State constraints in optimal impulsive controls

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

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

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

Analysis of a sub-optimal scheme of drug dosage in the AIDS treatment

Here the results for CD4+T cells count and the viral load obtained from HIV sero-positive patients are compared with results from numerical simulations by computer. Also, the standard scheme of administration of drugs anti HIV (HAART schemes) which uses constant doses is compared with an alternative sub-optimal teatment scheme which uses variable drug dosage according to the evolution of a quantitative measure of the side effects. The quantitative analysis done here shows that it is possible to obtain, using the alternative scheme, the same performance of actual data but using variable dosage and having fewer side effects. Optimal control theory is used to solve and also to provide a prognosis related to the strategies for control of viraemia.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

Continuous versus intermittent stochastic resonance whole body vibration and its effect on pelvic floor muscle activity

To determine the optimal stochastic whole body vibration (SR-WBV) load modality regarding pelvic floor muscle (PFM) activity in order to complete the SR-WBV training methodology for future PFM training with SR-WBV.

Cardiovascular risk factor control and outcomes in peripheral artery disease patients in the Reduction of Atherothrombosis for Continued Health (REACH) Registry

OBJECTIVES: To examine differences in risk factor (RF) management between peripheral artery disease (PAD) and coronary artery (CAD) or cerebrovascular disease (CVD), as well as the impact of RF control on major 1-year cardiovascular (CV) event rates. METHODS: The REACH Registry recruited >68000 outpatients aged >/=45 years with established atherothrombotic disease or >/=3 RFs for atherothrombosis. The predictors of RF control that were evaluated included: (1) patient demographics, (2) mode of PAD diagnosis, and (3) concomitant CAD and/or CVD. RESULTS: RF control was less frequent in patients with PAD (n=8322), compared with those with CAD or CVD (but no PAD, n=47492) [blood pressure; glycemia; total cholesterol; smoking cessation (each P<0.001)]. Factors independently associated with optimal RF control in patients with PAD were male gender (OR=1.9); residence in North America (OR=3.5), Japan (OR=2.5) or Latin America (OR=1.5); previous coronary revascularization (OR=1.3); and statin use (OR=1.4); whereas prior leg amputation was a negative predictor (OR=0.7) (P<0.001). Optimal RF control was associated with fewer 1-year CV ischemic symptoms or events. CONCLUSIONS: Patients with PAD do not achieve RF control as frequently as individuals with CAD or CVD. Improved RF control is associated with a positive impact on 1-year CV event rates.

The Effects of Credit Risk on Dynamic Portfolio Management: A New Computational Approach

The study investigates the role of credit risk in a continuous time stochastic asset allocation model, since the traditional dynamic framework does not provide credit risk flexibility. The general model of the study extends the traditional dynamic efficiency framework by explicitly deriving the optimal value function for the infinite horizon stochastic control problem via a weighted volatility measure of market and credit risk. The model's optimal strategy was then compared to that obtained from a benchmark Markowitz-type dynamic optimization framework to determine which specification adequately reflects the optimal terminal investment returns and strategy under credit and market risks. The paper shows that an investor's optimal terminal return is lower than typically indicated under the traditional mean-variance framework during periods of elevated credit risk. Hence I conclude that, while the traditional dynamic mean-variance approach may indicate the ideal, in the presence of credit-risk it does not accurately reflect the observed optimal returns, terminal wealth and portfolio selection strategies.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Effect of Medical Advice for Diet on Diabetes Self-Management and Glycemic Control for Haitian and African Americans with Type 2 Diabetes

Adequate care of type 2 diabetes is reflected by the individual’s adherence to dietary guidance; yet, few patients are engaged in diabetes self-care at the recommended level, regardless of race/ethnicity. Few studies on the effect of dietary medical advice on diabetes self-management (DSM) and glycemic control have been conducted on Haitian and African American adults with type 2 diabetes. These relationships were assessed in total of 254 Blacks with type 2 diabetes (Haitian Americans = 129; African Americans = 125) recruited from Miami-Dade and Broward Counties, Florida by community outreach methods. Although dietary advice received was not significantly different between the two Black ethnicities, given advice “to follow a diet” as a predictor of “using food groups” was significant for Haitian Americans, but not for African Americans. Haitian Americans who were advised to follow a diet were approximately 3 times more likely to sometimes or often use food groups (or exchange lists) in planning meals. Less than optimal glycemic control (A1C > 7.2) was inversely related to DSM for African Americans; but the relationship was not significant for Haitian Americans. A one unit increase in DSM score decreased the odds ratio point estimate of having less than optimal glycemic control (A1C > 7.2%) by a factor of 0.94 in African Americans. These results suggest that medical advice for diet plans may not be communicated effectively for DSM for some races/ethnicities. Research aimed at uncovering the enablers and barriers of diet management specific to Black ethnicities with type 2 diabetes is recommended.

