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We identify a general, i.e. not necessarily denominator-separable Roesser model from 2D discrete vector-geometric trajectories generated by a controllable, quarter-plane causal system. Our procedure consists of two steps: the first one is the computation of state trajectories from the factorization of constant matrices directly constructed from input-output data. The second step is the computation of the state, output, and input matrices of a Roesser model as solutions of a system of linear equations involving the given input-output data and the computed state trajectories. [ABSTRACT FROM AUTHOR]

We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years. [ABSTRACT FROM AUTHOR]

We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode. In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians. [ABSTRACT FROM AUTHOR]

Jatropha curcas plant is seriously affected by the mosaic disease caused by begomovirus which is carried through infected white-flies. It severely affects the Jatropha plants causing leaf damage, yellowing leaves and sap drainage. Traditionally, the diseased is controlled by roguing or removal of infected plant biomass, using insecticides or increasing resistance to host plant. In this article, a mathematical model is formulated to study mosaic disease dynamics in J. curcas plantations with roguing. Also, time delay has been incorporated in roguing and reformulates the mathematical model using delay differential equations. Sufficient conditions for the stability of the equilibrium points of the system are among the results obtained through qualitative analysis. Using the normal form theory and the center manifold theorem, the stability and direction of the bifurcating periodic solutions of the delayed system are determined. The findings are confirmed by means of numerical simulations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers. [ABSTRACT FROM AUTHOR]

A method for structural damage identification based on a modified Artificial Bee Colony algorithm is presented. A new formula is introduced to the onlooker bee phase to improve the convergence rate and the Tournament Selection Strategy is adopted instead of roulette to enhance global search ability of the algorithm. Test functions are introduced as benchmarks to verify the proposed algorithm. And then two numerical examples, including a supported beam and a plate, are conducted to investigate the efficiency and correctness of the proposed method. Final estimated results show that the present technique can produce more accurate damage identification results, comparing with other evolutionary algorithms, even with a few noise contaminated measurements. [ABSTRACT FROM PUBLISHER]

The purpose of this study is to investigate the possibility of applying some of the most widely known mathematical theories of war in the case of firms. In this research, Frederick William Lanchester's combat models, that seemed to be particularly useful to the U.S. Army at the Pacific campaign against the Japanese fleet during World War II, were examined. These mathematical models were based on differential equations and their main purpose was to predict the outcome of battles. After the appropriate theoretical assumptions were set, the examined models were applied to the case of Coca-Cola™ and Pepsi™ supply chains in the Greek market. These models have been applied to these firms by other researchers too. The results of the implementations have led to the conclusion that the theoretical models are almost identical to the reality, which means that they are applicable in business under the right conditions. [ABSTRACT FROM AUTHOR]

Cyclone separators are widely used in a variety of industrial applications. A low-mass loading gas cyclone is characterized by two performance parameters, namely the Euler and Stokes numbers. These parameters are highly sensitive to the geometrical design parameters defining the cyclone. Optimizing the cyclone geometry therefore is a complex problem. Testing a large number of cyclone geometries is impractical due to time constraints. Experimental data and even computational fluid dynamics simulations are time-consuming to perform, with a single simulation or experiment taking several weeks. Simpler analytical models are therefore often used to expedite the design process. However, this comes at the cost of model accuracy. Existing techniques used for cyclone shape optimization in literature do not take multiple fidelities into account. This work combines cheap-to-evaluate well-known mathematical models of cyclones, available data from computational fluid dynamics simulations and experimental data to build a triple-fidelity recursive co-Kriging model. This model can be used as a surrogate with a multi-objective optimization algorithm to identify a Pareto set of a finite number of solutions. The proposed scheme is applied to optimize the cyclone geometry, parametrized by seven design variables. [ABSTRACT FROM AUTHOR]

We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator matrices considered in (Trostorff in J Funct Anal 267(8):2787-2822, 2014), which can be characterized in terms of an associated boundary relation. [ABSTRACT FROM AUTHOR]

An important issue in the field of motion control of wheeled mobile robots is that the design of most controllers is based only on the robot's kinematics. However, when high-speed movements and/or heavy load transportation are required, it becomes essential to consider the robot dynamics as well. The control signals generated by most dynamic controllers reported in the literature are torques or voltages for the robot motors, while commercial robots usually accept velocity commands. In this context, we present a velocity-based dynamic model for differential drive mobile robots that also includes the dynamics of the robot actuators. Such model has linear and angular velocities as inputs and has been included in Peter Corke's Robotics Toolbox for MATLAB, therefore it can be easily integrated into simulation systems that have been built for the unicycle kinematics. We demonstrate that the proposed dynamic model has useful mathematical properties. We also present an application of such model on the design of an adaptive dynamic controller and the stability analysis of the complete system, while applying the proposed model properties. Finally, we show some simulation and experimental results and discuss the advantages and limitations of the proposed model. [ABSTRACT FROM AUTHOR]

