
Accession Number : AD0643495
Title : QUADRATIC CONTROL PROBLEM WITH AN ENERGY CONSTRAINT: APPROXIMATE SOLUTIONS,
Corporate Author : FRANK J SEILER RESEARCH LAB AIR FORCE ACADEMY COLO
Personal Author(s) : Cook,Gerald ; Funk,James
Report Date : OCT 1966
Pagination or Media Count : 31
Abstract : The quadratic control regulator problem with an energy constraint has been investigated from the viewpoint of having limited control energy available or as an indirect method of limiting the maximum control amplitude. The solution of this problem requires iteration on a parameter and therefore is not as straightforward to apply as the well known Kalman result where no constraints are imposed. However it is much simpler than the problem where control amplitude constraints are applied directly for which case one must iterate on an n dimensional vector. Also for the systems studied it was found that the parameter has a regular behavior as a function of initial state and that this behavior could be approximated by empirical equations. Therefore, the control law could be approximately known for all initial conditions without iterating. Three specific cases were considered in the numerical evaluation portion of the study: harmonic oscillator, single integrator with damping and double integrator. The numerical results indicated that constraining control energy did tend to constrain maximum control amplitude. (Author)
Descriptors : (*APPROXIMATION(MATHEMATICS), *CONTROL), ENERGY, HARMONIC GENERATORS, OPTIMIZATION, COMPLEX VARIABLES, DIFFERENTIAL EQUATIONS, INTEGRATORS, QUADRATIC PROGRAMMING
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE