Abstract
An approximate method is proposed for synthesizing the optimal control for a dynamical system in the presence of external random perturbations and measurement errors. The synthesis problem posed reduces, as is known, to solving a nonlinear parabolic partial differential equation (the Bellman equation) whose exact solutions are known only in a few cases. It is assumed that either the external perturbations acting on the system are sufficiently small or the measurement errors are large. Under these conditions the Bellman equation contains a small parameter in the leading derivative, and the solution is constructed by means of an expansion with respect to the small parameter. It is shown that the approximate synthesis of the optimal control for perturbed systems can be constructed in explicit form if the solution of the corresponding problem for the perturbation-free system is known. Estimates of the errors in the method are proved. Examples are given.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
