Scalable and Efficient Methods for Hierarchical and Robust Nonlinear Model Predictive Control

Since its inception, Model Predictive Control (MPC) has become a widely adopted and studied control technique, both for practitioners and academics, finding application in diverse fields. Some of the main reasons for its popularity are the ability to directly deal with state and input constraints while simultaneously optimizing the system operation with respect to some predefined criteria. This characteristic comes from the fact that an MPC controller solves an optimization problem at every time step during the system operation. As such, MPC formulations can be divided into two broad categories: Linear MPC and Nonlinear MPC. In Linear MPC, the controller uses a linear model of the system dynamics as part of the equality constraints in the optimization problem in addition to other linear constraints and a linear or quadratic objective function. This setup results in the need to solve a Linear Program (LP) or Quadratic Program (QP) at each time step. In Nonlinear MPC however, the controller uses a nonlinear model of the system dynamics with potentially other nonlinear constraints and a nonlinear objective function. This in turn requires a Nonlinear MPC controller to solve a Nonlinear Program (NLP) at each time step. In the last decades, there has been increased adoption of Linear MPC in a diverse range of applications, fueled by the availability of increasing computational power, the availability of robust and efficient convex solvers, and a large body of research that helped establish conditions for important theoretical properties of MPC formulations such as stability and recursive feasibility. While these improvements benefited the field of Nonlinear MPC as well, due to the inherent difficulty in dealing with nonlinear formulations, the progress in the adoption of Nonlinear MPC by industry has not been nearly as large as for Linear MPC. There are however many applications in which Linear MPC does not perform well due to strong nonlinear system behavior or because the system is not supposed to operate around an equilibrium point, which limits the prediction capabilities of linear models. Therefore, there is much potential for improved performance through the use of Nonlinear MPC in these applications. The wider adoption of Nonlinear MPC though has been hampered by issues such as a lack of theoretical guarantees, high computational cost in solving the underlying NLPs, or the need for expert knowledge for deployment due to the complexity of the formulations. Therefore, this dissertation aims to provide advances to the field of Nonlinear MPC to help the research community unlock more of the potential of this technique for practical applications that can benefit from its use. The contributions of this work focus on two particular types of Nonlinear MPC formulations: hierarchical Nonlinear MPC, applicable for systems with dynamics in multiple timescales, and robust Nonlinear MPC, where there is a need to guarantee constraint satisfaction even when the system is subject to external disturbances. The methods studied and proposed in this dissertation are tested through numerical simulations using a few different dynamical systems as benchmarks with a particular focus on thermal management systems. The proposed methods are compared to Linear MPC techniques to highlight the potential benefits of using nonlinear formulations.