We propose a model predictive control (MPC) strategy for sampled-data implementation (with the zero order hold assumption) of continuous-time controllers for general nonlinear systems. We assume that a continuous-time controller has been designed so that the continuous-time closed-loop satisfies all performance requirements. Then, we use this control law indirectly to compute numerically a sampled-data controller via an MPC strategy that minimizes the mismatch between the solutions of the sampled-data model and the continuous-time closed-loop model. We present conditions under which stability and sub-optimality of the closed loop can be proved.

We consider some recently developed schemes for treating van der Waals interactions within the density functional theory (DFT) on the widely discussed example of adsorption of Xe on Cu(111) and Pt(111) surfaces. Consistent with the overall weakness of the Xe surface and Xe-Xe interactions we assess the performance of the schemes that are appropriate to systems consisting of nearly isolated fragments in which the coefficients of the van der Waals expansion are deduced from DFT calculations. Such generalized DFT calculations of potential energy surfaces yield the structure of Xe adlayers in good agreement with experiments and retrieve the dilation of commensurate monolayer phase in which the intralayer Xe-Xe radial force constants are strongly reduced. This provides a first principles interpretation of the observed vibrational properties of adlayers, in general, and the much debated dispersion of in-plane polarized vibrations, in particular.