Inverse optimal control of stochastic systems driven by Lévy processes. (September 2019) - Do, K.D.
Abstract: This paper formulates and solves new problems of inverse optimal stabilization and inverse optimal gain assignment for stochastic nonlinear systems driven by Lévy processes. First, a theorem is developed to design inverse optimal stabilizers based on inverse pre-optimal stabilization controllers for stochastic systems with known noise characteristics, where it does not require to solve a Hamilton–Jacobi–Bellman equation. Second, another theorem is developed to design inverse optimal gain assignment controllers for stochastic systems with unknown noise characteristics, where there is no need to solve a Hamilton–Jacobi–Isaacs equation. Third, the results are applied to design inverse optimal stabilizers for Euler–Lagrange systems.