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Title: Approximate Solution of Optimal Control Problem by Using Linear Programming Technique
Authors: SAKAWA, Yoshiyuki
Issue Date: 27-Oct-1964
Publisher: Faculty of Engineering, Kyoto University
Journal title: Memoirs of the Faculty of Engineering, Kyoto University
Volume: 26
Issue: 4
Start page: 274
End page: 283
Abstract: This paper treats an approximate solution of optimal control problem by means of the linear programming technique. Let the system be linear, then the solution of a set of differential equations which governs the system is given by the variation-of-constants formula. The state variables of the system at a fixed time are described by the definite integral, the integrand of which is a linear form in control variables. Upon use of a suitable integration formula, the integrals are approximately represented by a weighted sum of a finite number of values of the integrand. By introducing auxiliary variables, the performance index which is required to be minimum is expressed as a linear function of the variables subject to constraints. Thus, the minimization of a functional is approximately reduced to the minimization of a linear function of many variables subject to linear constraints. This problem is a linear programming problem, and can be solved by using the simplex method. A feasible basic solution to the linear program is shown also.
URI: http://hdl.handle.net/2433/280603
Appears in Collections:Vol.26 Part 4

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