State-observer design for linear sequential machines

Abstract

The problem of designing a state observer for a linear deterministic q-observable sequential machine is considered. It is shown that this observer has the structure of Kalman's linear estimator, i.e. it is a linear sequential machine driven by the measured outputs and inputs of the original machine. The main feature of this observer is that after q steps it gives the state of the original machine without error whatever the initial state estimate chosen. The theory is then applied for estimating the state of stochastic sequential machines. Observers are necessary when applying state feedback control to sequential machines, the state variables of which are not all accessible to direct measurement.