Optimal Output Regulation Research Articles

Optimal control of linear systems with a modified quadratic performance index

A modified quadratic performance criterion for the optimal control of linear systems is proposed. This criterion includes terms which allow the designer to penalize deviations of states, outputs, and controls according to their sign, as well as their squared value. The optimal state regulator, output regulator, and output tracker with finite final time are developed for this performance criterion, and are found to consist of a feedback control and an open-loop control. It is shown that reduction of these laws to the infinite-time regulator case is not possible. The application of these control laws to a two-effect evaporator model is shown as an example.

Lower order generalized aggregated model and suboptimal control

A method for reducing the order of a linear time-invariant dynamic system is presented. It is shown that it is possible to retain the predominant eigenvalues (or any other set of eigenvalues) of the exact system in the lower order model that possesses the property that its state is an aggregation of the state variables of the original system. Also it is shown that the output of the reduced order model can be constrained to contain all the modes of the exact output and to be close to the actual output of the original system within a specified tolerance. The performance of the original system is investigated for an optimal output regulator problem, when it is controlled on the assumption that its behavior is governed by that of the lower order model. Relations are obtained for the performance degradation that results with the above suboptimal control policy. Numerical examples show that the suboptimal control can be used in practice to lessen the computational complexity required for the higher order optimal control. The stability of the suboptimal control is not guaranteed; however, it is reasonable to expect it to be asymptotically stable when the order of reduction is not excessively high, because the outputs of the exact and lower order models are tolerably close.