In this paper, a methodology to design fuel-efficient maneuvers for space-based interferometric imaging systems located in near-Earth orbits, under time and imaging constraints, is proposed. The methodology is hierarc...
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In this paper, a methodology to design fuel-efficient maneuvers for space-based interferometric imaging systems located in near-Earth orbits, under time and imaging constraints, is proposed. The methodology is hierarchical and consists of a higher-level nonlinear programming problem and a lower-level linear quadratic tracker. Solutions are obtained for the purpose of quantifying the relationship between the quality of an image obtained by a multispacecraft interferometric imaging system and the dynamic requirements of such imaging maneuvers. These maneuvers are then used for the design of a system capable of obtaining very-high-resolution images from a near-Earth orbital location. To relate the fuel requirements with image quality, the relationship between the imaging process and the error in the final image is studied, and a quality factor is designed to relate the reliability of an image to the trajectory of the spacecraft and, hence, the fuel usage. As an application, a midinfrared imager system located at geostationary orbit is studied and features of the design of such maneuvers are enumerated.
With the development and widespread use of large-scale nonlinear programming (NLP) tools for process optimization, there has been an associated application of NLP formulations with complementarity constraints in order...
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With the development and widespread use of large-scale nonlinear programming (NLP) tools for process optimization, there has been an associated application of NLP formulations with complementarity constraints in order to represent discrete decisions. Also known as mathematical programs with equilibrium constraints (MPECs), these formulations can be used to model certain classes of discrete events and can be more efficient than a mixed integer formulation. However, MPEC formulations and solution strategies are not yet fully developed in process engineering. In this study, we discuss MPEC properties, including concepts of stationarity and linear independence that are essential for well-defined NLP formulations. nonlinear programming based solution strategies for MPECs are then reviewed and examples of complementarity, drawn from chemical engineering applications are presented to illustrate the effectiveness of these formulations. (C) 2008 Elsevier Ltd. All rights reserved.
This paper explores the problem of finding a real-time optimal trajectory for unmanned aerial vehicles to minimize their probability of detection by opponent multiple radar detection systems. The problem is handled us...
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This paper explores the problem of finding a real-time optimal trajectory for unmanned aerial vehicles to minimize their probability of detection by opponent multiple radar detection systems. The problem is handled using the nonlinear trajectory generation method developed by Milam et al. (Milam, M., Mushambi, K., and Murray, R., "New Computational Approach to Real-Time Trajectory Generation for Constrained Mechanical Systems," Proceedings of the 39th IEEE Conference on Decision and Control, Vol. 1, Institute of Electrical and Electronics Engineers, New York, Dec. 2000, pp. 845-851.) The paper presents a formulation of the trajectory generation task as an optimal control problem, where temporal constraints allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent radar. The guidance is provided in the form of sampled tabular data. It is then shown that the success of nonlinear trajectory generation on the proposed low-observable trajectory generation problem depends upon an accurate parameterization of the guidance data. In particular, such an approximator is desired to have a compact architecture, a minimum number of design parameters, and a smooth continuously differentiable input-output mapping. Artificial neural networks as universal approximators are known to possess these features, and thus are considered here as appropriate candidates for this task. Comparison of artificial neural networks against B-spline approximators is provided, as well. Numerical simulations on multiple radar scenarios illustrate unmanned air vehicle trajectories optimized for both detectability and time.
In this paper, we propose a distributed algorithm to solve the yet explored distributed optimal power flow problem with discrete control variables of large distributed power systems. The proposed algorithm consists of...
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In this paper, we propose a distributed algorithm to solve the yet explored distributed optimal power flow problem with discrete control variables of large distributed power systems. The proposed algorithm consists of two distinguished features: 1) a distributed algorithm for solving continuous distributed optimal power flow to serve as a core technique in the framework of ordinal optimization (OO) strategy, and 2) implementing the OO strategy in a distributed power system to select a good enough discrete control variable solution. We have tested the proposed algorithm for several cases on the IEEE 118-bus and Tai Power 244-bus systems using a 4-PC network. The test results demonstrate the validity, robustness, and excellent computational efficiency of the proposed distributed algorithm in getting a good enough feasible solution.
