Model Predictive Control (MPC) optimizes an index
which includes a penalization parameter $\lambda$ in order to get
not too abrupt control actions, and at the same time to improve
the system robustness. The main drawback consists of the fact that
$\lambda$ is tuned by empirical criteria, without the objective of
improving the robustness.
There exist several techniques for improving robustness in MPC and
among them the Min-Max optimization can be emphasized, where an
optimization problem is solved for the worst model inside a
bounded region.
From another point of view, the least squares principle is present
in a big number of identification and control theories. In fact
MPC can be stated as a least squares problem. Its main drawback is
that the method is sensitive to data errors (ill-conditioning)
which can be improved by the empirically tuned regularization
parameter $\lambda$ (which is similar to the penalization
parameter $\lambda$ for the control effort in MPC).
The BDU (Bounded Data Uncertainties) is a regularization technique
for least squares problems, which has been originally developed
for estimation problems and not very used in control, except for
the linear quadratic regulator (LQR) with finite prediction
horizon under parametric uncertainty.
The technique designs the regularization parameter $\lambda$
taking into account the bound of the system uncertainty and the
problem is stated as a Min-Max optimization. So it is possible to
establish an analogy between BDU and the Min-Max problem in robust
MPC, and the main objective of the thesis consists of using BDU
for tuning $\lambda$ in a guided way in order to improve the
system robustness.
Another thesis objective is to ensure stability. So it is desired
to state a robust and stable LQR, called LQR-BDU, robust by using
BDU, and stable by taking into account either terminal constraint
or infinite prediction horizons.
The application to LQR is the precursor to the application to MPC,
where the attention is focused on the GPC, obtaining the GPC-BDU
in which $\lambda$ is chosen in an automatic manner depending on
the desired uncertainty bound.
On the other hand, from the stabilizing GPC version (CRHPC or
Constrained Receding-Horizon Predictive Control), which ensures
nominal stability, the CRHPC-BDU is stated, which tries to improve
the system robustness when discrepancies between model and process
are present. Therefore the CRHPC-BDU is the stable and robust GPC
which constitutes the thesis objective.