Series Solution of a Class of Nonlinear Optimal Regulators

B. F. Spencer, T. L. Timlin, M. K. Sain, S. J. Dyke

Research output: Contribution to journalArticlepeer-review


A class of nonlinear optimal regulators is studied by means of a series expansion of the equations of motion, the optimal cost function, and the optimal control function in a Hamilton-Jacobi context. An indicial formulation of the problem based on symmetric tensor representations is given, and an algorithm for solution of the resulting equations is developed. Associated computational issues are also discussed. An example for the optimal control of a double inverted pendulum is presented to illustrate the approach.

Original languageEnglish (US)
Pages (from-to)321-345
Number of pages25
JournalJournal of Optimization Theory and Applications
Issue number2
StatePublished - Nov 1996
Externally publishedYes


  • Hamilton-Jacobi-Bellman equation
  • Inverted pendulum
  • Nonlinear optimal regulator
  • Tensor expansion

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Management Science and Operations Research


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