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Abstract
This dissertation presents neural networks (NNs)-based approaches for data-driven modeling and learning-based control of nonlinear systems. First, an integrated structure of NNs, named state integrated matrix estimation (SIME) is designed to learn state-space linear parameter-varying (LPV) models of nonlinear systems from input-output data. SIME can simultaneously estimate states and explores structural dependency of matrix functions of the LPV models. Then, an online transfer learning framework is proposed for online adaptation of data-driven models using closed-loop data to improve the model accuracy and control performance. Next, a variational Bayesian inference Neural Network (BNN) approach is presented to quantify the uncertainties of data-driven models, which are used for robust and safe control. Furthermore, learning-based control design approaches are proposed using the models learned by the data-driven methods in this dissertation. A safe model-based reinforcement learning (RL) approach is presented to control nonlinear systems in the LPV framework using BNN models rather than direct interactions with systems. Then, a learning- and scenario-based model predictive control (MPC) approach with stability and safety guarantees is proposed to consider the joint uncertainties of matrix functions and scheduling variables in the BNN-based LPV models. Next, an adaptive-scenario-tree MPC approach is developed to realize a less conservative estimation of the model uncertainty, namely the mismatch between a nominal (physics-based or data-driven) model of a system and its actual dynamics, and thus improve the robust control performance. Moreover, a new approach using probabilistic Lipschitz bounds for training robust BNNs (RBNNs) and an approach to evaluate the credible intervals of RBNN predictions and determine the number of samples required for estimating the credible intervals given a credible level is proposed to provide a less conservative uncertainty quantification with verification for safe learning-based control. Additionally, a model-agnostic meta-learning (MAML) of BNN approach is presented to learn a precise description of model uncertainty for adaptive-scenario-tree model predictive control design of uncertain nonlinear systems with unknown dynamics. Numerical examples and applications including a reactivitycontrolled compression ignition (RCCI) engine, a 4 degree-of-freedom control moment gyroscope and a cold atmospheric plasma system are used to validate the proposed approaches in this dissertation.