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This paper proposes a new approach for adaptive sliding mode controller (ASMC) designs. The goal is to obtain robust, smooth, and fast transient performance for nonlinear systems with finite uncertainties of unknown bounds and limited available inputs so that the phenomena of the slow response and the gain overestimation in most ASMC designs can be greatly improved. Sufficient and necessary conditions for the existence of a sliding mode in the ASMC designs are discussed. Based on the sufficient conditions, we introduce an integral/exponential adaptation law targeting the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously speeding up the system response to the uncertainties. An illustrative example and numerical simulations are performed to convey the discussed results.

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