For Hammerstein output-error autoregressive systems, a decomposition based multi-innovation stochastic gradient (D-MISG) identification algorithm and a data filtering based multi-innovation stochastic gradient (F-MISG) identification algorithm are derived by means of the key-term separation principle and the multi-innovation identification theory. The D-MISG algorithm uses the decomposition technique to transform a Hammerstein system into two subsystems and requires less computational cost, and the F-MISG algorithm uses a linear filter to filter the input-output data and has a higher estimation accuracy for larger innovation lengths. The simulation results show that the proposed two algorithm can give satisfactory parameter estimates. [ABSTRACT FROM PUBLISHER]

We show how to combine numerical schemes and calibration of systems of o.d.e. to provide efficient feedback strategies for the biological decontamination of water resources. For natural resources, we retain to introduce any bacteria in the resource and treat it aside preserving a constant volume of the resource at any time. The feedback strategies are derived from the minimal time synthesis of the system of o.d.e. [ABSTRACT FROM AUTHOR]

A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method, we use an exterior calculus-based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how retinal hemodynamics is influenced by the ocular shape (sphere, oblate spheroid, prolate spheroid and barrel are compared) and vascular architecture (four vascular arcs and a branching vascular tree are compared). The model predictions show that changes in ocular shape induce non-uniform alterations of blood pressure and velocity in the retina. In particular, we found that (i) the temporal region is affected the least by changes in ocular shape, and (ii) the barrel shape departs the most from the hemispherical reference geometry in terms of associated pressure and velocity distributions in the retinal microvasculature. These results support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics. [ABSTRACT FROM AUTHOR]

A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnsebaet al.[A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2–11. Available athttp://www.math.u-bordeaux1.fr/∼pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost. [ABSTRACT FROM PUBLISHER]

We examine the spatial dynamics of individuals in small schools of banded killifish ( Fundulus diaphanus) that exhibit rhythmic, oscillating speed, typically with sustained, coordinated, out-of-phase speed oscillations as they move around a shallow water tank. We show that the relative motion among the fish yields a periodically time-varying network of social interactions that enriches visually driven social communication. The oscillations lead to the regular making and breaking of occlusions, which we term 'switching.' We show that the rate of convergence to consensus (biologically, the capacity for individuals in groups to achieve effective coordinated motion) governed by the switching outperforms static alternatives, and performs as well as the less practical case of every fish sensing every other fish. We show further that the oscillations in speed yield oscillations in relative bearing between fish over a range that includes the angles previously predicted to be optimal for a fish to detect changes in heading and speed of its neighbors. To investigate systematically, we derive and analyze a dynamic model of interacting agents that move with oscillatory speed. We show that coordinated circular motion of the school leads to systematic cycling of spatial ordering of agents and possibilities for enriched spatial density of measurements of the external environment. Our results highlight the potential benefits of dynamic communication topologies in collective animal behavior, and suggest new, useful control laws for the distributed coordination of mobile robotic networks. [ABSTRACT FROM AUTHOR]

Many systems can be represented as linear time-invariant (LTI) systems in state space with ordinary differential equations (ODE). Forced responses are often used for model parameter estimation; however, some models are not uniquely identifiable from the data of forced responses, or experiments with pure forced response may not be the optimal design. It is thus meaningful to look for other types of data for model parameter estimation through redesigning experiments. In this work, we compare the influence of forced and initial condition responses on the deterministic identifiability of LTI systems in state space with ODEs as model structure. It is clearly demonstrated that one initial condition vector is equivalent to one column vector of the control matrix for constraining system eigenvectors. The combination of forced and initial condition responses can improve the identifiability of models that are not identifiable only from forced responses. Explicit formulations and an algorithm are derived to identify model parameters from the combined data of forced and initial condition responses. [ABSTRACT FROM AUTHOR]

A mathematical model for infectious disease epidemics with behaviour change and treatment is formulated and analysed. It is indicated that behaviour modification by the population has a significant impact on the dynamics of the disease. Moreover, an optimal control theory is applied to propose the best possible combination of efforts in controlling a disease. It is shown that it may not be necessary to continuously apply treatment at a full rate to eradicate the disease, if the effort is supported by effective behaviour modification strategies. [ABSTRACT FROM AUTHOR]

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics ( e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions. [ABSTRACT FROM AUTHOR]

Alcohol dependence is among the main healthy risky behavior due to the high relevance of negative health and social effect. We study a mathematical model, given by nonlinear ordinary differential equations, describing the spread of high-risk alcohol consumption behavior within a community of individuals. We describe the peer-influence effects on alcohol addiction by assuming that susceptibles become heavy drinkers through the mechanism of imitation. We show that the model may exhibit the phenomenon of backward bifurcation. This means that alcohol problems may persist in the population even if the basic reproduction number is less than one. Nonlinear stability analysis of equilibria is also provided. [ABSTRACT FROM AUTHOR]

