The problem of radar target polarization enhancement is studied. A nonlinear programming model is constructed. Through the analysis via Lagrange multiplier method, this nonlinear optimization problem is equivalently t...
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The problem of radar target polarization enhancement is studied. A nonlinear programming model is constructed. Through the analysis via Lagrange multiplier method, this nonlinear optimization problem is equivalently transformed into a zero-search problem of a monotone function and a series of constrained linear optimization problems. Also the derivative properties of the monotone function are discussed.
A new approach to compute optimal forcing functions for nonlinear dynamic systems expressed by differential equations and stemming from the sliding mode control (SMC) problems is presented. SMC input achieves generati...
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A new approach to compute optimal forcing functions for nonlinear dynamic systems expressed by differential equations and stemming from the sliding mode control (SMC) problems is presented. SMC input achieves generation of a desired trajectory in two phases. In the first phase, the input is designed to steer the state of the nonlinear dynamic system towards a stable (hyper) surface (in practice, it is generally a subspace) in the state space. The second phase starts once the state enters a prespecified neighbourhood of the surface. In this phase, the control input is required to drive the system state towards the origin while keeping it in this neighbourhood. It is shown that by appropriate selection of the objective functions and the constraints, it is possible to model both phases of this problem in the form of constrained optimization problems, which provide an optimal solution direction and thus improve the chattering. Generally, these problems are not convex and therefore require a special solution approach. The modified subgradient algorithm, which serves for solving a large class of nonconvex optimization problems, is used here for solving the optimization problems so constructed. This article also proposes a generalized optimization problem with a unified objective function by taking a weighted sum of two objectives representing the two stages. Validity of the approach of this work is illustrated by stabilizing a two-link planar robot manipulator.
In this paper the solution of nonlinear programming problems by a Sequential Quadratic programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the n...
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In this paper the solution of nonlinear programming problems by a Sequential Quadratic programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a "filter" is introduced which allows a step to he accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl(1) QP.
This paper proposes a novel approach to solve the complex optimal train control problems that so far cannot be perfectly tackled by the existing methods, including the optimal control of a fleet of interacting trains,...
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This paper proposes a novel approach to solve the complex optimal train control problems that so far cannot be perfectly tackled by the existing methods, including the optimal control of a fleet of interacting trains, and the optimal train control involving scheduling. By dividing the track into subsections with constant speed limit and constant gradient, and assuming the train's running resistance to be a quadratic function of speed, two different methods are proposed to solve the problems of interest. The first method assumes an operation sequence of maximum traction-speedholding-coasting-maximum braking on each subsection of the track. To maintain the mathematical tractability, the maximum tractive and maximum braking functions are restricted to be decreasing and piecewisequadratic, based on which the terminal speed;travel distance and energy consumption of each operation can be calculated in a closed-form, given the initial speed and time duration of that operation. With these closed-form expressions, the optimal train control problem is formulated and solved as a nonlinear programming problem. To allow more flexible forms of maximum tractive and maximum braking forces, the second method applies a constant force on each subsection. Performance of these,two methods is compared through a case study of the classic single-train control on a single journey. The proposed methods are further utilised to formulate more complex optimal train control problems, including scheduling a subway line while taking train control into account, and simultaneously optimising the control of a leader-follower train pair under fixed-and moving-block signalling systems. (C) 2017 Elsevier Ltd. All rights reserved.
In today's competitive market, it is no longer practical to design by trial and error Yet, this remains the normal practice, whether through the testing of numerous prototype designs or the simulations of these de...
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In today's competitive market, it is no longer practical to design by trial and error Yet, this remains the normal practice, whether through the testing of numerous prototype designs or the simulations of these designs. Of course, the latter is preferred because it is cheaper, but there remains the issue of finding the best possible design. A trial-and-error approach simply does not address this task. In this paper, the authors describe their work combining computational process modeling and nonlinear programming to optimally design manufacturing processes.
