On applications of singular perturbation techniques in nonlinear optimal control
โ Scribed by J. Shinar
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 820 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0005-1098
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โฆ Synopsis
The technique of singular perturbations (SPT) has bean 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 solution as a classical singularly perturbed model (where a small parameter of physical significance appears as a consequence of a scaling transformation). 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 integration; (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.
๐ SIMILAR VOLUMES
Linear control techniques have been widely used for controlling both linear and nonlinear systems. In this paper we show the design of a kind of nonlinear controllers starting from the standard procedure for designing linear controllers by pole placement. After the linear controller is designed, we