Accession Number : AD0682995

Title :   ON A FUNCTION SPACE APPROACH TO A CLASS OF LINEAR STOCHASTIC OPTIMAL CONTROL SYSTEMS.

Descriptive Note : Technical rept.,

Corporate Author : PURDUE UNIV LAFAYETTE IND SCHOOL OF ELECTRICAL ENGINEERING

Personal Author(s) : Luh,J. Y. S. ; Lukas,M. P.

Report Date : DEC 1968

Pagination or Media Count : 18

Abstract : The stochastic optimal control problem considered in this report is characterized by a dynamic system which is linear in the state and control vectors, and which is disturbed by additive Gaussian white noise. Incomplete, noisy observations of the state vector are available, and the control is required to be a linear feedback function of the estimated state vector. The components of the state vector and control vector which are of interest are lumped together in a response vector, and the performance index to be minimized is then a function of the statistics of the response vector. It is shown that a well-known stochastic control problem, whose performance index is the expected value of a quadratic form on the state and control, is a special case of the more general problem described above. The general problem is then reformulated as a problem of minimizing a nonlinear functional on a set in a Hilbert space. In this formulation, the well-known 'quadratic' problem becomes one of minimizing a linear functional on the same set in the space. Conditions are derived under which the two problems are 'equivalent'; that is, the linear and nonlinear functionals which specify the problems take on their minimum value at the same point in the space. (Author)

Descriptors :   (*INFORMATION THEORY, CONTROL SYSTEMS), (*FUNCTIONAL ANALYSIS, CONTROL SYSTEMS), (*CONTROL SYSTEMS, STOCHASTIC PROCESSES), (*GUIDED MISSILE TRAJECTORIES, GUST LOADS), LAUNCH VEHICLES, PERTURBATION THEORY, DIFFERENTIAL GEOMETRY, DIFFERENTIAL EQUATIONS, CONVEX SETS, HILBERT SPACE, ITERATIONS, OPTIMIZATION, ALGORITHMS, FEEDBACK, THEOREMS, GUSTS, THESES

Subject Categories : Statistics and Probability
      Cybernetics
      Guided Missile Traj, Accuracy and Ballistics

Distribution Statement : APPROVED FOR PUBLIC RELEASE