Basic Implementation of Multiple-Interval Pseudospectral Methods to Solve Optimal Control Problems
نویسنده
چکیده
A short discussion of optimal control methods is presented including indirect, direct shooting, and direct transcription methods. Next the basics of multiple-interval pseudospectral methods are given independent of the numerical scheme to highlight the fundamentals. The two numerical schemes discussed are the Legendre pseudospectral method with LGL nodes and the Chebyshev pseudospectral method with CGL nodes. A brief comparison between time-marching direct transcription methods and pseudospectral direct transcription is presented. The canonical Bryson-Denham state-constrained double integrator optimal control problem is used as a test optimal control problem. The results from the case study demonstrate the effect of user’s choice in mesh parameters and little difference between the two numerical pseudospectral schemes. ∗Ph.D pre-candidate in Systems and Entrepreneurial Engineering, Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, [email protected] c ©2015 Daniel R. Herber 1
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