Output Feedback H ∞ Control for Uncertain Piecewise Linear Systems

This paper is concerned with the design of robust H _∞ output feedback controller for uncertain piecewise-linear systems based on piecewise-quadratic Lyapunov function technique. We assume that the uncertainty is norm-bounded and enters all system matrices. By constructing piecewise-continuous Lyapunov function for the closed-loop augmented system, we construct the H _∞ output feedback controller design procedure as solving a set of bilinear matrix inequalities (BMIs). The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities (LMIs) which can be efficiently solved numerically. A numerical example is used to illustrate the proposed method. This work was supported by the National Natural Science Foundation of China (project No. 70471049).     

Rigidity Theorems for Multiparametric Deformations of Algebraic Structures,Associated with the Knizhnik–Zamolodchikov Equations

The paper is concerned to a version of the multidimensional Riemann–Hilbert problem in the class of Knizhnik–Zamolod-chikov (KZ) equations associated with root systems, more exactly, to the extension of the Drinfeld–Kohno theorem proved for the KZ equation of the type A _n − 1 to the generalized KZ equation associated with the root system B _n . The rigidity theorems for the corresponding braided quasi-bialgebra structures connected with two-parametric deformations of the universal enveloping algebra for the Lie algebra of B _n type are proved. In the proof the cyclic cohomology is used. This work was partially supported by the Russian Foundation for Basic Research (project No. 02-01-22000), CNRS PICS 2094, and the Grant of President of RF for support of leading scientific schools (project No. 457.2003.1).     

Group specialties in the problem of the maximum principle for systems with deviating argument

The problem of equivalence of the maximum principle in strong pointwise and integral forms is investigated in an optimum control problem in which dynamics is described by a functional-differential equation of pointwise type (a differential equation with deviating argument). The maximum principle in the strong pointwise form is formulated in the aspect of a two-parametrical set of finite-dimensional extremal problems [1,2]. Like it is in ordinary systems, the first parameter is time t and the second parameter is a length of the words which are composed by the generators of finitely generated group Q of homeomorphisms of the real line and which are generated by the functions of a deviation of the argument (for the ordinary systems the corresponding group Q is trivial). The maximum principle in the strong pointwise form follows from the maximum principle in the integral form. The basic obstacle for the equivalence of two forms is a combinatorial condition on the group Q. The presence of noted combinatorial property involves the existence of metric invariants for the group Q that allows to describe its structure in more detail.     

NILPOTENT (n, n(n + 1)/2) SUB-RIEMANNIAN PROBLEM

In this paper, we integrate nilpotent (n, n(n + 1)/2) sub-Riemannian problem. 2000 Mathematics Subject Classification. 93B29. The author was supported by the Russian Foundation for Basic Research (project No. 050100458) and the grant UNIROS 0501016.     

Local Controllability for Linear Control Systems on Lie Groups

Abtract  In this work, we study controllability properties of linear control systems on Lie groups. Using Lie theory of semigroups, we obtain local controllability results for this type of systems. In addition, properties for the flow of the drift vector field X and for the reachable set of the system are presented. Finally, an example on the Heisenberg Lie group is considered, and its properties are proved using the theory developed. 2000 Mathematics Subject Classification. Primary 93B05; Secondary 93C25, 93B27. The authors want to thank the Fachbereich Mathematik of the Technische Universit?t Darmstadt for warm hospitality during the production of this work. The first author is pleased to thank Professor Guillermo Ferreyra and the department of mathematics at LSU for their support.     

Robust Gradient-Like Property and Controller Design for Uncertain Pendulum-Like Systems

In this paper the gradient-like behavior for the pendulum-like systems with additive, multiplicative, and H _∞ uncertainties is analyzed. Then some conditions ensuring existence of controllers for uncertain pendulum-like systems are given. The corresponding controller design problem is transformed into H _∞ control problem. Two examples are given to illustrate the effectiveness of the method. 2000 Mathematics Subject Classification. 93C10. This work was partially supported by National Science Foundation of China under Grant 60334030, 10472001, 10272001, 60204007.     

