NDLI: Solving optimal control problems using a gegenbauer transcription method

Content Provider	IEEE Xplore Digital Library
Author	Elgindy, K.T. Smith-Miles, K.A. Miller, B.
Copyright Year	2012
Description	Author affiliation: Sch. of Math. Sci., Monash Univ., Clayton, VIC, Australia (Elgindy, K.T.; Smith-Miles, K.A.; Miller, B.)
Abstract	In this paper we describe a novel direct optimization method using Gegenbauer-Gauss (GG) collocation for solving continuous-time optimal control (OC) problems (CTOCPs) with nonlinear dynamics, state and control constraints. The time domain is mapped onto the interval [0; 1], and the dynamical system formulated as a system of ordinary differential equations is transformed into its integral formulation through direct integration. The state and the control variables are fully parameterized using Gegenbauer expansion series with some unknown Gegenbauer spectral coefficients. The proposed Gegenbauer transcription method (GTM) then recasts the performance index, the reduced dynamical system, and the constraints into systems of algebraic equations using optimal Gegenbauer quadratures. Finally, the GTM transcribes the infinite-dimensional OC problem into a parameter nonlinear programming (NLP) problem which can be solved in the spectral space; thus approximating the state and the control variables along the entire time horizon. The high precision and the spectral convergence of the discrete solutions are verified through two OC test problems with nonlinear dynamics and some inequality constraints. The present GTM offers many useful properties and a viable alternative over the available direct optimization methods.
Starting Page	417
Ending Page	424
File Size	564761
Page Count	8
File Format	PDF
e-ISBN	9781922107633
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-11-15
Publisher Place	Australia
Access Restriction	Subscribed
Rights Holder	Institute of Engineers, Australia
Subject Keyword	Optimization methods Cost function Vectors Trajectory Approximation methods Mathematical model Equations
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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