We propose a general framework for the parameter-free identification of a class of dynamical systems. Here, the propagator is approximated in terms of an arbitrary function of the state, in contrast to a polynomial or Galerkin expansion used in traditional approaches. The proposed formulation relies on variational data assimilation using measurement data combined with assumptions on the smoothness of the propagator. This approach is illustrated using a generalized dynamic model describing oscillatory transients from an unstable fixed point to a stable limit cycle and arising in nonlinear stability analysis as an example. This 3-state model comprises an evolution equation for the dominant oscillation and an algebraic manifold for the low- and high-frequency components in an autonomous descriptor system. The proposed optimal model identification technique employs mode amplitudes of the transient vortex shedding in a cylinder wake flow as example measurements. The reconstruction obtained with our technique features distinct and systematic improvements over the well-known mean-field (Landau) model of the Hopf bifurcation. The computational aspect of the identification method is thoroughly validated showing that good reconstructions can also be obtained in the absence of accurate initial approximations. [ABSTRACT FROM AUTHOR]

A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton–Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number ℛ0and the stability of the model in the equilibrium is studied using ℛ0in terms of the model parameters. [ABSTRACT FROM PUBLISHER]

Dielectrophoresis (DEP) is an electrokinetics-based phenomenon that involves the motion of a particle due to the interaction between an applied nonuniform electric field and an induced dipole moment. This technique is very effective in particle manipulation and separation. Earlier studies on control-amenable models to describe the motion of a neutrally buoyant, neutrally charged particle in a chamber with a parallel electrode array have restricted the motion of the particle to one dimension. Here, incorporating the electro-thermal fluid motion as well, we present a 2D-planar DEP model and study the effect of electro-thermal fluid motion on particle trapping. [ABSTRACT FROM AUTHOR]

We describe a set of extensions to the AMPL modeling language to conveniently model mixed-integer optimal control problems for ODE or DAE dynamic processes. These extensions are realized as AMPL user functions and suffixes and do not require intrusive changes to the AMPL language standard or implementation itself. We describe and provide TACO, a Toolkit for AMPL Control Optimization that reads AMPL stub.nl files and detects the structure of the optimal control problem. This toolkit is designed to facilitate the coupling of existing optimal control software packages to AMPL. We discuss requirements, capabilities, and the current implementation. Using the example of the multiple shooting code for optimal control MUSCOD-II, a direct and simultaneous method for DAE-constrained optimal control, we demonstrate how the problem information provided by the TACO toolkit is interfaced to the solver. In addition, we show how the MS-MINTOC algorithm for mixed-integer optimal control can be used to efficiently solve mixed-integer optimal control problems modeled in AMPL. We use the AMPL extensions to model three control problem examples and we discuss how those extensions affect the representation of optimal control problems. Solutions to these problems are obtained by using MUSCOD-II and MS-MINTOC inside the AMPL environment. A collection of further AMPL control models is provided on the web site . MUSCOD-II and MS-MINTOC have been made available on the NEOS Server for Optimization, using the TACO toolkit to enable input of AMPL models. [ABSTRACT FROM AUTHOR]

Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The 'best' subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets. [ABSTRACT FROM AUTHOR]

Based on the input–output representation of one-step state-delay systems, we use the auxiliary model-based recursive least-squares algorithm to estimate the parameters of the systems and study the convergence of the proposed algorithm by using the stochastic process theory. A simulation example is provided. [ABSTRACT FROM PUBLISHER]

This work is aimed to show that various problems from different fields can be modeled more efficiently using multiplicative calculus, in place of Newtonian calculus. Since multiplicative calculus is still in its infancy, some effort is put to explain its basic principles such as exponential arithmetic, multiplicative calculus, and multiplicative differential equations. Examples from finance, actuarial science, economics, and social sciences are presented with solutions using multiplicative calculus concepts. Based on the encouraging results obtained it is recommended that further research into this field be vested to exploit the applicability of multiplicative calculus in different fields as well as the development of multiplicative calculus concepts. [ABSTRACT FROM AUTHOR]

A maximum likelihood parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) models based on the maximum likelihood principle. In this derivation, we use an estimated noise transfer function to filter the input–output data. The simulation results show that the proposed estimation algorithm can effectively estimate the parameters of such class of CARAR systems and give more accurate parameter estimates than the recursive generalized least-squares algorithm. [ABSTRACT FROM PUBLISHER]

We describe Pyomo, an open source software package for modeling and solving mathematical programs in Python. Pyomo can be used to define abstract and concrete problems, create problem instances, and solve these instances with standard open-source and commercial solvers. Pyomo provides a capability that is commonly associated with algebraic modeling languages such as AMPL, AIMMS, and GAMS. In contrast, Pyomo's modeling objects are embedded within a full-featured high-level programming language with a rich set of supporting libraries. Pyomo leverages the capabilities of the Coopr software library, which together with Pyomo is part of IBM's COIN-OR open-source initiative for operations research software. Coopr integrates Python packages for defining optimizers, modeling optimization applications, and managing computational experiments. Numerous examples illustrating advanced scripting applications are provided. [ABSTRACT FROM AUTHOR]