Search NASA⌕ Search

SEARCH · Search NASA

Results for “PONTRYAGIN PRINCIPLE”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1967

The matrix minimum principle.

Pontryagin maximum principle restated to apply to systems described by matrix, optimizing performance of linear system

Athans, M.↗
NASA NTRS1967

The matrix minimum principle

Extension of Pontryagin maximum principle and application of matrix minimum principle in solving simple optimal linear regulator problem

MATRIX ANALYSIS↗
NASA NTRS1965

A maximum principle re-entry study

Mathematical model of maximum principle of Pontryagin used to find point-to-point reentry trajectory of space vehicle

REENTRY TRAJECTORY↗
NASA NTRS1969

The reverse Goddard problem.

Fuel-time optimal retrothrust control for vertical and gravity turn ballistic trajectories of soft landing nonlifting bodies based on Pontryagin principle

Bejczy, A. K.↗
NASA NTRS1972

Application of Contraction Mappings to the Control of Nonlinear Systems

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Killingsworth, W. R., Jr.↗