# Accession Number:

## AD0673385

# Title:

## ON THE LINEAR OPTIMAL SERVO PROBLEM.

# Descriptive Note:

## Research rept.,

# Corporate Author:

## GRUMMAN AIRCRAFT ENGINEERING CORP BETHPAGE N Y RESEARCH DEPT

# Personal Author(s):

# Report Date:

## 1968-08-01

# Pagination or Media Count:

## 21.0

# Abstract:

Optimal control theory is usually formulated for the regulator problem, i.e., for returning a system from a given initial state to a desired state or set of states in an optimal fashion. In practice, one is often more interested in the servo problem, i.e., in having the system follow a class of command input functions. The servo problem can be converted to a regulator problem by considering the command inputs as outputs of another dynamical system - the command generator - and annexing its equations to those of the plant. Each initial condition vector in the command generator produces an element of the class of command inputs. When the command generator is not asymptotically stable, as when it produces step or ramp functions, the Riccati equation whose solution defines the feedback gains may be unstable. It is shown that the Riccati equation can be partitioned and under certain conditions the unstable part deleted. The tracking problem and the model following problem, i.e., following specific command inputs and following the response of a model to the command inputs, respectively, are also studied. Author

# Descriptors:

# Subject Categories:

- Operations Research