An enhanced scheme of transcribing the system dynamics for the numerical solution of optimal control problems is proposed. This new scheme is based on the standard method of direct collocation that converts an optimal...
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An enhanced scheme of transcribing the system dynamics for the numerical solution of optimal control problems is proposed. This new scheme is based on the standard method of direct collocation that converts an optimal control problem into a nonlinear programming problem via simultaneous state and control discretization. When compared with the standard method, the enhanced scheme has the advantage of higher solution accuracy with minimal additional computational effort. It is particularly suited for systems with states that are related to each other in a special form. For such systems, the ensuing nonlinear programming problem has the same number of constraints as those using the standard method, Numerical results on several optimal control problems using the enhanced scheme are presented, together with comparisons with the results obtained from the standard scheme.
Correlation coefficient of random variables has wide applications in statistical analysis. This paper extends the applications to fuzzy environment, with a methodology for calculating the correlation coefficient of fu...
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Correlation coefficient of random variables has wide applications in statistical analysis. This paper extends the applications to fuzzy environment, with a methodology for calculating the correlation coefficient of fuzzy numbers developed. Different from previous studies, the correlation coefficient calculated in this paper is a fuzzy number, rather than a crisp value. The idea is based on Zadeh's extension principle. A pair of nonlinear programs is formulated to find the alpha-cut of the fuzzy correlation coefficient. From different values of alpha, the membership function of the fuzzy correlation coefficient is constructed. To illustrate how to interpret the fuzzy correlation coefficient in real world applications, the correlation between the technology level and management achievement from a sample of 15 machinery firms in Taiwan is exemplified. All indications show that the correlation between technology and management in Taiwan machinery firms is rather low. (C) 2002 Elsevier Science B.V. All rights reserved.
We propose a novel control algorithm, probabilistically constrained predictive control, to deal with the uncertainties of system disturbances. The output is to be controlled in the constrained range with a desired pro...
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We propose a novel control algorithm, probabilistically constrained predictive control, to deal with the uncertainties of system disturbances. The output is to be controlled in the constrained range with a desired probability. Under the assumption of a linear system, the formulated joint probabilistically constrained problem is convex. Thus, it can be solved with a nonlinear programming solver. The probabilities and gradients of the constraints, composed of disturbance sequences with multivariate normal distribution, are computed using an efficient simulation approach. The results of a test problem show the effectiveness of the proposed algorithm. (C) 2002 Elsevier Science Ltd. All rights reserved.
A model for constructing quadratic objective functions (=utility functions) from interviewing a decision maker is considered. The interview is designed to guarantee a unique non-trivial output of the model and to enab...
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A model for constructing quadratic objective functions (=utility functions) from interviewing a decision maker is considered. The interview is designed to guarantee a unique non-trivial output of the model and to enable estimating both cardinal and ordinal utility, depending on interview scenarios. The model is provided with operational restrictions for the monotonicity of the objective function (= either only growth, or only decrease in every variable) and its quasi-concavity (=convexity of the associated preference). Thereby constructing a monotonic quasi-concave quadratic objective function is reduced to a problem of non-linear programming. To support interactive editing of a quadratic objective function, the stability of the model (the continuous dependence of the output ordinal preference on the input data) is proved. In illustration, we construct a quadratic objective function of ski station customers. Then it is used to adjust prices of 10 ski stations in the south of Stuttgart. (C) 2002 Elsevier Science B.V. All rights reserved.
In this work we present an analytical robustness comparison of two methods for inequality-equality constrained optimization or nonlinear programming. The methods compared are (1) a Feasibility Method (FM) and (2) rudi...
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In this work we present an analytical robustness comparison of two methods for inequality-equality constrained optimization or nonlinear programming. The methods compared are (1) a Feasibility Method (FM) and (2) rudimentary sequential quadratic programming with an L1 merit function (L1-SQP). We then also make note of a very recent global convergence result (similar to that of FM) for a new Filter-type SQP algorithm. And, we claim no analytical robustness advantage of FM over the Filter-type SQP algorithm. The problem statement assumptions include nonstationarity of constraint error norms except at zero constraint error, without which we are not aware of any algorithm that is provably guaranteed to converge to a tolerance-feasible stationary point of a penalty function or a Kuhn-Tucker point. Global convergence of FM is proved analytically. Rudimentary L1-SQP is shown to exhibit potential failure even from a feasible starting point, due to an onset of infeasible subproblems.
作者：
Bretthauer, KMShetty, BTexas A&M Univ
Lowry Mays Coll Business Dept Informat & Operat Management College Stn TX 77843 USA Indiana Univ
Kelley Sch Business Dept Operat & Decis Technol Bloomington IN 47405 USA
We present a survey of algorithms and applications for the nonlinear knapsack problem (or, the nonlinear resource allocation problem). In its most general form, the nonlinear knapsack problem will be defined as a nonl...
