Inverse optimal control of stochastic systems driven by Lévy processes. (September 2019)

• Record Type: Journal Article
• Authors: Do, K.D.
• Is Part Of: Automatica. Volume 107(2019)
• Page Start: 539
• Page End: 550
• Publication Date: 2019-09
• Subjects: Lyapunov-type theorem -- Well-posedness -- Inverse optimality -- Almost sure stability -- Lévy processes; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.06.016
• Languages: English
• ISSNs: 0005-1098

Abstract

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.