Ring‐opening polymerization of L‐lactide using half‐titanocene complexes of the ATiCl2Nu type: Synthesis,characterization, and thermal properties

Various half‐titanocene complexes of the ATiCl₂Nu type, where A is the pentamethylcyclopentadienyl (Cp*) or indenyl (Ind) group and Nu a nucleophile (ethoxy group or chloride), were used for the polymerization of L ‐lactide, LLA. In the cases where Nu is an ethoxy group, a 5% excess of ATiCl₃ was used to accelerate the polymerization reaction. These systems were proven to be very efficient initiators for the ring‐opening polymerization (ROP) of LLA in toluene at 130 °C. Kinetic studies revealed that in most cases the polymerization yield was quantitative and the molecular weight increased linearly with time, leading to well‐defined PLLA with narrow molecular weight distributions (M_w/M_n ≤ 1.1). LLA was also polymerized by the in situ formation of the initiating system after mixing IndTiCl₃, benzyl alcohol, BzOH, and NEt₃. The thermal properties of the produced polymers were examined by differential scanning calorimetry and thermogravimetric analysis. The activation energy of the thermal decomposition was calculated by the Ozawa–Flynn–Wall and Kissinger methods. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Approximate Solutions to the Time-Invariant Hamilton–Jacobi–Bellman Equation

In this paper, we develop a new method to approximate the solution to the Hamilton–Jacobi–Bellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equation to a sequence of linear partial differential equations. These equations are then approximated via the Galerkin spectral method. The resulting algorithm has several important advantages over previously reported methods. Namely, the resulting control is in feedback form and its associated region of attraction is well defined. In addition, all computations are performed off-line and the control can be made arbitrarily close to optimal. Accordingly, this paper presents a new tool for designing nonlinear control systems that adhere to a prescribed integral performance criterion.