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This paper addresses higher order sliding mode control for continuous nonlinear systems. We propose a new method of reaching control design while the sliding surface and equivalent control can be designed conventionally. The deviations of the sliding variable and its high order derivatives from zero are penalized. This is realized by minimizing the amplitudes of the higher order derivatives of the sliding variable. An illustrative example— a field-controlled DC motor— is given at the end.

HIGHER ORDER SLIDING MODE CONTROL FOR CONTINUOUS TIME NONLINEAR SYSTEMS BASED ON OPTIMAL CONTROL