A new latching control technology for improving wave energy conversion

Extracting wave energy from seas has been proven to be very difficult although various technologies have been developed since 1970s. Among the proposed technologies, only few of them have been actually progressed to the advanced stages such as sea trials or pre-commercial sea trial and engineering. One critical question may be how we can design an efficient wave energy converter or how the efficiency of a wave energy converter can be improved using optimal and control technologies, because higher energy conversion efficiency for a wave energy converter is always pursued and it mainly decides the cost of the wave energy production. In this first part of the investigation, some conventional optimal and control technologies for improving wave energy conversion are examined in a form of more physical meanings, rather than the purely complex mathematical expressions, in which it is hoped to clarify some confusions in the development and the terminologies of the technologies and to help to understand the physics behind the optimal and control technologies. As a result of the understanding of the physics and the principles of the optima, a new latching technology is proposed, in which the latching duration is simply calculated from the wave period, rather than based on the future information/prediction, hence the technology could remove one of the technical barriers in implementing this control technology. From the examples given in the context, this new latching control technology can achieve a phase optimum in regular waves, and hence significantly improve wave energy conversion. Further development on this latching control technologies can be found in the second part of the investigation.

Active transonic aerofoil design optimization using robust multiobjective evolutionary algorithms

The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary-layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. Two test cases are conducted: the first test assumes the boundary-layer transition position is at 45% of chord from the leading edge, and the second test considers robust design optimization for the shock control bump at the variability of boundary-layer transition positions. The numerical result shows that the optimization method coupled to uncertainty design techniques produces Pareto optimal shock-control-bump shapes, which have low sensitivity and high aerodynamic performance while having significant total drag reduction.

An innovative approach to the assessment of nutrient intake in adults with type 2 diabetes : the development, trial and evaluation of a mobile phone photo/voice dietary record

Nutrition interventions in the form of both self-management education and individualised diet therapy are considered essential for the long-term management of type 2 diabetes mellitus (T2DM). The measurement of diet is essential to inform, support and evaluate nutrition interventions in the management of T2DM. Barriers inherent within health care settings and systems limit ongoing access to personnel and resources, while traditional prospective methods of assessing diet are burdensome for the individual and often result in changes in typical intake to facilitate recording. This thesis investigated the inclusion of information and communication technologies (ICT) to overcome limitations to current approaches in the nutritional management of T2DM, in particular the development, trial and evaluation of the Nutricam dietary assessment method (NuDAM) consisting of a mobile phone photo/voice application to assess nutrient intake in a free-living environment with older adults with T2DM. Study 1: Effectiveness of an automated telephone system in promoting change in dietary intake among adults with T2DM The effectiveness of an automated telephone system, Telephone-Linked Care (TLC) Diabetes, designed to deliver self-management education was evaluated in terms of promoting dietary change in adults with T2DM and sub-optimal glycaemic control. In this secondary data analysis independent of the larger randomised controlled trial, complete data was available for 95 adults (59 male; mean age(±SD)=56.8±8.1 years; mean(±SD)BMI=34.2±7.0kg/m2). The treatment effect showed a reduction in total fat of 1.4% and saturated fat of 0.9% energy intake, body weight of 0.7 kg and waist circumference of 2.0 cm. In addition, a significant increase in the nutrition self-efficacy score of 1.3 (p<0.05) was observed in the TLC group compared to the control group. The modest trends observed in this study indicate that the TLC Diabetes system does support the adoption of positive nutrition behaviours as a result of diabetes self-management education, however caution must be applied in the interpretation of results due to the inherent limitations of the dietary assessment method used. The decision to use a close-list FFQ with known bias may have influenced the accuracy of reporting dietary intake in this instance. This study provided an example of the methodological challenges experienced with measuring changes in absolute diet using a FFQ, and reaffirmed the need for novel prospective assessment methods capable of capturing natural variance in usual intakes. Study 2: The development and trial of NuDAM recording protocol The feasibility of the Nutricam mobile phone photo/voice dietary record was evaluated in 10 adults with T2DM (6 Male; age=64.7±3.8 years; BMI=33.9±7.0 kg/m2). Intake was recorded over a 3-day period using both Nutricam and a written estimated food record (EFR). Compared to the EFR, the Nutricam device was found to be acceptable among subjects, however, energy intake was under-recorded using Nutricam (-0.6±0.8 MJ/day; p<0.05). Beverages and snacks were the items most frequently not recorded using Nutricam; however forgotten meals contributed to the greatest difference in energy intake between records. In addition, the quality of dietary data recorded using Nutricam was unacceptable for just under one-third of entries. It was concluded that an additional mechanism was necessary to complement dietary information collected via Nutricam. Modifications to the method were made to allow for clarification of Nutricam entries and probing forgotten foods during a brief phone call to the subject the following morning. The revised recording protocol was evaluated in Study 4. Study 3: The development and trial of the NuDAM analysis protocol Part A explored the effect of the type of portion size estimation aid (PSEA) on the error associated with quantifying four portions of 15 single foods items contained in photographs. Seventeen dietetic students (1 male; age=24.7±9.1 years; BMI=21.1±1.9 kg/m2) estimated all food portions on two occasions: without aids and with aids (food models or reference food photographs). Overall, the use of a PSEA significantly reduced mean (±SD) group error between estimates compared to no aid (-2.5±11.5% vs. 19.0±28.8%; p<0.05). The type of PSEA (i.e. food models vs. reference food photograph) did not have a notable effect on the group estimation error (-6.7±14.9% vs. 1.4±5.9%, respectively; p=0.321). This exploratory study provided evidence that the use of aids in general, rather than the type, was more effective in reducing estimation error. Findings guided the development of the Dietary Estimation and Assessment Tool (DEAT) for use in the analysis of the Nutricam dietary record. Part B evaluated the effect of the DEAT on the error associated with the quantification of two 3-day Nutricam dietary records in a sample of 29 dietetic students (2 males; age=23.3±5.1 years; BMI=20.6±1.9 kg/m2). Subjects were randomised into two groups: Group A and Group B. For Record 1, the use of the DEAT (Group A) resulted in a smaller error compared to estimations made without the tool (Group B) (17.7±15.8%/day vs. 34.0±22.6%/day, p=0.331; respectively). In comparison, all subjects used the DEAT to estimate Record 2, with resultant error similar between Group A and B (21.2±19.2%/day vs. 25.8±13.6%/day; p=0.377 respectively). In general, the moderate estimation error associated with quantifying food items did not translate into clinically significant differences in the nutrient profile of the Nutricam dietary records, only amorphous foods were notably over-estimated in energy content without the use of the DEAT (57kJ/day vs. 274kJ/day; p<0.001). A large proportion (89.6%) of the group found the DEAT helpful when quantifying food items contained in the Nutricam dietary records. The use of the DEAT reduced quantification error, minimising any potential effect on the estimation of energy and macronutrient intake. Study 4: Evaluation of the NuDAM The accuracy and inter-rater reliability of the NuDAM to assess energy and macronutrient intake was evaluated in a sample of 10 adults (6 males; age=61.2±6.9 years; BMI=31.0±4.5 kg/m2). Intake recorded using both the NuDAM and a weighed food record (WFR) was coded by three dietitians and compared with an objective measure of total energy expenditure (TEE) obtained using the doubly labelled water technique. At the group level, energy intake (EI) was under-reported to a similar extent using both methods, with the ratio of EI:TEE was 0.76±0.20 for the NuDAM and 0.76±0.17 for the WFR. At the individual level, four subjects reported implausible levels of energy intake using the WFR method, compared to three using the NuDAM. Overall, moderate to high correlation coefficients (r=0.57-0.85) were found across energy and macronutrients except fat (r=0.24) between the two dietary measures. High agreement was observed between dietitians for estimates of energy and macronutrient derived for both the NuDAM (ICC=0.77-0.99; p<0.001) and WFR (ICC=0.82-0.99; p<0.001). All subjects preferred using the NuDAM over the WFR to record intake and were willing to use the novel method again over longer recording periods. This research program explored two novel approaches which utilised distinct technologies to aid in the nutritional management of adults with T2DM. In particular, this thesis makes a significant contribution to the evidence base surrounding the use of PhRs through the development, trial and evaluation of a novel mobile phone photo/voice dietary record. The NuDAM is an extremely promising advancement in the nutritional management of individuals with diabetes and other chronic conditions. Future applications lie in integrating the NuDAM with other technologies to facilitate practice across the remaining stages of the nutrition care process.

Ongoing Adaptation as a Feature of Complexity : Further Thoughts and Possible Ideas for Pedagogy in Physical Activity

This chapter takes as its central premise the human capacity to adapt to changing environments. It is an idea that is central to complexity theory but receives only modest attention in relation to learning. To do this we will draw from a range of fields and then consider some recent research in motor control that may extend the discussion in ways not yet considered, but that will build on advances already made within pedagogy and motor control synergies. Recent work in motor control indicates that humans have far greater capacity to adapt to the ‘product space’ than was previously thought, mainly through fast heuristics and on-line corrections. These are changes that can be made in real (movement) time and are facilitated by what are referred to as ‘feed-forward’ mechanisms that take advantage of ultra-fast ways of recognizing the likely outcomes of our movements and using this as a source of feedback. We conclude by discussing some possible ideas for pedagogy within the sport and physical activity domains, the implications of which would require a rethink on how motor skill learning opportunities might best be facilitated.