Synthesis of an approximate feedback nonlinear control based on optimization methods

In the present work, we propose a novel polynomial approach to approximate the Input-State feedback linearization control. The aim of this new method is to simplify the implementation complexity of the exact InputState feedback linearization. Indeed, the present approach leads to an analytical control law via analytical nonlinear transformations without need to resolve a set of partial differential equations. In fact, the analytical control law, determined via the proposed work, is dependent to an arbitrary choice of some parameters. So and in order to ensure a satisfactory evolution of the control input, we resort to optimization methods to have the optimal values of parameters. A study simulation is presented to show the effectiveness of the proposed approach. Key–Words: Nonlinear system control, Input-State feedback linearization, Analytical representations, probabilistic algorithms, Monte Carlo optimization.