In this paper, the Linear Quadratic Regulator Problem with a positivity constraint on the admissible control set is addressed. Necessary and sucient conditions for optimality are presented in terms of inner products, projections on closed convex sets, Pontryagin's maximumprinciple and dynamic programming. Sucient and sometimes necessary conditions for the existence of positive stabilizing controls are incorporated. Convergence properties between the nite and innite horizon case are presented. Besides these analytical methods, we describe briey a method for the approximation of the optimal controls for the nite and innite horizon problem.

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An accurate description of typical finite-array behavior such as edge effects and array resonances is essential in the design of various types of antennas. The analysis approach proposed in this paper is essentially based on the concept of eigencurrents and is capable of describing finite-array behavior. In the approach numerical simulation is carried out, first, by computing element eigencurrents from chosen expansion functions and, second, by expanding a limited set of array eigencurrents in terms of element eigencurrents that contribute to the mutual coupling in the array. Both types of eigencurrents are eigenfunctions of an impedance operator that relates the current to the excitation field. Highlighting both mathematical and physical features we describe the basic concepts of the approach, in particular the relation between eigenvalues and mutual coupling. We illustrate these features for uniform linear arrays of loops and dipoles, and demonstrate that the approach provides significant improvements in terms of computation time and memory use.Index Terms-Antenna arrays, dipole arrays, eigenvalues and eigenfunctions, integrodifferential equations, loop antenna arrays, method of moments (MoM), mutual coupling, resonance.

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We report the development and application of a refined version of the classical Cassie-Baxter wetting model for the prediction of surface topographies with superomniphobic traits. The sagging height defined through the capillary length was utilized to assess the relation between a curved liquid-air interface and the surface texture. The wettability, expressed in terms of the static apparent contact angle, was quantified for single-and double-scale surface topographies and for three representative liquids and the results were compared to those of the classical Cassie-Baxter model. Of the three single-scale topographies considered in this work, the fiber case exhibited the highest contact angle across length scales of surface topographies, whereas decreasing the length scale of surface patterns from a few hundreds of micrometers to a few hundreds of nanometers led to contact angle increase by 15-20%. A generic expression for modeling multiscale hierarchical roughness of arbitrarily large multiplicity n was derived and applied. Multiscale hierarchical roughness was corroborated to be a promising way for achieving enhanced liquid repellency. Double-scale roughness was more efficient when the two length scales differed in size by at least one order of magnitude. The "fiber on sinusoid" hierarchical topography exhibiting re-entrant geometry yielded contact angles over 150 o for all considered wetting liquids.