Estimation of input impulses by means of continuous finite memory observers

This paper deals with the estimation of impulsive input signals in systems with linear time-invariant dynamics. The problem arises e.g. in the context of hybrid systems with intrinsic pulse-modulated feedback that have been recently used for mathematical modeling of endocrine systems with pulsatile hormone secretion. In such systems, the impulsive signal generated by a pulse-modulated feedback controller is typically not accessible for measurement. Classical deconvolution-based methods are not directly applicable since the signal to be estimated is unbounded. Instead, a solution making use of continuous finite-memory observers is suggested where both the input impulse weight and its firing time are estimated from the difference of the observers' state estimates. The feasibility of the approach is illustrated by a simulation example.