Adaptive estimation and stochastic control for uncertain models†

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Abstract
Ordinarily, in sequential state estimation problems, it is assumed that the parameters describing the system are completely known including the statistics of the noise terms. In many physical processes, however, the parameters, and even the mathematical model, may not be completely known. Hence, another class of problems may be considered in which the system model is in doubt. This type of problem is commonly referred to as ‘ Estimation-Under-Uncertainty ’. In this paper general formulations and solutions of state estimation and control problems are presented for a large class of linear stochastic systems with uncertain models, A general structure with continuous dynamical equations and discrete observations is adopted, since many physical situations are best modelled in this way. The problem of estimation-under-uncertainty is formulated using the assumption that the model is one of a set of finite number of candidate models. Recursive estimation and identification algorithms are presented. A feedback control strategy is also developed for uncertain systems using the results derived for estimation-under-uncertainty,

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