Guest Molecule-Responsive Functional Calcium Phosphonate Frameworks for Tuned Proton Conductivity

We report the synthesis, structural characterization, and functionality of an open-framework hybrid that combines Ca2+ ions and the rigid polyfunctional ligand 5-(dihydroxyphosphoryl) isophthalic acid (PiPhtA). Ca-PiPhtA-I is obtained by slow crystallization at ambient conditions from acidic (pH≈3) aqueous solutions. It possesses a high water content (both Ca coordinated and in the lattice), and importantly, it exhibits water-filled 1D channels. At 75 °C, Ca-PiPhtA-I is partially dehydrated and exhibits a crystalline diffraction pattern that can be indexed in a monoclinic cell with parameters close to the pristine phase. Rietveld refinement was carried out for the sample heated at 75 °C, Ca-PiPhtA-II, using synchrotron powder X-ray diffraction data.All connectivity modes of the “parent” Ca-PiPhtA-I framework are retained in Ca-PiPhtA-II. Upon Ca-PiPhtA-I exposure to ammonia vapors (28% aqueous NH3) a new derivative is obtained (Ca-PiPhtA-NH3) containing 7 NH3 and 16 H2O molecules according to elemental and thermal analyses. Ca-PiPhtA-NH3 exhibits a complex X-ray diffraction pattern with peaks at 15.3 and 13.0 Å that suggest partial breaking and transformation of the parent pillared structure. Although detailed structural identification of Ca-PiPhtA-NH3 was not possible, due in part to nonequilibrium adsorption conditions and the lack of crystallinity, FT-IR spectra and DTA-TG analysis indicate profound structural changes compared to the pristine Ca-PiPhtA-I. At 98% RH and T = 24 °C, proton conductivity, σ, for Ca PiPhtA-I is 5.7 ×10−4 S·cm−1. It increases to 1.3 × 10−3 S·cm−1 upon activation by preheating the sample at 40 °C for 2 h followed by water equilibration at room temperature under controlled conditions. Ca-PiPhtA-NH3 exhibits the highest proton conductivity, 6.6 × 10−3 S·cm−1, measured at 98% RH and T = 24 °C. Ea for proton transfer in the above-mentioned frameworks range between 0.23 and 0.4 eV, typical of a Grothuss mechanism of proton conduction.Proyecto nacional MAT2010-1517

Inversion in indirect optimal control: constrained and unconstrained cases

International audienceThis paper focuses on using non linear inversion in optimal control problems. This technique allows us to rewrite the stationarity conditions derived from the calculus of variations under a higher order form with a reduced number of variables. After a brief tutorial overview of the multi- input multi-output cases for which the cost functions have a positive definite Hessian with respect to control variables, we address the case of linear systems with a control affine cost to be minimized under input constraints. This is the main contribution of this paper. We study the switching function between singular and regular arcs and explain how higher order stationarity conditions can be obtained. An example from the literature (energy optimal trajectory for a car) is addressed

A FULLY UNCONSTRAINED INTERIOR POINT ALGORITHM FOR MULTIVARIABLE STATE AND INPUT CONSTRAINED OPTIMAL CONTROL PROBLEMS.

Abstract. This paper exposes a methodology to solve constrained optimal control problems for non linear systems using interior penalty methods. A constructive choice for the penalty functions that are introduced to account for the constraints is established in the article. It is shown that this choice allows one to approach a solution of the non linear optimal control problem using a sequence of unconstrained problems, whose solutions are readily characterized by the simple calculus of variations. An illustrative example is given. The paper extends recent contributions, originally focused on single input single output systems. P. Malisani, F. Chaplais, and N. Petit

On Numerical Differentiation Algorithms for Nonlinear Estimation

Practical methods of differentiating a sig- nal known only through its on-line samples are much needed, given the numerous areas in control theory and practice where differentiation is encountered. This communication presents theoretical as well as imple- mentation details on several numerical differentiation algorithms which may be useful in the area of nonlinear estimation. In particular, these algorithms may be used as ingredients for alternative solutions to the longstanding problem of observer design for nonlinear sys- tems