Parametric uncertainty handling of under-actuated nonlinear systems using an online optimal input–output feedback linearization controller

Abstract

This research introduces a new online optimal control based on the input–output feedback linearization and a multi-crossover genetic algorithm for under-actuated nonlinear systems having parametric uncertainties. At first, the input–output feedback linearization method is successfully implemented to derive the control law for a two degrees of freedom cart-pole nonlinear system. Then, the regarded optimization algorithm is applied to find the design parameters of the controller for different values of the uncertain variables. Next, an approximation function is suggested to calculate the optimum gains of the controller in the presence of the uncertainties in the system parameters. The simulation results are illustrated to prove the effectiveness and adeptness of the introduced scenario to overcome some common issues in the actual systems, i.e. under-actuating nonlinearities and uncertainties.

Keywords

• online optimal control
• input–output feedback linearization
• multi-crossover
• cart-pole nonlinear system
• parametric uncertainty