A novel adaptive Runge–Kutta controller for nonlinear dynamical systems

This paper introduces a new Runge–Kutta (RK) integration-based adaptive controller by considering control law as an ODE for nonlinear MIMO systems. It is aimed to derive a novel adaptive controller by regarding the control law as an ODE with limited information about control law structure. Adaptive parameters are adjusted via an RK predictive system model where Levenberg–Marquardt (LM) technique is deployed. The adjustment mechanism enables to utilize RK both in adaptive controller and system model. The performance evaluation has been delved into on Van de Vusse (VdV) system for diverse situations, and reasonable results have been acquired for introduced adaptation mechanism.