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

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Abstract

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.

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Additional information

This research was supported by NSF Grant No. ENG-78-10232. This paper was presented at the 1982 Conference on Information Sciences and Systems, Princeton, New Jersey, and appears in the Proceedings.

Communicated by J. V. Breakwell

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Özgören, M.K., Longman, R.W. Automated derivation of optimal regulators for nonlinear systems by symbolic manipulation of Poisson series. J Optim Theory Appl 45, 443–476 (1985). https://doi.org/10.1007/BF00938446

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Key Words

  • Optimal control theory
  • perturbation methods
  • Lie series
  • Poisson series