Theoretical and algorithmic advances in multi-parametric programming and control

This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system.     

Multicritical phenomena in flow of viscoelastic liquids. 3. Liquid-crystalline polymers. The Akay-Leslie anisotropic liquid. Viscometric functions

The advances in determination of the rheological material functions of liquid-crystalline polymers (LCP) in a wide range of concentrations or temperatures are briefly examined. Special attention is focused on a discussion of the concentration region of the existence of liquid-crystalline order and textures initiated by shear flow. The phenomenological rheological equation for an anisotropic liquid proposed by Akay and Leslie (A-L model) was selected for describing the flow resistance of LCP, and the problem of simple shear flow of a liquid was solved. It was shown that the A-L model can describe all of the basic characteristics of the viscometric functions of LCP, including the phenomenon of negative values of the first normal stress difference for some range of concentrations and shear rates. The available data on the initial viscosity of lyotropic LCP were classified based on the types of cohesion (dimensionality) of the system, characterized by the exponent of the concentration dependence of the viscosity. It was found that each type of cohesion has its own kind of viscometric functions and that the A-L rheological model can reflect their basic characteristics. It was shown that by varying the initial ordering parameter of the A-L model, linear (or almost linear) functions N₁(q) and ₁₂(q) can be described in the region of low shear rates. It was hypothesized that region 1 of the flow curve (Onogi and Asada) inevitably exists in the continuous liquid crystalline phase, which could be outside of the region of measurements accessible to rheometry.See [23] for Communication 2.Institute of Polymer Mechanics. Riga. LV-1047 Latvia. Translated from Mekhanika Kompozitnykh Materialov. No. 6. pp. 821–839. November–December, 1997.     

A Second-Order Semi-Implicit Method for the Inertial Landau-Lifshitz-Gilbert Equation

Electron spins in magnetic materials have preferred orientations collectively and generate the macroscopic magnetization. Its dynamics spans over a wide range of timescales from femtosecond to picosecond, and then to nanosecond. The Landau-Lifshitz-Gilbert (LLG) equation has been widely used in micromagnetics simulations over decades. Recent theoretical and experimental advances have shown that the inertia of magnetization emerges at sub-picosecond timescales and contributes significantly to the ultrafast magnetization dynamics, which cannot be captured intrinsically by the LLG equation. Therefore, as a generalization, the inertial LLG (iLLG) equation is proposed to model the ultrafast magnetization dynamics. Mathematically, the LLG equation is a nonlinear system of parabolic type with (possible) degeneracy. However, the iLLG equation is a nonlinear system of mixed hyperbolic-parabolic type with degeneracy, and exhibits more complicated structures. It behaves as a hyperbolic system at sub-picosecond timescales, while behaves as a parabolic system at larger timescales spanning from picosecond to nanosecond. Such hybrid behaviors impose additional difficulties on designing efficient numerical methods for the iLLG equation. In this work, we propose a second-order semi-implicit scheme to solve the iLLG equation. The second-order temporal derivative of magnetization is approximated by the standard centered difference scheme, and the first-order temporal derivative is approximated by the midpoint scheme involving three time steps. The nonlinear terms are treated semi-implicitly using one-sided interpolation with second-order accuracy. At each time step, the unconditionallyunique solvability of the unsymmetric linear system is proved with detailed discussions on the condition number. Numerically, the second-order accuracy of the proposed method in both time and space is verified. At sub-picosecond timescales, the inertial effect of ferromagnetics is observed in micromagnetics simulations, in consistency with the hyperbolic property of the iLLG model; at nanosecond timescales, the results of the iLLG model are in nice agreements with those of the LLG model, in consistency with the parabolic feature of the iLLG model.     

The relevance of system dynamics to engineering systems design

With the recent advent of new technology using micro computers for the centralised monitoring of information, the scope for totally automatic, real time control of large engineering systems has been advanced. We are entering a period which, retrospectively, may well be seen as the era of control; where for the first time it is both feasible and necessary to design system in terms of the way in which they will be operated, as well as in the traditional terms of their capacity requirements. However, before such comprehensive design can be undertaken compatible advances are required in information usage technology.The purpose of this paper is to demonstrate how the subject of System Dynamics can be used to assist with this problem, though its capacity to model information feedback and hence to model and test alternative system control rules based on the information retrieved. This type of application in the hard system area of engineering provides a strong contrast to the more usual applications of System Dynamics in softer socio-economic systems.The problem described is taken from the coal mining industry and related to the design of large scale underground conveyor belt systems used for the clearance of coal from mines. The demonstration presented, therefore, concerns research in this field, but has considerable scope for application in the general area of large scale bulk handling system.Of particular importance in the results is an indication of the potential savings in physical capacity which can stem from the careful design and implementation of control in such systems.     

A Lévy input fluid queue with input and workload regulation

We consider a controlled queuing model with Lévy input. The controls take place at random times. They involve the current workload and the input processes and may also depend on whether the workload process has reached certain critical values since the last control epoch. We propose a solution strategy for deriving the steady-state distribution of this model which is based on recent advances in the fluctuation theory of spectrally one-sided Lévy process. We provide illustrative examples involving a clearing model, an inventory model, and a model for the TCP protocol.     

On stability in one critical case : PMM vol. 43, no. 6, 1979, pp. 963–969

The problem on the stability of the trivial solution of an autonomous system of ordinary differential equations is solved in the critical case of one zero root, m pairs of pure imaginary roots, and q roots with negative real parts. It is proved that the presence of the zero root, as a rule, leads to instability, which can be detected already from the form of the second-order series expansion of the right hand sides of the equations. In the degenerate case necessary and sufficient stability conditions have been indicated for a model (simplified)system; it is shown that the absence of additional degeneracy the instability of the original system follows from that of the model. Sufficient conditions for the asymptotic stability and instability of the original system have been obtained under the fulfilment of the necessary stability conditions for the model system.     

Optimal scheduling of income tax prepayments under stochastic incomes

This paper presents a stochastic model for the optimal scheduling of income tax prepayments (or advances) when the tax-payer has to choose his prepayments under stochastic incomes and incurs penalties for insufficient prepayments. We present an exact optimal solution and an approximate conditional decision rule. We also provide an error bound on the approximate solution. We then study various taxation laws and show that the error bound on the approximate solution is low when the taxation system tends to promote more regular prepayments.     

Recent advances in methods for numerical solution of O.D.E. initial value problems

This is a review paper which describes recent advances in numerical methods and computer codes for solving initial value problems of ordinary differential equations. Particular emphasis is placed upon stiff systems.     

The design of colliery information and control systems

The paper is concerned with describing an investigation of information usage in the control of colliery operations. The premise of the work is that to make the most of new information retrieval technology currently being installed in collieries research in needed to provide compatible advances in methods of information usage. The approach adopted was to construct a continuous simulation model using system dynamics capable of providing a laboratory assessment of alternative managerial control policies based on alternative sources and levels of aggregation of information.The model developed represents a typical colliery situation composed of three working coal-faces and incorporating planning, production, development and manpower sectors. The face sectors transform coal reserves to mined coal output, under manpower constraints and geological shocks, and these are all interlinked by means of allocation policies for manpower and machine shifts.A range of policies for the exercise of control through these allocations are considered subject to a range of shocks. It is concluded that, although there are difficulties in designing single policies which are universally best, there are clear advantages associated with fully integrated colliery policies based on information inputs from all aspects of the operations.     

Data-based prediction and causality inference of nonlinear dynamics

Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which cannot only recover nonlinear behaviors but also predict future dynamics. Due to the advances of modern technology, big data becomes increasingly accessible and consequently the problem of reconstructing systems from measured data or time series plays a central role in many scientic disciplines. In recent decades, nonlinear methods rooted in state space reconstruction have been developed, and they do not assume any model equations but can recover the dynamics purely from the measured time series data. In this review, the development of state space reconstruction techniques will be introduced and the recent advances in systems prediction and causality inference using state space reconstruction will be presented. Particularly, the cutting-edge method to deal with short-term time series data will be focused on. Finally, the advantages as well as the remaining problems in this field are discussed.     

N.E.W.S.: A model for the evaluation of non-life insurance companies

This paper describes a model which can be used by the Dutch insurance supervisor to determine the priority a non-life insurer should have for further examination. This model combines a traditional statistical technique (an ordered logit model) with artificial intelligence techniques (a neural network and an expert system). The output of the model consists of the priority for further examination (high, medium, or low), and a report which summarizes the main findings of the model. The model was able to adequately classify 93% of the companies in a 1993 data set.     

Modelling length of stay and patient flows: methodological case studies from the UK neonatal care services

The number of babies needing neonatal care is increasing mainly because of technological and therapeutic advances. These advances have implied a decreasing neonatal mortality rate for low birth weight infants and also a falling incidence of preterm stillbirth. Given the structural changes in the National Health Service in England, coupled with recession and capacity constraints, the neonatal system is facing some serious challenges, such as nurse shortages and the lack of cots, which could inevitably impact neonates’ length of stay, and the performance of the system as a whole. These constraints have forced neonatal managers to better understand their organisation and operations in order to optimise their systems. As a result, we have developed three unique methodologies based on length of stay modelling, physical patient pathways, and system dynamics modelling. This paper evaluates these techniques applied to neonatal services in London and showcases their usefulness and implications in practice, particularly focusing on patient flow to determine major drivers of the system, which could reduce inefficiencies, improve patient experience, and reduce cost.     

Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model

Infection with HIV-1, degrading the human immune system and recent advances of drug therapy to arrest HIV-1 infection, has generated considerable research interest in the area. Bonhoeffer et al. (1997) [1], introduced a population model representing long term dynamics of HIV infection in response to available drug therapies. We consider a similar type of approximate model incorporating time delay in the process of infection on the healthy T cells which, in turn, implies inclusion of a similar delay in the process of viral replication. The model is studied both analytically and numerically. We also include a similar delay in the killing rate of infected CD4⁺ T cells by Cytotoxic T-Lymphocyte (CTL) and in the stimulation of CTL and analyse two resulting models numerically.The models with no time delay present have two equilibria: one where there is no infection and a non-trivial equilibrium where the infection can persist. If there is no time delay then the non-trivial equilibrium is locally asymptotically stable. Both our analytical results (for the first model) and our numerical results (for all three models) indicate that introduction of a time delay can destabilize the non-trivial equilibrium. The numerical results indicate that such destabilization occurs at realistic time delays and that there is a threshold time delay beneath which the equilibrium with infection present is locally asymptotically stable and above which this equilibrium is unstable and exhibits oscillatory solutions of increasing amplitude.     

The Role of Queueing Network Models in Performance Evaluation of Manufacturing Systems

Models of manufacturing systems are used for performance evaluation during the design stage, allowing system designers to fine tune their system before proceeding to the implementation phase. In recent years, several queueing network model implementations have been used in the performance evaluation of manufacturing systems. Although these implementations incorporate many of the recent advances in queueing theory, we find significant departures from simulation results when applied to realistic manufacturing systems, even for those within the stated domain of assumptions and limitations of these implementations. While utilization estimates are usually quite accurate, the flowtime and work in process results are not as robust.     

OR and energy: Problems of modelling

Attention is focused on three problem areas in energy modelling: (1) identifying the essential elements of the system, (2) coping with multiple criteria, (3) incorporating learning in the system. These aspects are illustrated through examples in current energy systems research, involving the oil market, power systems planning, and the role of nuclear energy.In modelling the word oil market, too heavy emphasis is placed on economic forces, but practically non on the political forces. However, certain economics-oriented studies indicate that financial gains of OPEC may actually be intensitive to the oil pricing policy followed. If that is indeed the case, the significant (political) elements and their motives have to be captured in the model in order to arrive at consistent results.Modelling the different objectives in power systems planning is an area where advances are urgently needed. A method is proposed, where decision alternatives are generated a posteriori, in contrast to recent approaches involving a priori articulation of preferences, or interactive methods. A multicriterion dynamic linear programming model and a fast algorithm are used in generating efficient solutions, which are then grouped, based on the clustering in objective values.The problem associated with changing system objectives is discussed and the nuclear programme is given as an example of how the system objectives move from costs to perceived risks. In line with the real system that ‘learns’ from its experience, we need models that change their objective functions as a result of their own outputs at prior times.     

A New Model for Nonlinear Wind Waves. Part 2. Theoretical Model

A first-order theory for the development of a wind-driven wave field is proposed. This takes advantage of the physical interpretation presented by Lake and Yuen (1978) that a nonlinear wind-wave system can be completely characterized, to first approximation, by a single nonlinear wave train with carrier frequency coinciding with the local dominant frequency. The result is the nonlinear Schrodinger equation for the wave envelope, supplemented by an equation describing the change of dominant-wave frequency (or wavenumber) with fetch (or duration). The latter equation is a consequence of a form-drag model proposed by Deardorff (1967) for the input of wind energy into the dominant wave. The extension of the model to a random wave field is briefly discussed.     

Dynamic Equilibrium of a Coupled ODE-PDE Problem for Surface Nanobubbles

We consider a mathematical model for surface nanobubbles arising from hydrogen electrolysis in polymer electrolyte membrane (PEM) electrolyzers. Experimental advances in recent years indicated longer lifetimes of surface nanobubbles than may be explained by classical theories. Contrary to [5], we state a full model of an evolving single surface nanobubble yielding a coupled system consisting of a partial differential equation (PDE) for the hydrogen concentration in water and an ordinary differential equation (ODE) for the radius evolution. In the special case of dynamic equilibrium conditions, we prove the well-posedness of this steady state problem by a fixed-point strategy, assuming an acute-angled contact angle, and that the corresponding algorithm allows for its numerical simulation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards an Operational Model for Prevention and Treatment of Asthma Attacks

Asthma is one of the major chronic diseases in many countries. At present there is no cure for asthma, but medical advances can help to reduce the chances of attacks of the condition. Efficient care for asthma involves complexity, uncertainty, variability and the use of scarce resources, and these are the same conditions that indicate a possible use for the modelling approach of operational research. This paper is concerned with a pilot model that was developed through joint work by medical professionals and operational researchers. The development of the model is explained and illustrative results indicate the potential value of the modelling approach for the care of asthma in the community.     

基于最优估计的数据融合理论

本文提出了一种最优加权的数据融合方法，分析了最优权值的分配原则；给出了多源信息统一的线性融合模型，使其表示不受数据类型和融合系统结构的限制，并指出在噪声协方差阵正定的前提下，线性最小方差估计融合和加权最小二乘估计融合是等价的；介绍了数据融合中的Bayes极大后验估计融合方法，给出了利用极大后验法进行传感器数据融合的一般表示公式；最后以两传感器数据融合为例，证明了利用Bayes极大后验估计进行两传感器数据融合所得到的融合状态的精度比相同条件下极大似然估计得到的精度要高，同时它们均优于任一单传感器局部估计精度。