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.