Sub-optimal bang-bang control of stochastic systems†

Abstract

Much attention has been paid to the statistical linearization approach to the optimizing problem for stochastic systems. In this paper, a technique is presented for designing a sub-optimal bang-bang control law with a class of non-linear switching functions. The structural form of the non-linear switching function is prespecifled, while leaving free parameters to be chosen in a optimal fashion. Using statistical linearization, the free parameters are chosen so as to be independent of the external noise levels as well as to minimize the average cost. Detailed discussions are given of two typical examples.