作者：
Fahroo, FRoss, IMUSN
Postgrad Sch Dept Math Monterey CA 93943 USA USN
Postgrad Sch Dept Aeronaut & Astronaut Monterey CA 93943 USA
We present a Legendre pseudospectral method for directly estimating the costates of the Bolza problem encountered in optimal control theory. The method is based on calculating the state and control variables at the Le...
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We present a Legendre pseudospectral method for directly estimating the costates of the Bolza problem encountered in optimal control theory. The method is based on calculating the state and control variables at the Legendre-Gauss-Lobatto (LGL) points. An Nth degree Lagrange polynomial approximation of these variables allows a conversion of the optimal control problem into a standard nonlinear programming (NLP) problem with the st ate and control values at the LGL points as optimization parameters. By applying the Karush-Kuhn-Tucker (KKT) theorem to the NLP problem, we show that the KKT multipliers satisfy a discrete analog of the costate dynamics including the transversality conditions. Indeed, we prove that the costates at the LGL points are equal to the KKT multipliers divided by the LGL weights. Hence, the direct solution by this method also automatically yields the costates by way of the Lagrange multipliers that can be extracted from an NLP solver. One important advantage of this technique is that it allows a very simple way to check the optimality of the direct solution. Numerical examples are included to demonstrate the method.
A branch and cut algorithm is developed for solving convex 0-1 Mixed Integer nonlinear programming (MINLP) problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the i...
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A branch and cut algorithm is developed for solving convex 0-1 Mixed Integer nonlinear programming (MINLP) problems. The algorithm integrates Branch and Bound, Outer Approximation and Gomory Cutting Planes. Only the initial Mixed Integer Linear programming (MILP) master problem is considered. At integer solutions nonlinear programming (NLP) problems are solved, using a primal-dual interior point algorithm. Ile objective and constraints are linearized at the optimum solution of these NLP problems and the linearizations are added to all the unsolved nodes of the enumeration tree. Also, Gomory cutting planes, which are valid throughout the tree, arc generated at selected nodes. These cuts help the algorithm to locate integer solutions quickly and consequently improve the linear approximation of the objective and constraints held at the unsolved nodes of the tree. Numerical results show that the addition of Gomory cuts can reduce the number of nodes in the enumeration tree.
The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function that includes only the nonlinear constraints subject to ...
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The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function that includes only the nonlinear constraints subject to the linear constraints and simple bounds. It is then necessary to estimate the multipliers of the nonlinear constraints and variable reduction techniques can be used to carry out the successive minimizations. The viability of estimating the multipliers of the nonlinear constraints from the Kuhn-Tucker system is analyzed and an acceptability test on the residual of the estimation is put forward. The computational performance of the procedure is compared with that of the inexpensive Hestenes-Powell multiplier update. Scope and purpose It is possible to minimize a nonlinear function with linear and nonlinear constraints and simple bounds through the successive minimization of an augmented Lagrangian function including only the nonlinear constraints subject to the linear constraints and simple bounds. This method is particularly interesting when the linear constraints are flow conservation equations, as there are efficient techniques for solving nonlinear network problems. Regarding the successive estimation of the multipliers of the nonlinear constraints there is some doubt as to whether using the Kuhn-Tucker system could improve upon the inexpensive Hestenes-Powell update, especially considering that the Kuhn-Tucker system with partial augmented Lagrangians may not always lead to an acceptable multiplier estimation. Clarifying the computational efficiency of the multiplier update when there are linear or nonlinear side constraints is also a necessary previous step regarding the comparison between partial augmented Lagrangian techniques and either primal partitioning techniques for linear side constraints or projected Lagrangian methods in the case of nonlinear side constraints. (C) 2000 Elsevier Science Ltd. All rights reserved.
The conceptual development and a design methodology are presented for life-extending control where the objective is to achieve high performance and structural durability of complex dynamic systems. A life-extending co...
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The conceptual development and a design methodology are presented for life-extending control where the objective is to achieve high performance and structural durability of complex dynamic systems. A life-extending controller is designed for a reusable rocket engine via damage mitigation in both the fuel (H-2) and oxidizer (O-2) turbine blades while satisfying the dynamic performance requirements of the combustion chamber pressure and O-2/H-2 mixture ratio. The design procedure makes use of a combination of linear and nonlinear techniques and also allows adaptation of the life-extending controller module to augment a conventional performance controller of the rocket engine. The nonlinear part of the controller is designed by optimizing selected parameters in a prescribed dynamic structure of damage compensation.
