Inverse optimal control for asymptotic trajectory tracking of discrete-time stochastic nonlinear systems in block controllable form

This paper concerns an inverse optimal control-based trajectory tracking of discrete-time stochastic nonlinear systems. It is assumed that the nonlinear system can be transformed to the so called nonlinear block controllable form. Additionally, the synthesized control law minimizes a cost functional, which is posteriori determined. In contrast to the optimal control technique, this scheme avoids to solve the stochastic Hamilton-Jacobi-Bellman equation, which is not an easy task. Based on a discrete-time stochastic control Lyapunov function, the proposed optimal controller is analyzed. The proposed approach is applied successfully to the two degrees-of-freedom helicopter with uncertainties in real time.