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