# Accession Number:

## AD0750973

# Title:

## Truncated Power Series Control Representations for Optimization of Dynamic Systems.

# Descriptive Note:

## Technical rept. 1 Sep 70-1 May 72,

# Corporate Author:

## AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING

# Personal Author(s):

# Report Date:

## 1972-08-01

# Pagination or Media Count:

## 161.0

# Abstract:

The set of candidate controls for the solution of an optimal control problem is defined as a finite set of constant coefficient truncated power series. The variables present in the truncated power series are limited to the state variables in the system and the independent variable time. The control solution may thus be limited to a form which can be simply and inexpensively implemented into a system. Multistage optimal control problems with both equality and inequality boundary conditions are considered. A set of necessary conditions and a set of sufficient conditions for a relative minimum solution are developed for an optimal control problem with equality constraints. Solutions to the equations comprising these necessary conditions can be obtained using recursive algorithms. A method called the vector cost method is developed to obtain quasi-optimal solutions to optimal control problem with equality constraints is defined whose solution is a quasi-optimal solution to the original problem. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics