Adaptive control of underactuated mechanical systems using improved "sigmoid Generated Fixed Point Transformation" and scheduling strategy

With the aim of evading the difficulties of the Lyapunov function-based techniques in the control of nonlinear systems recently the Sigmoid Generated Fixed Point Transformation (SGFPT) has been introduced. This systematic method has been presented for the generation of whole families of Fixed Point Transformations that can be used in nonlinear adaptive control of Single Input Single Output (SISO) as well as Multiple Input Multiple Output (MIMO) systems. This paper proposes a new control strategy based on the combination of the adaptive and optimal control by applying time-sharing in the SGFPT method. The scheduling strategy supports error containment by cyclic control of the different variables. Further, this paper introduces new improvements on SGFPT technique by introducing Stretched Sigmoid Functions. The efficiency of the presented control solution has been applied in the adaptive control of an underactuated mechanical system. Simulation results validate that the proposed scheme is far promising.