Min-max control of systems approximated by simple models:L 1-Type cost functionals

A control problem for actual processes, modeled by simple dynamic linear systems, is studied. A min-max approach is taken, since the problem is reduced to the control of a model, whose output is affected by an input-dependent signal constrained in norm.Particular attention is given to the features of the penalty functional, since it is desired to synthesize the min-max control by means of a feedback on the states of the model; for example, a quadratic functional does not have this property. AnL ₁-type functional is then proposed, which is not differentiable; by means of duality techniques, however, the minimization can be carried out. The min-max is obtained both by iterative algorithms, both as a function of the actual value of the model state: this function is the solution of a set of partial differential equations.This work was supported by the CENS and the Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni, Consiglio Nazionale delle Ricerche (CNR), Roma, Italy.     

Hydrogenation of carbon monoxide over nanostructured systems: A mechanochemical approach

In this study we investigated the mechanochemical hydrogenation of carbon monoxide over nanostructured FeCo- and Mg₂Ni-based catalysts. To this aim powdered materials, prepared by mechanical alloying, were subjected to mechanical treatment under CO + H₂ atmosphere. A methodology to evaluate the activity of the solid catalysts on an absolute basis was developed. Conversion data were, indeed, expressed as turnover frequency, TOF, and related to the occurrence of ball to powder collision events through the mechanochemical turnover frequency parameter, MTOF. Differences in the catalytic activity and selectivity were observed for the two FeCo-based studied systems, the solid solution Fe₅₀Co₅₀ and its dispersion on TiO₂ support. As for the Mg₂Ni system, we explored the possibility to estimate the specific role of hydrogen pre-activation step. The catalytic properties of the mechanically alloyed Mg₂Ni system were compared with the conversion data shown by the same system pre-hydrogenated and subsequently milled under CO atmosphere.