Automatica, Vol.107, 539-550, 2019
Inverse optimal control of stochastic systems driven by Levy processes
This paper formulates and solves new problems of inverse optimal stabilization and inverse optimal gain assignment for stochastic nonlinear systems driven by Levy 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. (C) 2019 Elsevier Ltd. All rights reserved.
Keywords:Lyapunov-type theorem;Well-posedness;Inverse optimality;Almost sure stability;Levy processes