Time–mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles

AbstractDirect methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are most frequently used. However, in some cases, these meshes cannot cope accurately with nonlinear behaviour unless a very large number of mesh nodes is used. One way to improve the solution involves adaptive mesh refinement algorithms which allow a non uniform node collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. The technique was applied to solve two problems involving nonholonomic vehicles and it led to results with higher accuracy and yet with lower overall computational time when compared to a mesh having equidistant nodes

Decision Tools to Analyse immigrant Territorial Distribution

The main purpose of this study consists in the development of a set of mathematical tools - based on decision tree methodologies - that allows the systematised approach to the spatial immigrant population distribution in metropolitan areas.The case study reported is applied to Porto city (Portugal), and analyses the spatial distribution of immigrant dwellings (according to theircountry of origin), as well as the distribution of work places consideringimmigrant dwelling locations.The developed tools, as well as their cartographic interface, also developed in this research study, are particularly important in demographicand population studies, because they allow the cross-sectional characterization of defnite population groups, as well as the anticipation of probable dwelling and work location behaviours. They are also relevant in thedefnition of immigrants policies, namely in relation to employment and habitation, and in the monitoring of their respective evolution processes.The main purpose of this study consists in the development of a set of mathematical tools - based on decision tree methodologies - that allows the systematised approach to the spatial immigrant population distribution in metropolitan areas.The case study reported is applied to Porto city (Portugal), and analyses the spatial distribution of immigrant dwellings (according to theircountry of origin), as well as the distribution of work places consideringimmigrant dwelling locations.The developed tools, as well as their cartographic interface, also developed in this research study, are particularly important in demographicand population studies, because they allow the cross-sectional characterization of defnite population groups, as well as the anticipation of probable dwelling and work location behaviours. They are also relevant in thedefnition of immigrants policies, namely in relation to employment and habitation, and in the monitoring of their respective evolution processes

Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms

We address optimal control problems for nonlinear systems with pathwise state-constraints. These are challenging nonlinear problems for which the number of discretization points is a major factor determining the computational time. Also, the location of these points has a major impact in the accuracy of the solutions. We propose an algorithm that iteratively finds an adequate time-grid to satisfy some predefined error estimate on the obtained trajectories, which is guided by information on the adjoint multipliers. The obtained results show a highly favorable comparison against the traditional equidistant spaced time grid methods, including the ones using discrete time models. This way, continuous time plant models can be directly used. The discretization procedure can be automated and there is no need to select a priori the adequate time step. Even if the optimization procedure is forced to stop in an early stage, as might be the case in real time problems, we can still obtain a meaningful solution, although it might be a less accurate one. The extension of the procedure to a Model Predictive Control (MPC) context is proposed here. By defining a time dependent accuracy threshold, we can generate solutions that are more accurate in the initial parts of the receding horizon, which are the most relevant for MPC

Reference Tracking of Depth of Anesthesia Using Optimal Control

Optimal control theory has gained increasing importance in biomedical applications, e.g., in the automatic administration of anesthetics during general anesthesia. In this context, one of the features that needs to be monitored is the depth of anesthesia. This is usually achieved by the joint administration of hypnotics and analgesics. The depth of anesthesia is quantified by the bispectral index that varies between 97.7% and 0%. This index should usually be kept at a reference level between 40% and 60% during surgeries with general anesthesia. In this contribution, we consider an open-loop control strategy to achieve this goal. In order to determine a suitable controller, we formulate a nonlinear optimal control problem and we solve it using direct methods. These methods have become increasingly useful when computing the numerical solution of an optimal control problem. Moreover, they are known to provide a very robust and general approach

An optimal control approach to reference level tracking in general anesthesia

In this paper the neuromuscular blockade level and the bispectral index level tracking problems by means of automatic control are considered in the context of general anesthesia. These tracking problems are formulated as optimal control problems that are numerically solved using direct methods. The results shown in this paper are preliminary but illustrate a good performance of this strategy when applied to biomedical problems. © 2015 IEEE

A trajectory controller for kite power systems with wind gust handling capabilities

In this paper, we address the generation of electrical power using Airborne Wind Energy Systems, comprising a kite connected through a tether to a generator on the ground. We design a controller to steer the kite to follow a pre-defined periodic path, which includes a production mode, a tether retrieval mode, and a safe mode capable of handling wind gusts. Copyrigh

