Generalised Predictive Control of Nonlinear Systems Using the Echo State Network and the Nelder-Mead Method

Although generalised predictive control (GPC) has been widely attractive in the industry as a popular model predictive control, its control performance could sometimes decrease because linear transfer function models in the GPC could become hard to estimate system states precisely when the object plant process/dynamic systems are affected by nonlinearity effects. Therefore, to overcome this problem and achieve optimal predictive control of nonlinear systems, this study explored a more comprehensive approach to the GPC, using an echo state network (ESN) as the nonlinear model, after which we investigated its capability in controlling nonlinear dynamic systems. By optimisation using a Nelder-Mead method without gradient computations of the objective function, the predicted quadratic error function based on the future system output estimated using the ESN was then minimised, resulting in optimal control input. Finally, we conducted computational experiments on controlling discrete-time nonlinear plants to assess the feasibility of the ESN-based GPC, followed by simulations to clarify the characteristics of the proposed method.