Up to date, the direct nonlinear predictor-corrector primal-dual interior point algorithm (PCPDIPA) is recognized as an effective method for many power system optimization problems. Its efficiency depends on sparsity ...
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Up to date, the direct nonlinear predictor-corrector primal-dual interior point algorithm (PCPDIPA) is recognized as an effective method for many power system optimization problems. Its efficiency depends on sparsity techniques and a dynamic estimation scheme to decrease the so-call barrier parameter. However, if the value of the barrier parameter is decreased too fast, it would result in small step sizes that halt the convergence of PCPDIPA. In this paper, a hybrid method is proposed to tackle this difficulty. Numerical results of several different sized power systems are presented to illustrate the performance of the proposed method. It is found that the hybrid method reduces the number of iterations by 9%similar to 25% and the CPU time by 6%-22% for all test cases.
In this work a distributed optimal control problem for rime-dependent Burgers equation is analyzed. To solve the nonlinear control problems the augmented Lagrangian-SQP technique is used depending upon a second-order ...
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In this work a distributed optimal control problem for rime-dependent Burgers equation is analyzed. To solve the nonlinear control problems the augmented Lagrangian-SQP technique is used depending upon a second-order sufficient optimality condition. Numerical test examples are presented.
作者：
Liu, XUniv Alberta
Dept Elect & Comp Engn Edmonton AB T6G 2G7 Canada
The Filled Function Method is an approach to finding global minima of multidimensional nonconvex functions. The traditional filled functions have features that may affect the computability when applied to numerical op...
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The Filled Function Method is an approach to finding global minima of multidimensional nonconvex functions. The traditional filled functions have features that may affect the computability when applied to numerical optimization. This paper proposes a new filled function. This function needs only one parameter and does not include exponential terms. Also, the lower bound of weight factor a is usually smaller than that of one previous formulation. Therefore, the proposed new function has better computability than the traditional ones.
A game theoretical approach is presented for numerically computing the capture set of an optimally guided medium-range air-to-air missile against a given target. Realistic point mass models are used because long fligh...
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A game theoretical approach is presented for numerically computing the capture set of an optimally guided medium-range air-to-air missile against a given target. Realistic point mass models are used because long flight times prevent simplifications such as coplanarity or constant speed target. The capture set is obtained by constructing saddle point trajectories on its boundary, or the barrier, numerically. Instead of solving a game of kind, the trajectories are identified by setting up an auxiliary game of degree. The necessary conditions of the auxiliary game are shown to coincide with those of the game of kind. The game of degree is solved from systematically varied initial states with a decomposition method that does not require setting up or solving the necessary conditions. Examples are calculated for a generic fighter and a missile.
作者：
Conway, BAUniv Illinois
Dept Aeronaut & Astronaut Engn Talbot Lab 306 Urbana IL 61801 USA
The process of optimizing the deflection of dangerous asteroids is addressed. It is demonstrated that a near-optimal determination of the direction in which impulse should be applied to the asteroid, as well as the re...
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The process of optimizing the deflection of dangerous asteroids is addressed. It is demonstrated that a near-optimal determination of the direction in which impulse should be applied to the asteroid, as well as the resulting deflection, can be found without any explicit optimization. The method is easily applied to the true, three-dimensional geometry of the problem.
A global optimization algorithm of simulating evolutionary process, called Line-up Competition Algorithm (LCA), was recently proposed. In the LCA, all families are independent and parallel during evolution. According ...
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A global optimization algorithm of simulating evolutionary process, called Line-up Competition Algorithm (LCA), was recently proposed. In the LCA, all families are independent and parallel during evolution. According to the value of their objective function, all families are ranked a line-up and are allocated different search spaces based on their positions in the line-up. The preceding excellent families in the line-up gain less search space, which is favorable for local search, accelerating to find optimal point, while the latter worse families gain larger search space, which is helpful for global search. Through the competition of two levels of inside a family and between families, the first family in the line-up is continually replaced by other families, or the value of objective function of the first family is updated continually. As a result, the optimal solution is approached rapidly. In this paper, the superior performances of the LCA were demonstrated in detail by solving some difficult non-convex nonlinear programming problems constrained and unconstrained. (C) 2001 Elsevier Science Ltd. All rights reserved.
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