Control and Optimization
Rasoul Hatamian; Seyed Amjad Samareh Hashemi
Abstract
This paper presents an iterative computational method for addressing constrained nonlinear optimal control problems, specifically those involving terminal state, state saturation, and control saturation constraints. The proposed approach reformulates the original ...
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This paper presents an iterative computational method for addressing constrained nonlinear optimal control problems, specifically those involving terminal state, state saturation, and control saturation constraints. The proposed approach reformulates the original problem into a sequence of constrained linear time-varying quadratic optimal control problems. This is achieved by iteratively approximating the nonlinear dynamic system using constrained linear time-varying models. Each reformulated problem is then converted into a standard quadratic programming problem by applying Chelyshkov polynomials in conjunction with a collocation method. Finally, the resulting problems are solved to obtain optimal control solutions
Control and Optimization
Mehdi Ahmadi; Hamid Esmaeili; R Erfanifar
Volume 1, Issue 2 , October 2016, , Pages 53-62
Abstract
In this paper, we suggest a fifth order convergence three-step method for solving system of nonlinear equations. Each iteration of the method requires two function evaluations, two first Fr\'{e}chet derivative evaluations and two matrix inversions. Hence, ...
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In this paper, we suggest a fifth order convergence three-step method for solving system of nonlinear equations. Each iteration of the method requires two function evaluations, two first Fr\'{e}chet derivative evaluations and two matrix inversions. Hence, the efficiency index is $5^{1/({2n+4n^{2}+\frac{4}{3}n^{3}})}$, which is better than that of other three-step methods. The advantages of the method lie in the feature that this technique not only achieves an approximate solution with high accuracy, but also improves the calculation speed. Also, under several mild conditions the convergence analysis of the proposed method is provided. An efficient error estimation is presented for the approximate solution. Numerical examples are included to demonstrate the validity and applicability of the method and the comparisons are made with the existing results.
