Inverse optimal design of a class of stochastic nonlinear systems with uncontrollable linearization

The global asymptotic stochastic stability and inverse optimal control problem are developed for a class of stochastic nonlinear systems with lower triangular form. The systems considered are not feedback linearizable and the Jacobian linearization is uncontrollable. By the use of adding a power integrator, a feedback domination design approach is presented and a smooth controller is constructed to guarantee the global asymptotic stability in probability and the inverse optimality. The simulation result shows the effectiveness of the control schemes.