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We present a survey of algorithms and applications for the nonlinear knapsack problem (or, the nonlinear resource allocation problem). In its most general form, the nonlinear knapsack problem will be defined as a nonlinear optimization problem with just one constraint, bounds on the variables, and, in some cases, a set of specially structured constraints such as generalized upper bounds (GUBs). This problem is encountered either directly, or as a subproblem, in a variety of applications, including production planning, financial modeling, stratified sampling, and capacity planning in manufacturing, health care, and computer networks. By taking advantage of the special structure of the problem, efficient solution methods can be developed. Problem classes addressed here include continuous and integer problems, convex and nonconvex problems, separable and nonseparable problems, and problems with additional specially structured constraints. (C) 2002 Elsevier Science B.V. All rights reserved.
A singular optimal control problem with a performance index given by the total energy of the system is formulated, and functional analysis ideas are used to reduce the control problem to consider certain integral equa...
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A singular optimal control problem with a performance index given by the total energy of the system is formulated, and functional analysis ideas are used to reduce the control problem to consider certain integral equations. In particular, the optimal control profile for minimum-energy control is obtained in an analytic manner. It is not necessary for the approach to take the second variation into consideration in spite of singular problems. The number of integral equations to be solved is equal to the number of control variables, which is usually much smaller than that of the state variables in the case of large space structures. The time-optimized control can be obtained numerically for the minimum-energy maneuver as the least-time maneuver that does not violate the constraints on the control inputs. The results of the present formulation are compared with that of multiple bang-bang time-optimal control using a simple model. The advantages of the present formulation are discussed on such control performance issues as the reduction of the control effort and the appropriate implementation of continuous controlled jets.
The "gold-mining" decision problem is concerned with the efficient utilization of a delicate mining equipment working in a number of different mines, Richard Bellman was the first to consider this type of a ...
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The "gold-mining" decision problem is concerned with the efficient utilization of a delicate mining equipment working in a number of different mines, Richard Bellman was the first to consider this type of a problem. The solution found by Bellman for the finite-horizon, continuous-time version of the problem with two mines is not overly realistic since he assumed that fractional parts of the same miming equipment could be used in different mines and this fraction could change instantaneously. In this paper, we provide some extensions to this model in order to produce more operational and realistic solutions. Our first model is concerned with developing an operational policy where the equipment may be switched from one mine to the other at most once during a finite horizon. In the next extension we incorporate a cost component in the objective function and assume that the horizon length is not fixed but it is the second decision variable. Structural properties of the optimal solutions are obtained using nonlinear programming. Each model and its solution is illustrated with a numerical example. The models developed here may have potential applications in other areas including production of items requiring the same machine or choosing a sequence of activities requiring the same resource. (C) 2002 Wiley Periodicals, Inc.
The acceleration guidance concept is to plan an aerodynamic acceleration profile that integrates to the desired final position and velocity and satisfies all vehicle constraints and to track the acceleration profile. ...
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The acceleration guidance concept is to plan an aerodynamic acceleration profile that integrates to the desired final position and velocity and satisfies all vehicle constraints and to track the acceleration profile. The longitudinal entry guidance for the space shuttle is acceleration guidance: a drag deceleration profile that integrates to the desired downrange and satisfies the vehicle constraints is planned and tracked primarily by bank-angle adjustments. The kinematics relating the drag profile to the downrange assume that the entry trajectory is a great circle arc. In this paper we consider lateral as well as longitudinal motion in acceleration planning. Three differential equations that are the kinematic relations between the aerodynamic accelerations and the position and velocity variables with energy as the independent variable are used as the basis for two methods of planning the drag and lateral acceleration profiles. The first is simpler and produces a feasible trajectory for a given angle-of-attack profile. The second requires more computation, but produces an optimal trajectory using both angle-of-attack and angle-of-bank variations to control the entry trajectory and has greater capability to shape the entry trajectory. Both methods are demonstrated using an X-33 vehicle model. The optimal method is capable of achieving a specified final heading angle and adjusting the number of bank reversals.
In this paper a general strategy for process design using nonlinear goal programming is developed and applied to machining operations. The developed strategy allows different priority levels for each objective. The re...
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In this paper a general strategy for process design using nonlinear goal programming is developed and applied to machining operations. The developed strategy allows different priority levels for each objective. The resulting design and optimization problem can be solved using unconstrained nonlinear techniques with no need for linearization. Evaluation of the developed strategy was conducted using single pass machining operations. The study proved the effectiveness of the strategy in selecting the optimum process conditions under different production priorities. The developed strategy is also compared with a strategy based on a fuzzy nonlinear programming model. The fuzzy-based solution can be considered as the fuzzy alternative or the approximation of the multiple objective solution.
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