Simultaneous input and parameter estimation with input observers and set-membership parameter bounding: theory and an automotive application

The paper addresses an on-line, simultaneous input and parameter estimation problem for a first-order system affected by measurement noise. This problem is motivated by practical applications in the area of engine control. Our approach combines an input observer for the unknown input with a set-membership algorithm to estimate the parameter. The set-membership algorithm takes advantage of a priori available information such as (i) known bounds on the unknown input, measurement noise and time rate of change of the unknown input; (ii) the form of the input observer in which the unknown parameter affects only the observer output; and (iii) the input observer error bounds for the case when the parameter is known exactly. The asymptotic properties of the algorithm as the observer gain increases are delineated. It is shown that for accurate estimation the unknown input needs to approach the known bounds a sufficient number of times (these time instants need not be known). Powertrain control applications are discussed and a simulation example based on application to engine control is reported. A generalization of the basic ideas to higher order systems is also elaborated. Copyright # 2006 John Wiley & Sons, Ltd.