Localization of the optimal solution and a posteriori bounds for aggregation

After an aggregated problem has been solved, it is often desirable to estimate the accuracy loss due to the fact that a simpler problem than the original one has been solved. One way of measuring this loss in accuracy is the difference in objective function values. To get the bounds for this difference, Zipkin (Operations Research 1980;28:406) has assumed, that a simple (knapsack-type) localization of an original optimal solution is known. Since then various extensions of Zipkin's bound have been proposed, but under the same assumption. A method to compute the bounds for variable aggregation for convex problems, based on general localization of the original solution is proposed. For some classes of the original problem it is shown how to construct the localization. Examples are given to illustrate the main constructions and a small numerical study is presented.

Aggregation-based decomposition for multi-divisional models

The aggregation theory of mathematical programming is used to study decentralization in convex programming models. A two-level organization is considered and a aggregation-disaggregation scheme is applied to such a divisionally organized enterprise. In contrast to the known aggregation techniques, where the decision variables/production planes are aggregated, it is proposed to aggregate resources allocated by the central planning department among the divisions. This approach results in a decomposition procedure, in which the central unit has no optimization problem to solve and should only average local information provided by the divisions.

Robust state-derivative feedback LMI-based designs for multivariable linear systems

In some practical problems, for instance in the control systems for the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. New necessary and sufficient linear matrix inequalities (LMI) conditions for the design of state-derivative feedback for multi-input (MI) linear systems are proposed. For multi-input/multi-output (MIMO) linear time-invariant or time-varying plants, with or without uncertainties in their parameters, the proposed methods can include in the LMI-based control designs the specifications of the decay rate, bounds on the output peak, and bounds on the state-derivative feedback matrix K. These design procedures allow new specifications and also, they consider a broader class of plants than the related results available in the literature. The LMIs, when feasible, can be efficiently solved using convex programming techniques. Practical applications illustrate the efficiency of the proposed methods.

H-2 and H-infinity - norm control of intelligent structures using LMI techniques

Linear Matrix Inequalities (LMIs) is a powerful too] that has been used in many areas ranging from control engineering to system identification and structural design. There are many factors that make LMI appealing. One is the fact that a lot of design specifications and constrains can be formulated as LMIs [1]. Once formulated in terms of LMIs a problem can be solved efficiently by convex optimization algorithms. The basic idea of the LMI method is to formulate a given problem as an optimization problem with linear objective function and linear matrix inequalities constrains. An intelligent structure involves distributed sensors and actuators and a control law to apply localized actions, in order to minimize or reduce the response at selected conditions. The objective of this work is to implement techniques of control based on LMIs applied to smart structures.

Growth and home range size of the gracile mouse opossum Gracilinanus microtarsus (Marsupialia: Didelphidae) in Brazilian cerrado

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gênese e Classificação da Coquina de Camaquã, Formação Corumbataí (Neopermiano), na Região de Rio Claro, SP

Analysis of the taphonomic signatures of a well preserved, silicifled coquina (Pinzonella neotropica assemblage) from the Camaquã outcrop, upper part of the Corumbataí Formation (Late Permian), in the Rio Claro region, state of Sáo Paulo, allowed interpretation of processes involved in its origin as related to high energy events (storms). The coquina occurs as a lenticular body, 2-11 cm thick and extending laterally for about 120 m. Basal contact of the coquina is sharp and erosive. Its upper contact is sharp. The concentration is dominated by pelecypods including the shallow burrowers (Pinzonella neotropica, Jacquesia brasiliensis), intermediate burrower (Pyramus anceps) and semi-infaunal forms (Naiadopsis lamellosus). All these species are suspension feeders. Besides sand-sized or even smaller shell fragments, there occur disarticulated, complete shells which are commonly abraded but do not show any signs of bioerosion or incrustation. In vertical side view, the shells are mainly convex-up, nested or stacked, while in plan-view they show random orientation. Multiple discontinuous grading is visible. These taphonomic signatures suggest that the origin of the skeletal accumulation is related to high energy events (possibly storm flows) in a proximal environment. The amalgamated nature of the Camaquã coquina records several episodes of erosion and deposition.

Analog nonderivative optimizers

Analog networks for solving convex nonlinear unconstrained programming problems without using gradient information of the objective function are proposed. The one-dimensional net can be used as a building block in multi-dimensional networks for optimizing objective functions of several variables.

