Model Error Quantification for Robust Control based on Quasi-Bayesian Estimation in Closed Loop

This paper presents a procedure for quantifying the errors in the estimation of the parameters of systems described by ARMAX models when operating in closed loop. We include stochastic disturbances on the output and consider the case where the true open loop plant is not a member of the chosen set of identifier models. This latter problem is dealt with by considering the impulse response of the undermodelling to be a particular realisation of a random vector with known characteristics but unknown parameters. We show how the parameters which characterize the undermodelling may be estimated from the data using Maximum Likelihood. For the case of Gaussian probability density functions we show how this information may be used to obtain a quasi-Bayesian estimate of the conditional distribution of the true system model. This in turn allows confidence regions to be established which would be suitable for use in robust control system design.