (non-convex) constrained matrix optimization problem. Then, a decentralized constrained trust region method is developed for this problem class exploiting the diagonal structure of the problem and using inexact computations. Finally, numerical results are given for the proposed method.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.315-328
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• 2005

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

• 전기의세계
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• v.21 no.1
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• pp.13-16
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• 1972

Dynamic Programming is regarded as a very powerful tool for solving nonlinear optimization problem subject to a number of constraints of state and control variables, but has definite disadvantages that it requires much more computing time and consumes much more memory spaces than other technigues. In order to eliminate the above-mentioned demerits, this paper suggests a news technique called Multiple Dynamic Programming. The underlying principles are based on the concept of multiple passes that, instead of forming fin lattices in time-state plane as adopted in the conventional Dynamic Programming, the Multiple Dynamic Programming constitutes, at the first pass, coarse lattices in the feasible domain of time-state plane and determines the optimal state trajectory by the usual method of Dynamic Programming, and at the second pass again constitutes finer lattices in the narrower domain surrounded by both the upperand lower edges next to the lattice edges through which the first pass optimal trajectory passes and determines the more accurate optimal trajectory of state, and then at the third pass repeats the same processes, and so on. The suggested technique insures remarkable curtailment in amounts of computer memory spaces and conputing time, and its applicability has been demonstrated by a case study on the hydro-thermal power coordination in Korean power system.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.6
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• pp.582-587
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• 1997

This paper deals with the control problem under nonlinear boiler systems with noise, and input constraints. MCMBPC(Multivariable Constrained Model-Based Predictive Controller) proposed by Wilkinson et al.[10,11] is used and nominal model is modified in this paper in order to applied to nonlinear boiler systems with feed-forward terms. The solution of the cost function optimization constrained on input and/or output variables is achieved using quadratic programming, via singular value decomposition(SVD). The controller designed is shown to satisfy the constraints and to have excellent tracking performance via simulation applied to nonlinear dynamic drum boiler turbine model for 16OMW unit.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.236-247
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• 1992

Optimization has been developed to minimize the cost function while satisfying constraints. Nonlinear Programming method is used as a tool for the optimization. Usually, cost and constraint function calculations are required in the engineering applications, but those calculations are extremely expensive. Especially, the function and sensitivity analyses cause a bottleneck in structural optimization which utilizes the Finite Element Method. Also, when the functions are quite noisy, the informations do not carry out proper role in the optimization process. An algorithm called "Second-order Approximation Method" has been proposed to overcome the difficulties recently. The cost and constraint functions are approximated by the second-order Taylor series expansion on a nominal points in the algorithm. An optimal design problem is defined with the approximated functions and the approximated problem is solved by a nonlinear programming numerical algorithm. The solution is included in a candidate point set which is evaluated for a new nominal point. Since the functions are approximated only by the function values, sensitivity informations are not needed. One-dimensional line search is unnecessary due to the fact that the nonlinear algorithm handles the approximated functions. In this research, the method is analyzed and the performance is evaluated. Several mathematical problems are created and some standard engineering problems are selected for the evaluation. Through numerical results, applicabilities of the algorithm to large scale and complex problems are presented.presented.

• Advances in aircraft and spacecraft science
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• v.6 no.5
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• pp.391-407
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• 2019

Flight trajectory optimization has become an important factor not only to reduce the operational costs (e.g.,, fuel and time related costs) of the airliners but also to reduce the environmental impact (e.g.,, emissions, contrails and noise etc.) caused by the airliners. So far, these factors have been dealt with in the context of 2D and 3D trajectory optimization, which are no longer efficient. Presently, the 4D trajectory optimization is required in order to cope with the current air traffic management (ATM). This study deals with a cubic spline approximation method for solving 4D trajectory optimization problem (TOP). The state vector, its time derivative and control vector are parameterized using cubic spline interpolation (CSI). Consequently, the objective function and constraints are expressed as functions of the value of state and control at the temporal nodes, this representation transforms the TOP into nonlinear programming problem (NLP). The proposed method is successfully applied to the generation of a minimum length optimal trajectories along 4D waypoints, where the method generated smooth 4D optimal trajectories with very accurate results.

• Journal of Korean Society of Steel Construction
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• v.16 no.1 s.68
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• pp.123-134
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• 2004

In this research, a multilevel decomposition technique to enhance the efficiency of the configuration optimization of truss structures was proposed. On the first level, the nonlinear programming problem was formulated considering cross-sectional areas as design variables, weight, or volume as objective function and behavior under multiloading condition as design constraint. Said nonlinear programming problem was transformed into a sequential linear programming problem. which was effective in calculation through the approximation of member forces using behavior space approach. Such approach has proven to be efficient in sensitivity analysis and different form existing shape optimization studies. The modified method of feasible direction (MMFD) was used for the optimization process. On the second level, by treating only shape design variables, the optimum problem was transformed into and unconstrained optimal design problem. A unidirectional search technique was used. As numerical examples, some truss structures were applied to illustrate the applicability. and validity of the formulated algorithm.