A Runge–Kutta neural network-based control method for nonlinear MIMO systems

Abstract

In this paper, a novel Runge–Kutta neural network (RK-NN)-based control mechanism is introduced for multi-input multi-output ( MIMO) nonlinear systems. The overall architecture embodies an online Runge–Kutta model which computes a forward model of the system, an adaptive controller with tunable parameters and an adjustment mechanism realized by separate online Runge–Kutta neural networks to identify the dynamics of each tunable controller parameter. Runge–Kutta identification block has the competency to approximate the time-varying parameters of the model and unmeasurable states of the controlled system. Thus, the strengths of radial basis function (RBF) neural network structure and Runge–Kutta integration method are combined in this structure. Adaptive MIMO proportional–integral–derivative (PID) controller is deployed in the controller block. The control performance of the proposed adaptive control method has been evaluated via simulations performed on a nonlinear three-tank system and Van de Vusse benchmark system for different cases, and the obtained results reveal that the RK-NN-based control mechanism and Runge–Kutta model attain good control and modelling performances.