On the One-Step-Bracket-Generating Motion Planning Problem

We consider the general motion planning problem for a sub-Riemannian metric with one-step bracket-generating distribution. Our results generalize earlier results in the corank-one case. Mostly, we completely solve the problem in generic situation for corank smaller or equal to 3. Our results are constructive: we explicitly construct the asymptotically optimal solutions.2000 Mathematics Subject Classification. 53C17, 53C99, 93B29.The second author was partially supported by the Russian Foundation for Basic Research (project No. 0201099) and UR 03099.     

Monitoring current–voltage characteristics and energy output of silicon photovoltaic modules

Photovoltaic (PV) system designers use performance data of PV modules to improve system design and make systems more cost effective. The collection of this valuable data is often not done due to the high costs associated with data acquisition systems. In this paper, we report on the design of a low-cost current–voltage (I–V) measuring system used to monitor the I–V characteristics of PV modules. Results obtained from monitoring seven crystalline silicon modules between October 2001 and November 2002 are presented and discussed. Results obtained also show the value of being able to continuously monitor the current–voltage characteristics of PV modules.     

一种控制燃煤机组SCR烟气脱硝系统氨逃逸的优化调整方法

以某烟气脱硝工程3号机组为例,针对选择性催化还原(SCR)脱硝反应器出口NO_x质量浓度偏差大、氨逃逸率高的问题,提出了一种喷氨均匀性调整优化方案。采用该方案对喷氨格栅每路供氨支管上的手动调节阀进行调整,最终在反应器出口建立均匀、稳定的NO_x分布。优化调整前后系统A、B两侧的NO_x不均匀度分别从55.1%和19.2%,降至27.6%和14.7%;SCR脱硝系统的平均氨逃逸率从3.289 6 m L·m~(-3)降至1.265 7 mL·m~(-3),表明采用该优化调整方法可使反应器出口NO_x分布均匀,降低氨逃逸率,有利于系统的安全、稳定运行。     

Positive Quadratic Differential Forms: Topological Equivalence Through Newton Polyhedra

The purpose of this article is to establish conditions under which a positive quadratic differential form is topologically equivalent to its principal part defined by Newton polyhedra. The problem is to study the simultaneous behavior of two foliations in the plane having a common point as a singularity. 2000 Mathematics Subject Classification. Primary: 37C15; Secondary: 34C20, 34A34. The first author was partially supported by FAPESP Grant No. 03/03107-9 and by CNPq Grant No. 306992/2003-5, Brazil. The second author was supported by CNPq-Brazil Grant No. 154150/01-1 and PROCAD-Brazil No. 092/01. The third author was supported by PRONEX No. 76.97.1080/00 and Fapesp-Brazil under Grant No. 97/10735-3.     

The dynamic interpolation problem: On Riemannian manifolds,Lie groups,and symmetric spaces

We consider the dynamic interpolation problem for nonlinear control systems modeled by second-order differential equations whose configuration space is a Riemannian manifoldM. In this problem we are given an ordered set of points inM and would like to generate a trajectory of the system through the application of suitable control functions, so that the resulting trajectory in configuration space interpolates the given set of points. We also impose smoothness constraints on the trajectory and typically ask that the trajectory be also optimal with respect to some physically interesting cost function. Here we are interested in the situation where the trajectory is twice continuously differentiable and the Lagrangian in the optimization problem is given by the norm squared acceleration along the trajectory. The special cases whereM is a connected and compact Lie group or a homogeneous symmetric space are studied in more detail.Work supported in part by NSF grant No. 89-14643 and NATO project CRG 910926.     

Global Stabilization for Systems Evolving on Manifolds

We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions of our systems in the “sample and hold” sense introduced by Clarke, Ledyaev, Sontag, and Subbotin (CLSS). We generalize their theorem which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds with respect to actuator errors, under small observation noise. 2000 Mathematics Subject Classification. 93B05.     

A Breiman Type Theorem for Gibbs Measures

For a translation invariant Gibbs measure on a suitable translation invariant configuration set X ⊂ S ^G , where G is an amenable group and S is a finite set, we prove the convergence of the Shannon–McMillan–Breiman ratio on a specific subset of “generic” configurations. Provided that the above Gibbs measure exists, we also prove the convergence in the definition of the pressure and the fact that this Gibbs measure is an equilibrium measure. The work of the first author is partially supported by the Russian Foundation for Basic Research (project No. 05–00–00449).     

