Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I

Regularization of Descriptor Systems by Derivative and Proportional State Feedback

For linear multivariable time-invariant continuous or discrete-time singular systems it is customary to use a proportional feedback control in order to achieve a desired closed loop behaviour. Derivative feedback is rarely considered. This paper examines how derivative feedback in descriptor systems can be used to alter the structure of the system pencil under various controllability conditions. It is shown that derivative and proportional feedback controls can be constructed such that the closed loop system has a given form and is also regular and has index at most 1. This property ensures the solvability of the resulting system of dynamic-algebraic equations. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. The problem of pole placement with derivative feedback alone and in combination with proportional state feedback is also investigated. A computational algorithm for improving the “conditioning” of the regularized closed loop system is derived.

Root growth models: towards a new generation of continuous approaches

Models of root system growth emerged in the early 1970s, and were based on mathematical representations of root length distribution in soil. The last decade has seen the development of more complex architectural models and the use of computer-intensive approaches to study developmental and environmental processes in greater detail. There is a pressing need for predictive technologies that can integrate root system knowledge, scaling from molecular to ensembles of plants. This paper makes the case for more widespread use of simpler models of root systems based on continuous descriptions of their structure. A new theoretical framework is presented that describes the dynamics of root density distributions as a function of individual root developmental parameters such as rates of lateral root initiation, elongation, mortality, and gravitropsm. The simulations resulting from such equations can be performed most efficiently in discretized domains that deform as a result of growth, and that can be used to model the growth of many interacting root systems. The modelling principles described help to bridge the gap between continuum and architectural approaches, and enhance our understanding of the spatial development of root systems. Our simulations suggest that root systems develop in travelling wave patterns of meristems, revealing order in otherwise spatially complex and heterogeneous systems. Such knowledge should assist physiologists and geneticists to appreciate how meristem dynamics contribute to the pattern of growth and functioning of root systems in the field.

A dynamical systems framework for intermittent data assimilation

We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.

Reactivity of Nellore steers in two feedlot housing systems and its relationship with plasmatic cortisol

To evaluate reactivity to assess the temperament of Nellore steers in two feedlot housing systems (group pen or individual pen) and its relationship with plasmatic cortisol, 36 experimental units were observed five times at 28-day intervals of weight management during a 112-day feedlot confinement. A reactivity score scale ranging from 1 to 5 was applied when an animal was in the chute system. To the calmest animal, a reactivity score of 1 was ascribed and to the most agitated, 5. Blood samples were collected for cortisol analysis. No differences were found in reactivity and feedlot system. There was a relationship noted between reactivity and feedlot time in both housing systems (P < 0.01). There was a relation between reactivity and cortisol levels for group animals (P = 0.0616) and for individual ones (P < 0.01). Cortisol levels varied among housing systems (P < 0.01). Feedlot time influenced the cortisol levels (P < 0.09 individual; P < 0.01 group) and when variable time was included, these levels changed, decreasing in the group pen and increasing in individual pens. The continuous handling reduces reactivity and plasmatic cortisol, and group pen system seems to be less stressfully than individual pens. (C) 2010 Elsevier B.V. All rights reserved.

THE POINCARE-BENDIXSON THEOREM ON THE KLEIN BOTTLE FOR CONTINUOUS VECTOR FIELDS

We present a version of the Poincare-Bendixson Theorem on the Klein bottle K(2) for continuous vector fields. As a consequence, we obtain the fact that K(2) does not admit continuous vector fields having a omega-recurrent injective trajectory.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Evolutionary model trees for handling continuous classes in machine learning

Model trees are a particular case of decision trees employed to solve regression problems. They have the advantage of presenting an interpretable output, helping the end-user to get more confidence in the prediction and providing the basis for the end-user to have new insight about the data, confirming or rejecting hypotheses previously formed. Moreover, model trees present an acceptable level of predictive performance in comparison to most techniques used for solving regression problems. Since generating the optimal model tree is an NP-Complete problem, traditional model tree induction algorithms make use of a greedy top-down divide-and-conquer strategy, which may not converge to the global optimal solution. In this paper, we propose a novel algorithm based on the use of the evolutionary algorithms paradigm as an alternate heuristic to generate model trees in order to improve the convergence to globally near-optimal solutions. We call our new approach evolutionary model tree induction (E-Motion). We test its predictive performance using public UCI data sets, and we compare the results to traditional greedy regression/model trees induction algorithms, as well as to other evolutionary approaches. Results show that our method presents a good trade-off between predictive performance and model comprehensibility, which may be crucial in many machine learning applications. (C) 2010 Elsevier Inc. All rights reserved.

