The technique of singular perturbations (SPT) has been applied with considerable success in several nonlinear optimal control problems. In many cases the zero-order approximation of the optimal control function has been expressed in a feedback form. This paper deals with topics involved in such closed-loop application, which seem to merit further discussion. It is formally demonstrated that a 'forced' singular perturbation model (obtained by artificial insertion of the perturbation parameter) results in the same zero-order composite feedback control solutions as a classical singularly perturbed model (where a small parameter of physical significance appears as a consequence of a scaling transofmration). The accuracy of the zero-order feedback approximation depends in both cases on the actual time scale separation of the variables. Two inherent limitations of the feedback solution are also pointed out: (1) first and higher-order correction terms of the zero-order approximation have to be computed by a predictive or off-line intergration; (2) on-line implementation of SPT control strategy in a terminal boundary layer requires iterative computations. A simple pursuit problem serves as an illustrative example.
On applications of singular perturbation techniques in nonlinear optimal control
Zur Anwendung der Einzelstoerungstheorie bei der Optimalwertregelung nichtlinearer Systeme
Automatica, Oxford ; 19 , 2 ; 203-211
1983
9 Seiten, 1 Bild, 1 Tabelle, 31 Quellen
Article (Journal)
English