This paper presents a study of the multi-objective optimal design of a sliding mode control for an under-actuated nonlinear system with the parallel simple cell mapping method. The multi-objective optimal design of the sliding mode control involves six design parameters and five objective functions. The parallel simple cell mapping method finds the Pareto set and Pareto front efficiently. The parallel computing is done on a graphics processing unit. Numerical simulations and experiments are done on a rotary flexible arm system. The results show that the proposed multi-objective designs are quite effective.
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