Glylphosate Determination In Soil, Water And Vegetables Using Dpv Optilmized By Response Surface Methodology

A voltammetric procedure optimized by experimental design for glyphosate determination in soil, water and vegetable samples is described. The voltammetry experiments were performed using a hanging mercury drop electrode (HMDE). The DPV variables involved in the optimization process were: voltage step, pulse amplitude, pulse interval, voltage step time and concentration of the supporting electrolyte. A full 25 factorial design was chosen to evaluate these effects. From the results obtained by the factorial design the three most important factors were determined. These variables were evaluated with a central composite design. Under the optimized conditions, the operational range was from 0.050 to 100.0 mg dm-3 and the detection and quantification limits were 14 and 48 μg dm-3, respectively. The optimized method was successfully applied to glyphosate determination in soil, water and vegetables after purifying with an ion exchange resin and derivation.264325337D.D. Baird R.P. Upchurch, W.B. Homesley, and J.E. Franz, in S.M. Carlisle and J.T. Trevors, Water Air Soil Pollut. 39 (1988) 409de Amarante, O.P., dos Santos, T., Brito, N.M., Ribeiro, M.L., (2002) Quim. Nova, 25, p. 589Morrison, M.L., Meslow, E.C., (1984) For. Sci, 30, p. 95Marsh, J., Davies, H.A., Grossbard, E., (1977) Weed Res, 17, p. 77de Amarante, O.P., dos Santos, T., Brito, N.M., Ribeiro, M.L., (2002) Quim. Nova, 25, p. 420Stalikas, C.D., Konidari, C.N., (2001) J. Chromatogr. A, 907, p. 1Sato, K., Jin, J.Y., Takeuchi, T., Miwa, T., Suenami, K., Takekoshi, Y., Kanno, S., (2001) J. Chromatogr. A, 919, p. 313Zhu, Y., Zhang, F.F., Tong, C.L., Liu, W.P., (1999) J. Chromatogr. A, 850, p. 297Borjesson, E., Torstensson, L., (2000) J. Chromatogr. A, 886, p. 207Royer, A., Beguin, S., Tabet, J.C., Hulot, S., Reding, M.A., Communal, P.Y., (2000) Anal. Chem, 72, p. 3826Stalikas, C.D., Pilidis, G.A., (2000) J. Chromatogr. A, 872, p. 215Kudzin, Z.H., Gralak, D.K., Drabowicz, J., Luczak, J., (2002) J. Chromatogr. A, 947, p. 129March, J., (1992) Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, , John Wiley and Sons, New YorkSmyth, W.F., Watkiss, P., Burmicz, J.S., Hanley, H.O., (1975) Anal. Chim. Acta, 78, p. 81Bronstad, J.O., Friestad, H.O., (1976) Analyst, 101, p. 820Friestad, H.O., Bronstad, J.O., (1985) J. Assoc. Off. Anal. Chem, 68, p. 76Gratteri, P., Furlanetto, S., LaPorta, E., Pinzauti, S., Leardi, R., (1996) Farmaco, 51, p. 231Alonso, M.A., Sanllorente, S., Sarabia, L.A., Arcos, M.J., (2000) Anal. Chim. Acta, 405, p. 123Furlanetto, S., Orlandini, S., Aldini, G., Gotti, R., Dreassi, E., Pinzauti, S., (2000) Anal. Chim. Acta, 413, p. 229Oduoza, C.F., (1992) Chemometrics Intell. Lab. Syst, 17, p. 243Teófilo, R.F., Reis, E.L., Reis, C., da Silva, G.A., Kubota, L.T., (2004) J. Braz. Chem. Soc, 15, p. 865Teófilo, R.F., Ferreira, M.M.C., (2006) Quim. Nova, 29, p. 338Neto, B.B., Scarminio, I.S., Bruns, R.E., (2001) Como Fazer Experimentos. Pesquisa e Desenvolvimento na Ciência e na Indústria, , Editora da Unicamp, CampinasMontgomery, D.C., (2001) Design and Analysis of Experiments, , John Wiley and Sons, New YorkMyers, R.H., Montgomery, D.C., Response Surface Methodology (2002) Process and Product Optimization Using Designed Experiments, , John Wiley and Sons, New YorkC. Burgess Valid Analytical Methods & Procedures, RS.C, Tyne and Wear (2000