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Spline approximations for nonlinear hereditary control systems

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Abstract

A spline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

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Additional information

This work was supported in part by the Air Force Office of Scientific Research under Contract No. AFOSR-76-3092D, in part by the National Science Foundation under Grants Nos. NSF-MCS-79-05774-05 and NSF-MCS-82-00883, and in part by the US Army Research Office under Contract No. ARO-DAAG29-79-C-0161. The results reported here are a portion of the author's doctoral dissertation written under the supervision of Professor H. T. Banks, Brown University. The author is indebted to Professor Banks for his many valuable comments and suggestions during the course of this work.

Part of this research was completed while the author was a visitor at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, Virginia.

Communicated by L. D. Berkovitz

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Lamm, P.K. Spline approximations for nonlinear hereditary control systems. J Optim Theory Appl 44, 585–624 (1984). https://doi.org/10.1007/BF00938398

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Key Words

  • Hereditary control systems
  • spline-based approximations
  • inertial controllers
  • Mach number control for wind tunnels