Stabilizing nonlinear model predictive control in presence of disturbances and off - line approximations of the control law

One of the more recent and promising approaches to control is the Receding Horizon one. Due to its intrinsic characteristics, this methodology, also know as Model Predictive Control, allows to easily face disturbances and model uncertainties: indeed at each sampling instant the control action is recalculated on the basis of the reached state (closed loop). More in detail, the procedure consists in the minimization of an adequate cost function with respect to a control input sequence; then the first element of the optimal sequence is applied. The whole procedure is then continuously reiterated. In this thesis, we will focus in particular on robust control of constrained systems. This is motivated by the fact that, in practice, every real system is subjected to uncertainties, disturbances and constraints, in particular on state and input (for instance, plants can work without being damaged only in a limited set of configurations and, on the other side, control actions must be compatible with actuators' physical limits). With regard to the first aspect, maintaining the closed loop stability even in presence of disturbances or model mismatches can result in an essential strategy: moreover it can be exploited in order to design an approximate stabilizing controller, as it will be shown. The control input values are obtained recurring to a Nearest Neighbour technique or, in more favourable cases, to a Neural Network based approach to the exact RH law, which can be then calculated off line: this implies a strong improvement related to the applicability of MPC policy in particular in terms of on line computational burden. The proposed scheme is capable to guarantee stability even for systems that are not stabilizable by means of a continuous feedback control law. Another interesting framework in which the study of the influence of uncertainties on stability can lead to significant contributions is the networked MPC one. In this case, due to the absence of physical interconnections between the controller and the systems to be controlled, stability can be obtained only taking into account of the presence of disturbances, delays and data losses: indeed this kind of uncertainties are anything but infrequent in a communication network. The analysis carried out in this thesis regards interconnected systems and leads to two distinct procedures, respectively stabilizing the linear systems with TCP protocol and nonlinear systems with non-acknowledged protocol. The core of both the schemes resides in the online solution of an adequate reduced horizon optimal control problem.