
Accession Number : AD0708125
Title : METHOD OF CONJUGATE GRADIENTS FOR OPTIMAL CONTROL PROBLEMS WITH STATE VARIABLE CONSTRAINT,
Corporate Author : CALIFORNIA UNIV LOS ANGELES SCHOOL OF ENGINEERING AND APPLIED SCIENCE
Personal Author(s) : Fong,Thomas Shu
Report Date : APR 1970
Pagination or Media Count : 98
Abstract : A review of the computational method of conjugate gradients for linear and nonlinear operator equations is given with emphasis in applying this technique to state variable constraint control problems. The first and second Frechet derivatives of the performance functional are derived. The search directions generated in the iteration process for the optimal control are locally conjugate with respect to the second Frechet derivative. The convergence is along the expanding sequence of sets, the intersections of the linear spaces spanned by the search directions and the set of admissible controls. The computational aspect of this class of control problems is discussed in detail. This computational technique is applied to two state variable constraint problems, in one of which a penalty function is employed to convert the constraint problem to an unconstrained one in addition to the approach considering the constraints directly. For this same problem the method of steepest descent also is studied, and comparison of the results obtained is made and discussed. (Author)
Descriptors : (*REENTRY VEHICLES, RANGE(DISTANCE)), (*ATMOSPHERE ENTRY, CONTROL), (*CONTROL SYSTEMS, MATHEMATICAL MODELS), (*DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), NONLINEAR DIFFERENTIAL EQUATIONS, STEEPEST DESCENT METHOD, PERTURBATION THEORY, ITERATIONS, CONVERGENCE, THESES
Subject Categories : Numerical Mathematics
Test Facilities, Equipment and Methods
Spacecraft Trajectories and Reentry
Distribution Statement : APPROVED FOR PUBLIC RELEASE