Adaptive model predictive control based on wavelet network and online sequential extreme learning machine for nonlinear systems

Wavelet networks (WNs) have been introduced as an alternative method of the neural networks for nonlinear system identification and used with model predictive control (MPC) techniques in many applications. Recently, an online sequential extreme learning machine (OSELM) algorithm has been introduced based on extreme learning machine (ELM) theories for single hidden layer feedforward neural networks (SLFN) and has been applied for different online applications. It is well known that SLFN with OSELM (NN-OSELM) is based on random initialization method for the input weights and the hidden layer nodes parameters. This might result in ill-conditioning, hence instability responses in nonlinear system modeling and consequently preventing the model based controller to perform best performances. In this thesis, the OSELM is introduced with wavelet network (WN-OSELM) and proposed for nonlinear system modeling and control applications. The ability of wavelets for localization in both time and frequency domain will help OSELM to train the WN in both uniform and non-uniform data sets. Moreover, the ability of initialization the hidden nodes parameters using density function and recursive algorithm will help WN-OSELM to perform useful generalization facility and modeling accuracy. Furthermore, to develop WN-OSELM ability to learn the nonlinear system dynamics minimally, a linear term is added to the WN frame (LWN) so that it is enough to stabilize the open-loop unstable systems in the initial stages. This allowed also learning unmodeled or time-varying dynamics of the system and enhancing the modeling accuracy. An analytical analysis based on ELM theories presented to prove the capability of the LWN to support the OSELM algorithm (LWN-OSELM). The proposed methods applied with simulations for system identification of different nonlinear systems and had shown well capability of the LWN-OSELM and WN-OSELM over NN-OSELM in terms of modelling accuracy and fast convergence performance. On the other hand, an adaptive model predictive controller (WNMPC) based on LWN-OSELM modelling method is proposed for nonlinear system control applications. The WNMPC is developed by a proposed algorithm named adaptive updating rule (AUR) used with gradient descent optimization method to minimize a constrained cost function over the prediction and control horizons and to offer a robust control performances. The AUR is established based on Lyapunov stability theorem to find the limits of the optimization step size that guarantee a stable path on the objective function trajectory. A comparison between the proposed controller and other common related controllers are carried out on different nonlinear systems. The results showed superiority of the proposed controller in both control performance and the robustness tests. Moreover, the proposed LWN-OSELM and WNMPC applied to a real conveyorbelt grain dryer system for modeling and control applications. The results showed better modeling accuracy and control performance over an existing modelling methods and the simplified adaptive neuro-fuzzy inference system (SANFIS) controller respectively. The robustness analysis and validation are carried out to prove the proposed controller reliability.

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