Robust Adaptive Model Predictive Control of Nonlinear Sample-Data Systems

In the past decades, model predictive control (MPC) has been widely used as an efficient tool in areas such as process control, power grids, transportation systems, and manufacturing. It provides an approach that aims to design stabilizing feedback to the system so that the performance criterion gets minimized while the state and input constraints get satisfied. In many situations, MPC may outperform other approaches to design and implement feedback control systems. Furthermore, MPC may solve optimization problems with large and practically important sets of multiple-input multiple-output (MIMO) systems efficiently. A typical implementation of MPC predicts the optimal control inputs that guarantee a certain level of optimality based on the interest of model behavior to the actual dynamical system. Many schemes of model predictive control have been addressed in the past years. Recently, the technology development of computers, sensors, and communications make the control systems much larger and more complex than ever before. These advances also increase the need for MPC to design the controllers for complex multiple-input multiple-output systems. Besides, the advanced computation hardware has significantly improved the speed and reliability of solving optimization problems. In general, we can differentiate the MPC scheme into linear and nonlinear model predictive control. Linear MPC refers to the MPC schemes that deal with linear models to predict the system dynamics. Besides, the constraints on the states and inputs should be linear, and the cost function can be as simple as quadratic. The optimal solutions of linear MPC rely on the dynamic models, the constraints, and the optimal problems that aim to minimize the system performance, which is usually expressed as the cost function. Nonlinear MPC refers to the MPC schemes based on nonlinear models or non-quadratic cost functionals with corresponding nonlinear constraints on the states and inputs. Nevertheless, linear models are often inadequate in describing the optimal problem because of higher product quality specifications, increasing productivity demands, tighter environmental regulations, and the requirements of operating conditions. In this case, people need to use nonlinear MPC to describe the models accurately. This dissertation studies several MPC algorithms for solving nonlinear continuous-time systems with uncertainties. The work focuses on systems with disturbances, system discretization, and explicit model predictive control. Meanwhile, we ensure these algorithms may provide a series of feasible solutions and stabilize the control systems along the prediction horizon