A perturbation method for sub-optimal feedback control of bilinear systems

Publisher Website
Google Scholar
Abstract
Several attempts have been made over several years to apply perturbation theory to optimal control problems. A recent investigation used the method of Lie transforms and canonical transformations to obtain sub-optimal state feedback for bilinear systems. The resulting feedback law is quite difficult to extract from the transformations and much algebraic manipulation is required before computation can be carried out. In the present paper it is shown that a straightforward asymptotic expansion of the control law leads to a sequence of simple matrix equations yielding the necessary feedback coefficients. Two examples are used to illustrate the simplicity of this approach compared with the Lie transform method and results of numerical computation are given for one of the examples.