An integrated algorithm that combines Dynamic Adaptive Backstepping (DAB), Sliding Mode Control (SMC), and a saturated proportional integral function (PI) is presented for the control of non-triangular nonlinear systems with unmatched uncertainties. Adaptive Backstepping is a recursive design methodology that uses of virtual functions as well as tuning functions, while sliding mode control is used to obtain more robustness towards disturbances and unmodeled dynamics. The main advantages of the PI function are the complete removal of chattering, a shorter transient period, and higher accuracy. A comparison of Dynamic Adaptive Backstepping Sliding Mode Control (DAB-SMC) and Dynamic Adaptive Backstepping Saturated Proportional Integral Sliding Mode Control (DAB-PISMC) is presented to show the effectiveness of the proposed algorithm