Problem formulations and algorithms are considered for optimization problems with differential-algebraic equation (DAE) models. In particular, we provide an overview of direct methods, based on nonlinear programming (...
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Problem formulations and algorithms are considered for optimization problems with differential-algebraic equation (DAE) models. In particular, we provide an overview of direct methods, based on nonlinear programming (NLP), and indirect, or variational, methods. We further classify each method and tailor it to the appropriate applications. For direct methods, we briefly describe current approaches including the sequential approach (or single shooting), multiple shooting method, and the simultaneous collocation (or direct transcription) approach. In parallel to these strategies we discuss NLP algorithms for these methods and discuss optimality conditions and convergence properties. In particular, we present the simultaneous collocation approach, where both the state and control variable profiles are discretized. This approach allows a transparent handling of inequality constraints and unstable systems. Here, large scale nonlinear programming strategies are essential and a novel barrier method, called IPOPT, is described. This NLP algorithm incorporates a number of features for handling large-scale systems and improving global convergence. The overall approach is Newton-based with analytic second derivatives and this leads to fast convergence rates. Moreover, it allows us to consider the extension of these optimization formulations to deal with nonlinear model predictive control and real-time optimization. To illustrate these topics we consider a case study of a low density polyethylene (LDPE) reactor. This large-scale optimization problem allows us to apply off-line parameter estimation and on-line strategies that include state estimation, nonlinear model predictive control and dynamic real-time optimization.
The distribution of ranging errors of time of arrival techniques fails to satisfy zero means and equal variances. It is one of the major causations of position error of least square-based localization algorithm. The o...
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The distribution of ranging errors of time of arrival techniques fails to satisfy zero means and equal variances. It is one of the major causations of position error of least square-based localization algorithm. The optimization of time of arrival ranging is defined as a nonlinear programming problem. Then, time of arrival ranging error model and geometric constraints are used to define the initial values, objective functions, and constraints of nonlinear programming, as well as to detect line of sight and nonline of sight. A three-dimensional localization algorithm of an indoor time of arrival-based positioning is proposed based on least square and the optimization algorithm. The performance of the ranging and localization accuracies is evaluated by simulation and field testing. Results show that the optimized ranging error successfully satisfies zero mean value and equal variances. Furthermore, the ranging and localization accuracies are significantly improved.
We show that an undiscounted stochastic game possesses optimal stationary strategies if and only if a global minimum with objective value zero can be found to an appropriate nonlinear program with linear constraints. ...
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We show that an undiscounted stochastic game possesses optimal stationary strategies if and only if a global minimum with objective value zero can be found to an appropriate nonlinear program with linear constraints. This nonlinear program arises as a method for solving a certain bilinear system, satisfaction of which is also equivalent to finding a stationary optimal solution for the game. The objective function of the program is a nonnegatively valued quadric polynomial.
The reduction of yarding costs by alternative optimization methods is examined. A general nonlinear programming approach is presented for selecting an optimal yarding strategy from two different skidder types. A reaso...
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The reduction of yarding costs by alternative optimization methods is examined. A general nonlinear programming approach is presented for selecting an optimal yarding strategy from two different skidder types. A reason that an optimal yarding strategy is not apparent is due to the complex interactions of skidders queueing at the landing. The nonlinear programming approach captures the effect of skidders queueing at the landing with the use of nonlinear equations, whereas a linear programming model is unable to include this important effect. The solutions to both nonlinear and linear programming models are compared to provide some insight into the effect of skidder congestion on an optimal yarding strategy.
A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-va...
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A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. The major characteristics of this approach are: (i) it does not require any grid refinement; (ii) the entire process of computation quickly converges to the acceptable level of accuracy, and (iii) the method employs specific sets of mesh points for specific variables, whereby it reduces the number of variables for the separable programming technique. Numerical examples were provided to illustrate the procedure.
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