Modeling error and external disturbances can severely degrade the performance of Model Predictive Control (MPC) in real-world scenarios. Robust MPC (RMPC) addresses this limitation by optimizing over control policies but at the expense of computational complexity. An alternative strategy, known as tube MPC, uses a robust controller (designed offline) to keep the system in an invariant tube centered around a desired nominal trajectory (generated online). While tube MPC regains tractability, there are several theoretical and practical problems that must be solved for it to be used in real-world scenarios. First, the decoupled trajectory and control design is inherently suboptimal, especially for systems with changing objectives or operating conditions. Second, no existing tube MPC framework is able to capture state-dependent uncertainty due to the complexity of calculating invariant tubes, resulting in overly-conservative approximations. And third, the inability to reduce state-dependent uncertainty through online parameter adaptation/estimation leads to systematic error in the trajectory design. This thesis aims to address these limitations by developing a computationally tractable nonlinear tube MPC framework that is applicable to a broad class of nonlinear systems.

This book offers a novel approach to adaptive control and provides a sound theoretical background to designing robust adaptive control systems with guaranteed transient performance. It focuses on the more typical role of adaptation as a means of coping with uncertainties in the system model.

Robust Adaptive Model Predictive Control of Nonlinear Systems.

The following topics are dealt with: adaptive control; constrained nonlinear systems; disturbance attenuation; robust adaptive economic MPC; and discrete-time systems.

The problem of plasma vertical stabilization based on the model predictive control has been considered. It is shown that MPC algorithms are superior compared to the LQR-optimal controller, because they allow taking constraints into account and provide high-performance control. It is also shown that in the case of the traditional MPC-scheme it is possible to reduce.

This book focuses on the applications of robust and adaptive control approaches to practical systems. The proposed control systems hold two important features: (1) The system is robust with the variation in plant parameters and disturbances (2) The system adapts to parametric uncertainties even in the unknown plant structure by self-training and self-estimating the unknown factors. The various kinds of robust adaptive controls represented in this book are composed of sliding mode control, model-reference adaptive control, gain-scheduling, H-infinity, model-predictive control, fuzzy logic, neural networks, machine learning, and so on. The control objects are very abundant, from cranes, aircrafts, and wind turbines to automobile, medical and sport machines, combustion engines, and electrical machines.

The performance of model predictive control (MPC) largely depends on the accuracy of the prediction model and of the constraints the system is subject to. However, obtaining an accurate knowledge of these elements might be expensive in terms of money and resources, if at all possible. In this thesis, we develop novel learning-based MPC frameworks that actively incentivize learning of the underlying system dynamics and of the constraints, while ensuring recursive feasibility, constraint satisfaction, and performance bounds for the closed-loop. In the first part, we focus on the case of inaccurate models, and analyze learning-based MPC schemes that include, in addition to the primary cost, a learning cost that aims at generating informative data by inducing excitation in the system. In particular, we first propose a nonlinear MPC framework that ensures desired performance bounds for the resulting closed-loop, and then we focus on linear systems subject to uncertain parameters and noisy output measurements. In order to ensure that the desired learning phase occurs in closed-loop operations, we then propose an MPC framework that is able to guarantee closed-loop learning of the controlled system. In the last part of the thesis, we investigate the scenario where the system is known but evolves in a partially unknown environment. In such a setup, we focus on a learning-based MPC scheme that incentivizes safe exploration if and only if this might yield to a performance improvement.