Solving Constrained Optimal Control Problems Using State-Dependent Factorization and Chebyshev Polynomials

Date

2018-03-01

Author

Gomroki, Mohammad Mehdi
Topputo, Francesco
Bernelli-Zazzera, Franco
Tekinalp, Ozan

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

287
views

0
downloads

The present work introduces a method to solve constrained nonlinear optimal control problems using state-dependent coefficient factorization and Chebyshev polynomials. A recursive approximation technique known as approximating sequence of Riccati equations is used to replace the nonlinear problem by a sequence of linear-quadratic and time-varying approximating problems. The state variables are approximated and expanded in Chebyshev polynomials. Then, the control variables are written as a function of state variables and their derivatives. The constrained nonlinear optimal control problem is then converted to quadratic programming problem, and a constrained optimization problem is solved. Different final state conditions (unspecified, partly specified, and fully specified) are handled, and the effectiveness of the proposed method is demonstrated by solving sample problems.

Subject Keywords

Optimal feedback-control, Trajectory optimization, Systems

URI

https://hdl.handle.net/11511/46647

Journal

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS

DOI

https://doi.org/10.2514/1.g002392

Collections

Department of Aerospace Engineering, Article

Suggestions

OpenMETU
Core

Efficient Three-Layer Iterative Solutions of Electromagnetic Problems Using the Multilevel Fast Multipole Algorithm Onol, Can; Ucuncu, Arif; Ergül, Özgür Salih (2017-05-19) We present a three-layer iterative algorithm for fast and efficient solutions of electromagnetic problems formulated with surface integral equations. The strategy is based on nested iterative solutions employing the multilevel fast multipole algorithm and its approximate forms. We show that the three-layer mechanism significantly reduces solution times, while it requires no additional memory as opposed to algebraic preconditioners. Numerical examples involving three-dimensional scattering problems are prese...
Large sparse matrix-vector multiplication over finite fields Mangır, Ceyda; Cenk, Murat; Manguoğlu, Murat; Department of Cryptography (2019) Cryptographic computations such as factoring integers and computing discrete logarithms require solving a large sparse system of linear equations over finite fields. When dealing with such systems iterative solvers such as Wiedemann or Lanczos algorithms are used. The computational cost of both methods is often dominated by successive matrix-vector products. In this thesis, we introduce a new algorithm for computing a large sparse matrix-vector multiplication over finite fields. The proposed algorithm is im...
Solving Fokker-Planck Equation By Two-Dimensional Differential Transform Cansu Kurt, Ümmügülsüm; Ozkan, Ozan (2011-07-29) In this paper, we implement a reliable algorithm to obtain exact solutions for Fokker-Planck equation and some similar equations. The approach rests mainly on two dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions are obtained easily without linearizing the problem. Some illustrative examples are given to demonstrate the effectivene...
Assessment of Transient Stability of Nonlinear Dynamic Systems by the Method of Tangent Hyperplanes and the Method of Tangent Hypersurfaces Eskicioglu, Ahmet M. (ASME International, 1989-9-1) Two direct methods, the method of tangent hyperplanes and the method of tangent hypersurfaces, are applied to an elementary nonlinear dynamic system for transient stability assessment. The former method is based on the approximation of the asymptotic stability boundary by hyperplanes at a certain class of unstable singular points in the state-space, and the latter replaces hyperplanes by hypersurfaces. The applicability and accuracy of both methods are evaluated through a comparison of results.
Solution of initial and boundary value problems by the variational iteration method Altintan, D.; Uğur, Ömür (2014-03-15) The Variational Iteration Method (VIM) is an iterative method that obtains the approximate solution of differential equations. In this paper, it is proven that whenever the initial approximation satisfies the initial conditions, vim obtains the solution of Initial Value Problems (IVPs) with a single iteration. By using this fact, we propose a new algorithm for Boundary Value Problems (BVPs): linear and nonlinear ones. Main advantage of the present method is that it does not use Green's function, however, it...

Citation Formats

M. M. Gomroki, F. Topputo, F. Bernelli-Zazzera, and O. Tekinalp, “Solving Constrained Optimal Control Problems Using State-Dependent Factorization and Chebyshev Polynomials,” JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, pp. 618–631, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46647.