Algorithms for network piecewise-linear programs: A comparative study

Piecewise-Linear Programming (PLP) is an important area of Mathematical Programming and concerns the minimisation of a convex separable piecewise-linear objective function, subject to linear constraints. In this paper a subarea of PLP called Network Piecewise-Linear Programming (NPLP) is explored. The paper presents four specialised algorithms for NPLP: (Strongly Feasible) Primal Simplex, Dual Method, Out-of-Kilter and (Strongly Polynomial) Cost-Scaling and their relative efficiency is studied. A statistically designed experiment is used to perform a computational comparison of the algorithms. The response variable observed in the experiment is the CPU time to solve randomly generated network piecewise-linear problems classified according to problem class (Transportation, Transshipment and Circulation), problem size, extent of capacitation, and number of breakpoints per arc. Results and conclusions on performance of the algorithms are reported.

A refinement of the gauss-lucas theorem

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society.

H2 and/or H∞-norm model reduction of uncertain discrete-time systems

This paper addresses the problem of model reduction for uncertain discrete-time systems with convex bounded (polytope type) uncertainty. A reduced order precisely known model is obtained in such a way that the H2 and/or the H∞ guaranteed norm of the error between the original (uncertain) system and the reduced one is minimized. The optimization problems are formulated in terms of coupled (non-convex) LMIs - Linear Matrix Inequalities, being solved through iterative algorithms. Examples illustrate the results.

Novos resultados sobre a estabilidade e controle de sistemas nao-lineares utilizando modelos fuzzy e LMI

Relaxed conditions for the stability study of nonlinear, continuous and discrete-time systems given by fuzzy models are presented. A theoretical analysis shows that the proposed method provides better or at least the same results of the methods presented in the literature. Digital simulations exemplify this fact. These results are also used for the fuzzy regulators design. The nonlinear systems are represented by the fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers are described by LMIs (Linear Matrix Inequalities), that can be solved efficiently by convex programming techniques. The specification of the decay rate, constraints on control input and output are also described by LMIs. Finally, the proposed design method is applied in the control of an inverted pendulum.

Shape-based features for cat ganglion retinal cells classification

This article presents a quantitative and objective approach to cat ganglion cell characterization and classification. The combination of several biologically relevant features such as diameter, eccentricity, fractal dimension, influence histogram, influence area, convex hull area, and convex hull diameter are derived from geometrical transforms and then processed by three different clustering methods (Ward's hierarchical scheme, K-means and genetic algorithm), whose results are then combined by a voting strategy. These experiments indicate the superiority of some features and also suggest some possible biological implications.

Robust control applications for smart truss structure

A finite element modeling of an intelligent truss structure with piezoelectric stack actuators for the purpose of active damping and structural vibration attenuation is presented. This paper concerns with the following issues aspects: the design of intelligent truss structure considering electro-mechanical coupling between the host structure and piezoelectric stack actuators; the H 2 norm approach to search for optimal placement of actuators and sensors; and finally some aspects in robust control techniques. The electro-mechanical behavior of piezoelectric elements is directly related to the successful application of the actuators in truss structures. In order to achieve the desired damping in the interested bandwidth frequency it is used the H ∞ output feedback solved by convex optimization. The constraints to be reached are written by linear matrix inequalities (LMI). The paper concludes with a numerical example, using Matlab and Simulink, in a cantilevered, 2-bay space truss structure. The results demonstrated the approach applicability.

Population dynamics of Ectatomma brunneum (Hymenoptera, Formicidae) under laboratory conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Active control in flexible plates with piezoelectric actuators using linear matrix inequalities

The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft, aerospace and automotive structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. The actuator/sensor materials are composed by piezoelectric ceramic (PZT - Lead Zirconate Titanate), commonly used as distributed actuators, and piezoelectric plastic films (PVDF-PolyVinyliDeno Floride), highly indicated for distributed sensors. The design process of such system encompasses three main phases: structural design; optimal placement of sensor/actuator (PVDF and PZT); and controller design. Consequently, for optimal design purposes, the structure, the sensor/actuator placement and the controller have to be considered simultaneously. This article addresses the optimal placement of actuators and sensors for design of controller for vibration attenuation in a flexible plate. Techniques involving linear matrix inequalities (LMI) to solve the Riccati's equation are used. The controller's gain is calculated using the linear quadratic regulator (LQR). The major advantage of LMI design is to enable specifications such as stability degree requirements, decay rate, input force limitation in the actuators and output peak bounder. It is also possible to assume that the model parameters involve uncertainties. LMI is a very useful tool for problems with constraints, where the parameters vary in a range of values. Once formulated in terms of LMI a problem can be solved efficiently by convex optimization algorithms.