Asymptotics of Solutions of Periodic Problem for Generalized Nonlinear Hamiltonian System Singularly Perturbed by a Matrix

The paper deals with the periodic problem for a generalized nonlinear Hamiltonian system, which appears from the control optimality condition for the periodic problem of the minimization of the functional on trajectories of the equation with the operator A + ɛB standing before the derivative, where the operator A is singular and A + ɛB is invertible for sufficiently small ɛ > 0. Under some conditions, the asymptotic solution of such problem has been constructed in the form of the series with respect to nonnegative integer powers of ɛ. The solvability of the considered problem has also been established for sufficiently small ɛ > 0. This work was supported by the Russian Fundamental Research Foundation (project No. 06–01–00296).     

Limit Cycles for a Class of Three-Dimensional Polynomial Differential Systems

Perturbing the system inside the family of polynomial differential systems of degree n in , we obtain at most n ² limit cycles using the first-order averaging theory. Moreover, there exist such perturbed systems having at least n ² limit cycles.      

Kinetics of photocurrent generation and quantum efficiency of a dye sensitized platinized solid state photovoltaic cell made from p-type CuCNS and n-SnO2 transparent film on glass

The mechanism of photocurrent enhancement of a platinized dye sensitized solid state photovoltaic cell based on p-CuCNS and SnO₂ coated transparent glass is discussed. The variation of photocurrent quantum efficiency (φ) with dye concentration (D₀) of the device is presented for both platinized and unplatinized systems. According to the experimental results the parameters A and B in the model equation φ=AD₀ − BD₀² are calculated. It is found that parameter B is decreased and parameter A is increased for platinized systems compared with unplatinized systems. Photocurrent enhancement due to platinization is further discussed with the photophysical processes and charge transfer processes associated with the device.     

Synthesis and transport properties of prospective photovoltaic systems related to CuInSe2 and CuGaSe2

Solid solutions in CuGaSe₂–ZnSe and CuInSe₂–ZnSe systems have been obtained by radio frequency heating. In order to prepare n-type phases based on CuGaSe₂, p-type (CuGa)_1−xZn_2xSe₄ and (CuIn)_1−xZn_2xSe₄ (0.05x0.1) single crystals were doped by Ag, Hg, Cd, Zn implantation. The crystal structure of the solid solutions was studied by X-ray diffraction; the substitutors as well as the implantant valence states were analyzed using X-ray photoelectron spectroscopy. Hall effect, electrical conductivity, and the charge carrier mobility of an n-type zinc-implantated solid solution (CuGa)_1−xZn_2xSe₄ and (CuIn)_1−xZn_2xSe₄ (0.05x0.1) were studied.     

Singular Curves Determine Generic Distributions of Corank at Least 3

We prove that generic distribution germ of even rank not divisible by 4 and of corank at least 3 is strongly determined by singular curves. 2000 Mathematics Subject Classification. Primary 58A30, 58K05; Secondary 53B99. The author was partially supported by Committee for Scientific Research (KBN), Poland (project No. 2P03A 00124).     

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy ² + 2b(x, y) dx dy + c(x, y)dx ² = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf’s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F _p  = 0, and F _pp  ≠ 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form ω = dy − pdx defined on the singular surface F = 0. This work was partially supported by Fapesp grant No. 02/09157-5.     

A design procedure for solar air heating systems

A natural extension of the design procedure for liquid-based solar space and water heating systems is a similar analysis for solar heating systems using air as the heat transfer fluid. In this paper, a solar air heating system incorporating a flat-plate air heater and packed bed thermal storage is described and a simulation model for the system is developed. The results of many simulations of the air heating system are used to establish the relationship between system performance and the system design and meteorological variables. The results are presented in analytic and graphical form, referred to as an f-chart for solar air heating systems. The results of simulations in several widely different climates suggest that the information presented in the f-chart is location independent. Methods of estimating the performance of air heating systems having a collector air capacitance rate and a storage capacity other than those used to generate the f-chart are included. A comparison of the performance of air and liquid based systems is afforded by a comparison of their respective f-charts. The air system is shown to perform better at high load fractions supplied by solar energy than a liquid-based system with the same collector thermal performance parameters.