This paper describes a new algorithm for solving nonlinear programming problems with equality constraints. The method introduces the idea of using trust cylinders to keep the infeasibility under control. Each time the...
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This paper describes a new algorithm for solving nonlinear programming problems with equality constraints. The method introduces the idea of using trust cylinders to keep the infeasibility under control. Each time the trust cylinder is violated, a restoration step is called and the infeasibility level is reduced. The radius of the trust cylinder has a nonincreasing update scheme, so eventually a feasible (and optimal) point is obtained. Global and local convergence of the algorithm are analyzed, as well as its numerical performance. The results suggest that the algorithm is promising.
The short-term electric hydrothermal scheduling (STEHS) problem consists in optimizing the production of hydro and thermal electric generation units over a short time period (up to one week long). The problem describe...
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The short-term electric hydrothermal scheduling (STEHS) problem consists in optimizing the production of hydro and thermal electric generation units over a short time period (up to one week long). The problem described in this work can be modelled as a nonlinear network flow problem with linear and nonlinear side constraints. The minimization of this kind of problem can be performed by exploiting the efficiency of network flow techniques. It lies in minimizing approximately a series of augmented Lagrangian functions including only the side constraints, subject to balance constraints in the nodes and capacity bounds. One of the drawbacks of the multiplier methods with quadratic penalty function is that the augmented Lagrangian is not twice differentiable when it is applied to problems with inequality constraints. This article overcomes this difficulty by using the exponential multiplier method. In order to improve the performance some parameters are tuned. The efficiency of this method over STEHS test problems is illustrated by comparing its CPU-times with those of the quadratic multiplier method and with those of the general purpose codes MINOS, SNOPT, and KNITRO. Numerical results are promising.
This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piec...
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This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piecewise-linear model to approximate the nonlinear objective function on a simplicial partition and determines an approximately globally optimal solution by solving a set of standard linear programs. The new approach is applicable to any continuous objective function rather than to sepal-able ones only and could be useful to treat more complex nonlinear problems. A numerical example is given to illustrate the practicability. (C) 2007 Elsevier B.V. All rights reserved.
Some constrained optimization approaches have been recently proposed for the system of nonlinear equations (SNE). Filter approach with line search technique is employed to attack the system of nonlinear equations in t...
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Some constrained optimization approaches have been recently proposed for the system of nonlinear equations (SNE). Filter approach with line search technique is employed to attack the system of nonlinear equations in this paper. The system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved by line search strategy. Furthermore, at each step, some equations are treated as constraints while the others act as objective functions, and filter strategy is then utilized. In essence, constrained optimization methods combined with filter technique are utilized to cope with the system of nonlinear equations. (C) 2007 Elsevier Ltd. All rights reserved.
This paper presents an up to date advances in time-domain system identification using fractional models. Both equation-error- and output-error-based models are detailed. In the former models, prior knowledge is genera...
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This paper presents an up to date advances in time-domain system identification using fractional models. Both equation-error- and output-error-based models are detailed. In the former models, prior knowledge is generally used to fix differentiation orders;model coefficients are estimated using least squares. The latter models allow simultaneous estimation of model coefficients and differentiation orders using nonlinear programing. As an example, a thermal system is identified using a fractional model and is compared to a rational one.
Configurations of a four-column simulated moving bed chromatographic process are investigated by multi-objective optimization. Various existing column configurations are compared through a multi-objective optimization...
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Configurations of a four-column simulated moving bed chromatographic process are investigated by multi-objective optimization. Various existing column configurations are compared through a multi-objective optimization problem. Furthermore, an approach based on an SMB superstructure is applied to find novel configurations which have been found to outperform the standard SMB configuration. An efficient numerical optimization technique is applied to the mathematical model of the SMB process. It has been confirmed that although the optimal configuration highly depends on the purity requirement, the superstructure approach is able to find the most efficient configuration without exploring various existing configurations.
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