Solving of time varying quadratic optimal control problems by using Bézier control points

Abstract

Abstract. In this paper, linear quadratic optimal control problems are solved by applying least square method based on Bézier control points. We divide the interval which includes t, into k subintervals and approximate the trajectory and control functions by Bézier curves. We have chosen the Bézier curves as piacewise polynomials of degree three, and determined Bézier curves on any subinterval by four control points. By using least square method, we introduce an optimization problem and compute the control points by solving this optimization problem.Numerical experiments are presented to illustrate the proposed method.Mathematical subject classification: 49N10.

Solution of optimal control problems with Payoff term and fixed state endpoint by using Bezier polynomials

“…There is a large number of research papers that employ this method to solve optimal control problems (see for example [2,3,5,7,8,9,10,11,12,13,14,17] and the references therein). Razzaghi, et.…”

“…The method is based on approximating the state variables and the control variables with Bezier polynomials [5,13,14]. Our method consists of reducing the optimal control problem to a NLP one by first expanding the state rateẋ(t) the control u(t) as a Bezier polynomial with unknown coefficients.…”

A Meshless Method For Solving Delay Differential Equation Using Radial Basis Functions With Error Analysis

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Legendre Coefficients Method for Linear-Quadratic Optimal Control Problems by Using Genetic Algorithms

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