
Foundation ::
Optimization ::
ORACLS

ORACLS
Optimal Regulator Algorithms for the Control of Linear Systems


Moderators: Adopt This Application! 
SOURCE CODE AVAILABLE


This control theory design package, called Optimal Regulator Algorithms
for the Control of Linear Systems (ORACLS), was developed to aid in
the design of controllers and optimal filters for systems which can be modeled
by linear, timeinvariant differential and difference equations.
Optimal linear quadratic regulator theory, currently referred to as the
LinearQuadraticGaussian (LQG) problem, has become the most widely accepted
method of determining optimal control policy. Within this theory,
the infinite duration timeinvariant problems, which lead to constant
gain feedback control laws and constant KalmanBucy filter gains for reconstruction
of the system state, exhibit high tractability and potential
ease of implementation. A variety of new and efficient methods in the field
of numerical linear algebra have been combined into the ORACLS program,
which provides for the solution to timeinvariant continuous or discrete
LQG problems. The ORACLS package is particularly attractive to the control
system designer because it provides a rigorous tool for dealing with
multiinput and multioutput dynamic systems in both continuous and discrete
form.
The ORACLS programming system is a collection of subroutines which
can be used to formulate, manipulate, and solve various LQG design problems.
The ORACLS program is constructed in a manner which permits the user
to maintain considerable flexibility at each operational state. This flexibility
is accomplished by providing primary operations, analysis of linear
timeinvariant systems, and control synthesis based on LQG methodology.
The inputoutput routines handle the reading and writing of numerical
matrices, printing heading information, and accumulating output information.
The basic vectormatrix operations include
 addition,
 subtraction,
 multiplication,
 equation,
 norm construction,
 tracing,
 transposition,
 scaling,
 juxtaposition, and
 construction of null and identity matrices.
The analysis routines provide for the following computations:
 the eigenvalues and eigenvectors of real matrices;
 the relative stability of a
given matrix;
 matrix factorization;
 the solution of linear constant coefficient
vectormatrix algebraic equations;
 the controllability properties
of a linear timeinvariant system;
 the steadystate covariance matrix of an
openloop stable system forced by white noise;
 and the transient response
of continuous linear timeinvariant systems.
The control law design routines of ORACLS implement some of the more
common techniques of timeinvariant LQG methodology. For the finiteduration
optimal linear regulator problem with noisefree measurements,
continuous dynamics, and integral performance index, a routine is provided
which implements the negative exponential method for finding both the transient
and steadystate solutions to the matrix Riccati equation.
For the
discrete version of this problem, the method of backwards differencing is
applied to find the solutions to the discrete Riccati equation. A routine
is also included to solve the steadystate Riccati equation by the Newton
algorithms described by Klein, for continuous problems, and by Hewer, for
discrete problems. Another routine calculates the prefilter gain to eliminate
control state crossproduct terms in the quadratic performance index
and the weighting matrices for the sampled data optimal linear regulator
problem. For cases with measurement noise, duality theory and optimal
regulator algorithms are used to calculate solutions to the continuous and
discrete KalmanBucy filter problems.
Finally, routines are included to
implement the continuous and discrete forms of the explicit (modelinthesystem)
and implicit (modelintheperformanceindex) model following
theory. These routines generate linear control laws which cause the output
of a dynamic timeinvariant system to track the output of a prescribed
model.
ORACLS carries the NASA case numbers LAR12953, LAR12313 and GSC13067. It was originally released as part of the NASA COSMIC collection.

More software from National Technology Transfer Center





