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Dynamic System Optimization Using Higher-Order Runge-Kutta Discretization

[+] Author Affiliations
Brian C. Fabien

University of Washington, Seattle, WA

Paper No. IMECE2010-39421, pp. 321-328; 8 pages
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 8: Dynamic Systems and Control, Parts A and B
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4445-8
  • Copyright © 2010 by ASME


This paper evaluates some numerical methods for the approximate solution dynamic system optimization problems. The paper considers the optimization of dynamic systems that are subject to equality and inequality constraints. These types of problems include optimal control and parameter identification optimization problems. The numerical solution technique is based on transforming the infinite dimensional dynamic system optimization problem into a finite dimensional nonlinear programming (NLP) problem. This solution method is realized by; (i) approximating the control input using a finite set of parameters; (ii) approximating the differential equations using an explicit Runge-Kutta method; and (iii) solving the resultant NLP problem using a sequential quadratic programming method. The paper evaluates the efficacy of approximating the control input using (I) piecewise constants, (II) piecewise linear polynomials, or (III) piecewise cubic polynomials. In addition, the paper compares the performance of various Runge-Kutta methods of order 3 through 9.

Copyright © 2010 by ASME



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