Optimal control of terminal processes using neural networks

Feedforward neural networks are capable of approximating continuous multivariate functions and, as such, can implement nonlinear state-feedback controllers. Training methods such as backpropagation-through-time (BPTT), however, do not deal with terminal control problems in which the specified cost function includes the elapsed trajectory-time. In this paper, an extension to BPTT is proposed which addresses this limitation. The controller design is reformulated as a constrained optimization problem defined over the entire field of extremals and in which the set of trajectory times is incorporated into the cost function. Necessary first-order stationary conditions are derived which correspond to standard BPTT with the addition of certain transversality conditions. The new gradient algorithm based on these conditions, called time-optimal backpropagation through time, is tested on two benchmark minimum-time control problems.     

UV‐Triggered Polymerization,Deposition, and Patterning of Plant Phenolic Compounds

Plant‐derived phenolic compounds, rich in catechol and pyrogallol moieties, can form multifunctional coatings on various substrates following polymerization under mildly alkaline conditions. Despite many appealing features of such coatings, the difficulty to control polymerization of phenolic compounds spatially and temporally limits their number of potential applications. In this study, it is demonstrated that UV irradiation can trigger oxidative polymerization and deposition of plant‐derived phenolic compounds, which opens the possibility to create 2D gradients and patterns of polyphenol coatings and control this polymerization temporally. UV–vis spectroscopy, electrospray ionization mass spectrometry, and cyclic voltammetry analyses are used to investigate the UV‐induced polymerization of several plant‐derived phenolic compounds including pyrogallol, tannic acid, caffeic acid, and gallic acid. Formation of polyphenol coatings on polar and nonpolar substrates after UV irradiation has been studied using water contact angle measurements, atomic force microscopy, time of flight secondary ion mass spectrometry, and X‐ray photoelectron spectroscopy (XPS). The possibility to use UV‐light to accelerate polymerization of phenolic compounds and perform micropatterning can extend the scope of potential applications of the large class of structurally diverse plant‐derived phenolic compounds.