Automated derivation of optimal regulators for nonlinear systems by symbolic manipulation of Poisson series

  • M. K. Özgören
  • R. W. Longman
Contributed Papers


Concepts of programmability and compact programmability are defined relative to a class of modified Poisson series. Lie-series-based canonical perturbation methods from astrodynamics are applied to the Hamiltonian system boundary-value problem, and more usual methods are applied to the perturbed Hamilton-Jacobi-Bellman partial differential equation, in order to obtain a complete set of equations for the perturbed optimal feedback control law for both infinite-time and finite-time regulator problems. The relative advantages of each approach are evaluated. A major aim of the paper is to determine the largest class of perturbations, within the set of Poisson series, for which the equations can be derived on a computer by symbolic manipulation. The more general the class, the more accurate the perturbation solution can be, for a given order. The solutions developed are complete; all that remains is to program them in order to have computerized derivations of the optimal nonlinear feedback control laws.

Key Words

Optimal control theory perturbation methods Lie series Poisson series 


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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • M. K. Özgören
    • 1
  • R. W. Longman
    • 2
  1. 1.Department of Mechanical EngineeringMiddle East Technical UniversityAnkaraTurkey
  2. 2.Department of Mechanical EngineeringColumbia UniversityNew York

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