Determination of optimal feedback terminal controllers for general boundary conditions using generating functions

Given a nonlinear system and a performance index to be minimized, we present a general approach to expressing the finite time optimal feedback control law applicable to different types of boundary conditions. Starting from the necessary conditions for optimality represented by a Hamiltonian system, we solve the Hamilton-Jacobi equation for a generating function for a specific canonical transformation. This enables us to obtain the optimal feedback control for fundamentally different sets of boundary conditions only using a series of algebraic manipulations and partial differentiations. Furthermore, the proposed approach reveals an insight that the optimal cost functions for a given dynamical system can be decomposed into a single generating function that is only a function of the dynamics plus a term representing the boundary conditions. This result is formalized as a theorem. The whole procedure provides an advantage over methods rooted in dynamic programming, which require one to solve the Hamilton-Jacobi-Bellman equation repetitively for each type of boundary condition. The cost of this favorable versatility is doubling the dimension of the partial differential equation to be solved.     

石油价格机制改革之对策

文章在阐述我国石油价格形成机制的演变过程的基础上,针对我国目前石油定价机制所导致的诸如石油价格变动滞后以及由此带来的市场信号失灵等问题思考了相应的改革对策,提出了调整政府价格管理职能、建立平等竞争的市场规则、完善稳定油价的调控体系以及加快建立石油战略储备等7个方面的建议。     

Synthesis and applications of heterobifunctional poly(ethylene oxide) oligomers

Poly(ethylene oxide) (PEO) oligomers are employed extensively in pharmaceutical and biomedical arenas mainly due to their excellent physical and biological properties, including solubility in water and organic solvents, lack of toxicity, and absence of immunogenicity. PEO can be chemically modified and reacted with, or adsorbed onto, other molecules and surfaces. Sophisticated applications for PEO have increased the demand for PEO oligomers with tailored functionalities, and heterobifunctional PEOs are often needed. This review discusses the synthesis and applications of heterobifunctional PEO oligomers possessing amine, carboxylate, thiol, and maleimide functional groups.     

Synthesis,extraction, and adsorption properties of calix[4]arene‐poly(ethylene‐glycol) crosslinked polymer

Novel calix[4]arene‐poly(ethylene glycol) crosslinked polymer (CCP) has been synthesized by the polycondensation reaction between a p‐tert‐butylcalix[4]arene derivative and dihydroxyl capped poly(ethylene glycol) (DHPEG, M_n = 1000) catalyzed by neodymium tosylate. The hydrogel, consisted of 66.9% water and 33.1% CCP, can selectively extract aromatic organic molecules from aqueous solution according to the diameter of the guest molecules, which infers that the diameter of the calix[4]arene cavity is about 5.4 Å and the conformation of calix[4]arene units altered from cone conformation to 1,3‐alternate conformation during the polycondensation reaction. Furthermore, CCP can also adsorb naphthalene from gas phase, showing much higher capacity than active carbon does, which may have some potential applications in the field of separation and environment protection. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Plasma power can make better powders

It may be a truism to say that round powders pack better, but spheroidisation of powder particles is one of the successful commercial applications of induction plasma technology and can play a key role in substantial improvement of powder quality and fluidity…     

Parametric circles and spheres

Formulations for parametric circles and spheres in terms of rational Gaussian (RaG) curves and surfaces are introduced. With the proposed formulations, a full circle is generated by interpolating a closed RaG curve to the vertices of an equilateral triangle, and a full sphere is generated by interpolating a closed RaG surface to the vertices of an octahedron with equilateral triangular faces. Generation of circles and spheres in this manner is very intuitive and easy to remember as the weights are all 1 and the nodes are all unique and uniformly spaced.