Effects of rainfall on water quality in six sequentially disposed fishponds with continuous water flow

O estudo foi efetuado durante o período de chuva (dezembro-fevereiro) em seis viveiros de produção semi-intensiva de peixes, a fim de avaliar o efeito da chuva na qualidade da água de viveiros que apresentam fluxo contínuo de água, a qual é passada de um viveiro para outro sem tratamento prévio. Foram amostrados oito pontos de coleta nas saídas dos viveiros. O viveiro P1 (próximo à nascente) apresentou as menores concentrações físicas e químicas da água e as maiores no viveiro P4 (considerado um ponto crítico recebendo material alóctone proveniente de outros viveiros e do escoamento do setor de criação de rãs). A disposição seqüencial dos viveiros estudados promoveu aumento nas concentrações dos nutrientes, clorofila-a e condutividade. As chuvas características desta época do ano aumentaram o fluxo de água nos viveiros e conseqüentemente, carreando material particulado e dissolvido de um viveiro para outro e, promovendo um aumento das variáveis limnológicas em direção do P3 ao P6. Os resultados sugerem que a chuva no período de estudo afetou positivamente a qualidade da água dos viveiros estudados, porém, como os sistemas analisados estão dispostos em distribuição seqüencial e escoamento constante da água de viveiros e tanques paralelos sem tratamento prévio, cuidados devem ser averiguados para que o aumento do fluxo de água provocado pelas chuvas não tenha efeito adverso nos viveiros estudados.

Sward canopy structure and performance of beef heifers under supplementation in Brachiaria brizantha cv. Marandu pastures maintained with three grazing intensities in a continuous stocking system

The objective of this study was to assess the sward canopy structure of Brachiaria brizantha cv. Marandu pastures maintained in three grazing intensities under continuous stocking system during the rainy season, along with the behavior and performance of grazing beef heifers supplemented with mineral salt or an energy/protein supplement. Three levels of forage allowance were assessed: 2.0, 2.5 and 3.0 kg of forage/kg of live weight, combined with two supplements (ad libitum mineral salt, and an energy/protein supplement at 0.3% of live weight/day, supplied daily). The experiment was designed as a randomized block study with two replications. The supplements did not influence the variables related to the canopy structure. Canopy height was greater at higher forage allowances during the late summer and early fall. Similarly, the stem mass was greater in pastures with higher forage allowances. Animals fed protein supplement spent less time grazing than animals supplemented with mineral salt. Stocking rate was higher in pastures with lower forage allowance levels, which increased the live weight gain per grazing area. Daily weight gain did not vary according to the forage allowance levels. The use of an energy/protein supplement did not affect the stocking rate; however, it increased individual live weight gain and live weight gain per grazing area compared with mineral salt supplementation. The use of energy/protein supplements is an efficient alternative to enhance animal performance and production under grazing systems during the rainy season

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A novel HPF voltage source rectifier for variable speed refrigeration systems

A novel single-phase voltage source rectifier capable to achieve High-Power-Factor (HPF) for variable speed refrigeration system application, is proposed in this paper. The proposed system is composed by a single-phase high-power-factor boost rectifier, with two cells in interleave connection, operating in critical conduction mode, and employing a soft-switching technique, controlled by a Field Programmable Gate Array (FPGA), associated with a conventional three-phase IGBT bridge inverter (VSI - Voltage Source Inverter), controlled by a Digital Signal Processor (DSP). The soft-switching technique for the input stage is based on zero-current-switching (ZCS) cells. The rectifier's features include the reduction in the input current ripple, the reduction in the output voltage ripple, the use of low stress devices, low volume for the EMI input filter, high input power factor (PF), and low total harmonic distortion (THD) in the input current, in compliance with the EEC61000-3-2 standards. The digital controller for the output stage has been developed using a conventional voltage-frequency control (scalar V/f control), and a simplified stator oriented Vector control, in order to verify the feasibility and performance of the proposed digital controls for continuous temperature control applied at a refrigerator prototype.