About one problem of optimal control synthesis

Abstract

This paper tackles the problem of characterizing the natural class, or Riccati rule space, of solutions to a specific equation. Despite the significant theoretical and practical implications, there is limited research exploring the application of spectral decomposition of non-self-adjoint differential operators to explicitly solve this nonlinear Riccati equation. Therefore, investigating operator Riccati equations holds potential to validate the dynamic programming method and address the synthesis problem.