Automated derivation of optimal regulators for nonlinear systems by symbolic manipulation of Poisson series
type: Item
instance of: scholarly article
title: Automated derivation of optimal regulators for nonlinear systems by symbolic manipulation of Poisson series
zbMATH Open document ID: 0544.93032
DOI: 10.1007/BF00938446
published in: Journal of Optimization Theory and Applications
publication date: 1985-01-01T00:00:00Z
review text: 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 Hamiltonian-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.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 3867162
zbMATH Keywords: Hamiltonian boundary-value problem
zbMATH Keywords: Hamilton-Jacobi-Bellman equation
zbMATH Keywords: Poisson series
zbMATH Keywords: Lie series
zbMATH Keywords: optimal nonlinear feedback control
author: M. Kemal Ozgoren
author: Richard W. Longman
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00938446
OpenAlex ID: W1986373748
description: scientific article; zbMATH DE number 3867162