Feasible Direction Algorithm for Optimal Control Problems with State and Control Constraints: Implementation

In this paper, we describe the implementation aspects of an optimization algorithm for optimal control problems with control, state, and terminal constraints presented in our earlier paper. The important aspect of the implementation is that, in the direction-finding subproblems, it is necessary only to impose the state constraint at relatively few points in the time involved. This contributes significantly to the algorithmic efficiency. The algorithm is applied to solve several optimal control problems, including the problem of the abort landing of an aircraft in the presence of windshear.     

Steam-Induced Coarsening of Single-Unit-Cell MFI Zeolite Nanosheets and Its Effect on External Surface Brønsted Acid Catalysis

Commonly used methods to assess crystallinity, micro-/mesoporosity, Brønsted acid site density and distribution (in micro- vs. mesopores), and catalytic activity suggest nearly invariant structure and function for aluminosilicate zeolite MFI two-dimensional nanosheets before and after superheated steam treatment. Yet, pronounced reaction rate decrease for benzyl alcohol alkylation with mesitylene, a reaction that cannot take place in the zeolite micropores, is observed. Transmission electron microscopy images reveal pronounced changes in nanosheet thickness, aspect ratio and roughness indicating that nanosheet coarsening and the associated changes in the external (mesoporous) surface structure are responsible for the changes in the external surface catalytic activity. Superheated steam treatment of hierarchical zeolites can be used to alter nanosheet morphology and regulate external surface catalytic activity while preserving micro- and mesoporosity, and micropore reaction rates.     

Some Finance Problems Solved with Nonsmooth Optimization Techniques

The purpose of this paper is to draw the attention of the nonsmooth analysis and mathematical finance communities to the scope for applications of nonsmooth optimization to finance by studying in detail two illustrative examples. The first concerns the maximization of a terminal utility function in an investment problem with transaction costs. The second concerns the calculation of the duration of a bond for general term structures of interest rates. The emphasis is on methodology.     

Optimization of a non-cryogenic quantum infrared detector

A study of the optimization of the detectivity of a mid-infrared double heterostructure photovoltaic detector is proposed. Simple approximate analytic expressions for the dark current are compared with full numerical calculations, and provide a physical insight into the mechanisms dominating the dark current. The analysis is performed step by step, from a simple p–n junction to the full double heterostructure. The influence of temperature, barrier band gap energy in a double heterostructure, doping density in the active region, on diffusion and generation–recombination mechanisms is analyzed. It is finally shown how the performances of a double heterostructure photovoltaic detector can be improved by controlled doping of the active region.     

Discontinuous feedback in nonlinear control: Stabilization under persistent disturbances

We consider a nonlinear control system which, under persistently acting disturbances, can be asymptotically driven to the origin by some non-anticipating strategy with infinite memory (such a strategy determines a value of control u(t) at moment t using complete information on the prehistory of disturbances until moment t). We demonstrate that this property is equivalent to the existence of a robust stabilizing (possibly discontinuous) feedback k(x).     

On the conditions under which the euler equation or the maximum principle hold

A variational problem is analyzed in which the integrand is a polynomial and satisfies the hypotheses of the classical existence theory. It is shown nonetheless that the solution does not satisfy the usual necessary conditions.