NEAR-OPTIMAL STOCHASTIC LINEAR CONTROLS.
Abstract
A class of optimal stochastic linear control problems is formulated in which the terminal time may be either fixed or free. The performance measure, which is to be minimized, is the expected value of any one element of a rather general set of scalar-valued functions of the instantaneous system error. The condition for optimal control is developed by utilizing results from optimal filter theory. It is found that this condition cannot be realized exactly in general, although there do exist some cases in which it can. An approximate or 'near-optimal' control law which is physically realizable is then derived for the general case. The resulting control law is exceedingly simple to mechanize, requiring only forward-time solution of a matrix, Riccati, ordinary, differential equation with given initial condition. Expressions for assessing the performance of the near-optimal control relative to that of the nonrealizable, optimal one are derived. Two examples dealing with the problems of turbojet engine speed control and aircraft yaw control are included to illustrate the theoretical results. The presentation in the main body of the paper is for continuous-time systems. An outline of the development for discrete-time systems is given in the appendix for completeness. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1967
- Accession Number
- AD0660056
Entities
People
- J. S. Meditch
Organizations
- Boeing