Adaptive Practical Nonlinear Model Predictive Control for Echo State Network Models

This article proposes an adaptive practical nonlinear model predictive (NMPC) control algorithm which uses an echo state network (ESN) estimated online as a process model. In the proposed control algorithm, the ESN readout parameters are estimated online using a recursive least-squares method that considers an adaptive directional forgetting factor. The ESN model is used to obtain online a nonlinear prediction of the system free response, and a linearized version of the neural model is obtained at each sampling time to get a local approximation of the system step response, which is used to build the dynamic matrix of the system. The proposed controller was evaluated in a benchmark conical tank level control problem, and the results were compared with three baseline controllers. The proposed approach achieved similar results as the ones obtained by its nonadaptive baseline version in a scenario with the process operating with the nominal parameters, and outperformed all baseline algorithms in a scenario with process parameter changes. Additionally, the computational time required by the proposed algorithm was one-tenth of that required by the baseline NMPC, which shows that the proposed algorithm is suitable to implement state-of-the-art adaptive NMPC in a computationally affordable manner.