Design of control systems with random parameters†

† Communicated by Professor A. H. Haddad. This work was supported in part by the U.S. Air Force under Grant AFOSR-68–1579, in part by the National Science Foundation under NSF Grant GK-3893 and in part by the Joint Services Electronics Program (U.S. Army, U.S. Navy and U.S. Air Force) under Contract DAAB-07–67-C-0199 with the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois.

Abstract

In this paper a method for designing control systems with random parameters and random initial state is presented. The observed signal available for feedback is a function of the state and system parameters corrupted by additive white Gaussian noise with zero mean. The proposed control consists of an open-loop term, which is the optimal control for the parameters and initial state equal to their mean values, plus a feedback correction term. The feedback correction term is a linear function of the estimated values of the deviation in initial state and system parameters from their mean values. The control tends to the optimally sensitive control when the measurement noise tends to zero, and the feedback correction tends to zero when the measurement noise tends to infinity. A numerical experiment with a simplified model for nuclear reactor control shows that in spite of fairly large measurement noise, significant improvement in performance can be achieved using the proposed control compared to open-loop control.

Notes

† Communicated by Professor A. H. Haddad. This work was supported in part by the U.S. Air Force under Grant AFOSR-68–1579, in part by the National Science Foundation under NSF Grant GK-3893 and in part by the Joint Services Electronics Program (U.S. Army, U.S. Navy and U.S. Air Force) under Contract DAAB-07–67-C-0199 with the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois.