Differential Games Controllers That Confine a System to a Safe Region in the State Space, With Applications to Surge Tank Control

Surge tanks are units employed in chemical processing to regulate the flow of fluids between reactors. A notable feature of surge tank control is the need to constrain the magnitude of the Maximum Rate of Change (MROC) of the surge tank outflow, since excessive fluctuations in the rate of change of outflow can adversely affect down-stream processing (through disturbance of sediments, initiation of turbulence, etc.). Proportional + Integral controllers, traditionally employed in surge tank control, do not take direct account of the MROC. It is therefore of interest to explore alternative approaches. We show that the surge tank controller design problem naturally fits a differential games framework, proposed by Dupuis and McEneaney, for controlling a system to confine the state to a safe region of the state space. We show furthermore that the differential game arising in this way can be solved by decomposing it into a collection of (one player) optimal control problems. We discuss the implications of this decomposition technique, for the solution of other controller design problems possessing some features of the surge tank controller design problem

Model predictive Control: a passive scheme

© IFAC.This note studies the formulation of model predictive control exploiting passivity properties. The introduction of passive constraints in model predictive control schemes is particularly appealing since robustness against model uncertainty is inherently guaranteed. The potential of the discussed control scheme is shown on the regulation problem of a robot manipulator

Effect of Photographs of Visible Genetic Conditions on Quality of Life Perceptions

Historically, medical photographs are used to demonstrate dysmorphic features and characteristic presentations of genetic conditions. Traditional, pictorial depictions of genetic conditions typically involve nude subjects against walls to emphasize their features. These stark, black and white photographs may negatively influence students’ perceptions of the depicted individual. Natural photographs which include individuals in non-clinical environments may impact perceptions. To assess the influence of photographs on a viewer’s perception, 649 students from medical, nursing, genetic counseling and dental programs were surveyed in a cross-over study. Students were randomized to view a traditional or a natural photograph of three distinct genetic conditions followed by a natural or a traditional photograph, respectively, of the same conditions. Perceptions of the individual and their quality of life were assessed using Likert scale and yes/no adjective-association questions. Affected individuals were more often associated with positive characteristics (e.g. beautiful, respectful, intelligence, higher quality of life, etc.) when presented in natural settings and negative characteristics (e.g. degrading, institutionalized, humiliating, neglected, etc.) when depicted in traditional photographs (

Generalized Stabilizing Conditions for Model Predictive Control

© 2015, The Author(s).This note addresses the tracking problem for model predictive control. It presents simple procedures for both linear and nonlinear constrained model predictive control when the desired equilibrium state is any point in a specified set. The resultant region of attraction is the union of the regions of attraction for each equilibrium state in the specified set and is therefore larger than that obtained when conventional model predictive control is employed

Early appearance and possible functions of non-neuromuscular cholinesterase activities

The biological function of the cholinesterase (ChE) enzymes has been studied since the beginning of the twentieth century. Acetylcholinesterase plays a key role in the modulation of neuromuscular impulse transmission in vertebrates, while in invertebrates pseudo cholinesterases are preeminently represented. During the last 40 years, awareness of the role of ChEs role in regulating non-neuromuscular cell-to-cell interactions has been increasing such as the ones occurring during gamete interaction and embryonic development. Moreover, ChE activities are responsible for other relevant biological events, including regulation of the balance between cell proliferation and cell death, as well as the modulation of cell adhesion and cell migration. Understanding the mechanisms of the regulation of these events can help us foresee the possible impact of neurotoxic substances on the environmental and human health

Spatiotemporal role of muscarinic signaling in early chick development: exposure to cholinomimetic agents by a mathematical model

Awareness is growing that, besides several neurotoxic effects, cholinomimetic drugs able to interfere the cholinergic neurotransmitter system may exert a teratogen effect in developing embryos of vertebrate and invertebrate organisms. Cholinomimetic substances exert their toxic activity on organisms as they inhibit the functionality of the cholinergic system by completely or partially replacing the ACh molecule both at the level of the AChE active site and at the level of acetylcholine receptors. In this work, we focused the attention on the effects of muscarinic antagonist (atropine) and agonist (carbachol) drugs during the early development and ontogenesis of chick embryos. An unsteady-state mathematical model of the drug release and fate was developed, to synchronize exposure to a gradient of drug concentrations with the different developmental events. Since concentration measures in time and space cannot be taken without damaging the embryo itself, the diffusion model was the only way to establish at each time-step the exact concentration of drug at the different points of the embryo body (considered two-dimensional up to the 50 h stage). This concentration depends on the distance and position of the embryo with respect to the releasing source. The exposure to carbachol generally enhanced dimensions and stages of the embryos, while atropine mainly caused delay in development and small size of the embryos. Both the drugs were able to cause developmental anomalies, depending on the moment of development, in a time- and dose-dependent way, regardless the expression of genes driving each event

Automatic scenario generation for efficient solution of robust optimal control problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2¹⁴⁺³×¹⁹² extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive

Application of energy storage in systems with high penetration of intermittent renewables

Nowadays, in Uruguay, a considerable amount of energy produced by renewable resources is curtailed inducing frequent substantial reductions in the spot market prices. This paper analyses the incorporation of energy storage into the Uruguayan network, taking the different perspectives of a private investor and a central planner. From the investor point of view, we investigate the option of doing energy arbitrage in the wholesale market, taking advantage of the spot price fluctuations. From the national perspective, we develop an optimal power flow planning model to perform a cost-benefit analysis of batteries’ integration in reducing thermal generation. We conclude that, from a private investor perspective, fluctuations in the spot prices are not enough to make investments in batteries profitable with current prices. On the other hand, from a national perspective, results are more promising, obtaining very high revenues in some case studies

Automatic scenario generation for efficient solution of robust optimal control problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2¹⁴+³ₓ¹⁹² extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive

Automatic Scenario Generation for Robust Optimal Control Problems

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 2 14+3×192 boundary scenarios are considered. A validation with randomly-drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used