Keywords: optimal regulator, stochastic uncertainty, feedback control, stochastic optimal feedback control, robust optimal control, stochastic optimization methods, computation of expectations, Taylor expansions..

The optimal design of regulators is often based on the use of given, fixed nominal values of initial conditions, external loads and other model parameters. However, as a result of variations in the material properties, measurement errors, modeling errors, task to be executed, etc., the external loadings, initial conditions, the model parameters, are not known exactly in practice. Moreover, the state of the system cannot be observed exactly in practice; there are always some observational errors. Hence, a predetermined (optimal) regulator should be robust, i.e., the controller should guarantee satisfying results also in case of observational errors, variations of the initial conditions, load parameters, and further model parameters. In the following we suppose that the parameters involved in the regulator design problem are realizations of a random vector having a known or at least partly known joint probability distribution. For the consideration of stochastic parameter variations within the optimal design process of a regulator one has to introduce an appropriate deterministic substitute problem. In the present case of stochastic optimal design of a regulator, one has an optimal control problem subject to stochastic uncertainty. For the solution of the occurring deterministic substitute problems the methods of stochastic optimization are applied. Appropriate approximations of the occurring expectations are developed.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)