Multiple Model Adaptive Estimation for open loop unstable plants

This paper addresses the problem of adaptive state and parameter estimation of open loop unstable plants using a multiple model structure. A state estimate is obtained as a probabilistically weighted sum of the estimates produced by a bank of individual observers. Model identification and convergence of the dynamic weights in the Multiple Model Adaptive Estimation (MMAE) for open-loop unstable plants are analyzed and the effect of the control action (by a controller in the loop) is studied. In the present paper we show that the techniques introduced in MMAE for open-loop stable plants and in the absence of control action are applicable to open-loop unstable plants with a stabilizing controller in the loop. A distance-like pseudo norm between the true plant and the identified model is developed and furthermore we show that the model identified is the one that is the closest to the true plant model in the defined norm among all models in the bank. The performance and convergence of the MMAE procedure are illustrated with Monte-Carlo simulation runs using the model of an inverted pendulum installed on a system of masses, springs, and dampers.