Multi-objective optimal backstepping control design for the under-actuated rotary flexible link

The aim of this paper is to present a study of the multi-objective optimal backstepping control design for the under-actuated rotary flexible link. The straightforward transformation is first applied to the under-actuated system for the backstepping control design. The backstepping control is then designed with Lyapunov functions to meet multiple objectives such as peak time, tracking error, overshoot, etc. Accordingly, the multi-objective optimization problem is formulated and solved with a hybrid method named GA-SCM which combines the strength of genetic algorithm (GA) and simple cell mapping method (SCM). Numerical simulations and experiments demonstrate the validity of the proposed control design method and effectiveness of the hybrid MOP method.