Journal of Process Control, Vol.21, No.6, 901-908, 2011
Shaping probability density functions using a switching linear controller
Linear controllers for dynamic systems have been used in a stochastic context to decrease the variance of certain key variables. An extension is to use nonlinear controllers for shaping the entire probability density function (PDF). Typically, polynomial controllers are preferred due to their flexibility and also because their continuity makes them mathematically attractive. However, due to restrictions on stability, these controllers tend to be quasi-linear around the desired operating point. So, in this paper, a switching linear controller is presented as an alternative for PDF shaping. It is shown that, despite the discontinuity, an analytical solution of the PDF can be obtained using the Fokker-Planck-Kolmogorov equation. Also, for a simple case, even the Gram-Charlier coefficients can be computed analytically. Thus, it is demonstrated that the PDF shaping problem with a switching controller does not cause any further complications than using polynomial controllers. It is then shown in simulation that switching controllers are more robust and could create more skewness due to their discontinuity. (C) 2011 Elsevier Ltd. All rights reserved.
Keywords:Shaping probability density function;Switching control;Nonlinear control;Fokker-Planck-Kolmogorov equation;Stochastic control