This paper presents a study of multi-objective optimal design of a slide mode control for an under-actuated nonlinear system with the parallel simple cell mapping method. The multi-objective optimal design of the slide mode control involves 6 design parameters and 5 objective functions. The parallel simple cell mapping method finds the Pareto set and Pareto front efficiently. The parallel computing is done on a graphic processing unit (GPU). 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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