Sensitivity and error analysis algorithms for combined estimation and control systems

Abstract

Sew algorithms for sensitivity and error analysis of combined estimation and control systems are presented. The control structure is constrained a priori to be a fixed configuration type in which the closed-loop control is generated by the summation of a gain matrix multiplying the measured states and another gain matrix multiplying an estimate of the unmeasured states. The estimator is constrained a priori to be a reduced-order Luenberger observer. An augmented state vector is formed consisting of the original system states plus the estimation errors for each of the states not measured. This vector is used in deriving a mean square closed-loop system propagation matrix equation which is a function of the feedback gains, observer dynamics, system modelling errors, and a priori state statistics. The standard quadratic form performance index is reformulated using trace notation in terms of the closed-loop mean square matrix. The performance index is then reduced to a simple expression by forcing a matrix Ri...