General Problem Formulation Research Articles

Modified Waterfilling Algorithms for MIMO Spatial Multiplexing with Asymmetric CSI

This paper studies the transmit power-multiplexing tradeoff in MIMO systems when two users with different priorities are to be accommodated simultaneously. In the general problem formulation, a minimum information rate must be guaranteed for a prioritized user whose channel state information (CSI) is known, while the data rate for the other user with completely unknown CSI is "best-effort." The drawbacks of the classic spatial water-filling algorithm are discussed, and two modified water-filling algorithms are proposed that either balance the required transmit power with the number of spatial dimensions available for each user, or minimize the number of transmit spatial dimensions allocated for the prioritized user. We then specialize to applications in the MIMO wiretap channel, the MIMO multiuser downlink channel, and spectrum underlay in MIMO cognitive radio networks, where existing methods are not applicable under the asymmetric CSI scenario. Numerical results verify the performance advantages of the proposed transmission schemes for each of these case studies.

Selection of Self-Optimizing Controlled Variables for Dynamic Processes

In literature, self-optimizing control (SOC) method has been shown to be useful to select controlled variables (CVs) among available measurements for steady-state processes. This work introduces the concept of ‘dynamic SOC' (dSOC) to select CVs for processes, which do not reach steady state (e.g. batch processes) or for which the operational cost during transient response must be accounted for. The general problem formulation is presented and shown to be equivalent to an optimal control problem. An exact local method for quick prescreening of CV candidates is presented, where perturbation control approach is proposed for the solution of the resulting optimization problem. The proposed dSOC method is applied to a linear process to illustrate the theoretical results.

Framework for Link-Level Energy Efficiency Optimization with Informed Transmitter

The dramatic increase of network infrastructure comes at the cost of rapidly increasing energy consumption, which makes optimization of energy efficiency (EE) an important topic. Since EE is often modeled as the ratio of rate to power, we present a mathematical framework called fractional programming that provides insight into this class of optimization problems, as well as algorithms for computing the solution. The main idea is that the objective function is transformed to a weighted sum of rate and power. A generic problem formulation for systems dissipating transmit-independent circuit power in addition to transmit-dependent power is presented. We show that a broad class of EE maximization problems can be solved efficiently, provided the rate is a concave function of the transmit power. We elaborate examples of various system models including time-varying parallel channels. Rate functions with an arbitrary discrete modulation scheme are also treated. The examples considered lead to water-filling solutions, but these are different from the dual problems of power minimization under rate constraints and rate maximization under power constraints, respectively, because the constraints need not be active. We also demonstrate that if the solution to a rate maximization problem is known, it can be utilized to reduce the EE problem into a one-dimensional convex problem.

Agent-Based System Design for Service Process Scheduling: Challenges, Approaches and Opportunities

Compared with traditional manufacturing scheduling, service process scheduling poses additional challenges attributable to the significant customer involvement in service processes. In services, there are typically no inventoried products, which make the service provider's capacity more sensitive to dynamic changes. Service process scheduling objectives are also more complicated due to the consideration of customer preferences, customer waiting costs and human resource costs. After describing the Unified Services Theory and analysing its scheduling implications, this paper reviews the research literature on service process scheduling system design with a particular emphasis on agent-based approaches. Major issues in agent-based service process scheduling systems design are discussed and research opportunities are identified. The survey of the literature reveals that despite of many domain-specific designs in agent-based service process scheduling, there is a lack of general problem formulations, classifications, solution frameworks, and test beds. Constructing these general models for service process scheduling system design will facilitate the collaboration of researchers in this area and guide the effective development of integrated service process scheduling systems.

Multi-Objective Traffic Engineering for Future Networks

An important goal towards the design of Future Networks is to achieve the best ratio of performance to energy consumption and at the same time assure manageability. This paper presents a general problem formulation for Energy-Aware Traffic Engineering and proposes a distributed, heuristic Energy-Aware Traffic Engineering scheme (ETE) that provides load balancing and energy-awareness in accordance with the operator's needs. Simulation results of ETE compared to the optimal network performance confirm the capability of ETE to meeting the needs of Future Networks.

Longitudinal force distribution using quadratically constrained linear programming

In this paper, a new method is presented for the optimisation of force distribution for combined traction/braking and cornering. In order to provide a general, simple and flexible problem formulation, the optimisation is addressed as a quadratically constrained linear programming (QCLP) problem. Apart from fast numerical solutions, different driveline configurations can be included in the QCLP problem in a very straightforward fashion. The optimisation of the distribution of the individual wheel forces using the quasi-steady-state assumption is known to be useful for the study of the influence of particular driveline configurations on the combined lateral and longitudinal grip envelope of a particular vehicle–driveline configuration. The addition of the QCLP problem formulation makes another powerful tool available to the vehicle dynamics analyst to perform such studies.

Flexible servers in tandem lines with setup costs

We study the dynamic assignment of flexible servers to stations in the presence of setup costs that are incurred when servers move between stations. The goal is to maximize the long-run average profit. We provide a general problem formulation and some structural results, and then concentrate on tandem lines with two stations, two servers, and a finite buffer between the stations. We investigate how the optimal server assignment policy for such systems depends on the magnitude of the setup costs, as well as on the homogeneity of servers and tasks. More specifically, for systems with either homogeneous servers or homogeneous tasks, small buffer sizes, and constant setup cost, we prove the optimality of "multiple threshold" policies (where servers' movement between stations depends on both the number of jobs in the system and the locations of the servers) and determine the values of the thresholds. For systems with heterogeneous servers and tasks, small buffers, and constant setup cost, we provide results that partially characterize the optimal server assignment policy. Finally, for systems with larger buffer sizes and various service rate and setup cost configurations, we present structural results for the optimal policy and provide numerical results that strongly support the optimality of multiple threshold policies.

Characterizing the retrieval of cloud properties from optical remote sensing

This paper presents a new approach to the formal characterization of the optical retrieval of cloud optical thickness and effective droplet radius based on a nonlinear methodology that is derived from a general stochastic inverse problem formulation similar to standard Bayesian estimation theory. The methodology includes efficient use of the precomputed radiative transfer model simulations which are already available in standard retrieval algorithms. Another important property of the methodology is that it does not require performing the retrieval with actual measurements in order to characterize the retrieval results. One utility of this analysis is the quantification of information content in the standard retrieval problem, and the increase of information through adding channels (radiances at different wavelengths) to the inversion. This was demonstrated for the five‐wavelength retrieval using airborne hyperspectral shortwave irradiance measurements. The ability of the method to evaluate the impact of observation and radiative transfer model uncertainties on the retrieved cloud properties is also demonstrated. Further benefits from this study will be in its application to the cloud retrieval algorithms to be developed for future space‐ and airborne instruments. The present study puts forth the framework necessary to quantify that increase in information and to optimize new retrieval algorithms that efficiently accommodate the enhanced measurement space.

Active base isolation of buildings subjected to seismic excitations

AbstractStructural control technology has been widely accepted as an effective means for the protection of structures against seismic hazards. Passive base isolation is one of the structural control techniques to enhance the performance of structures subjected to severe earthquake excitations. Isolation bearings employed at the base of a structure naturally increases its flexibility, but concurrently results in large base displacements. The combination of base isolation with active control, i.e. active base isolation, creates the possibility of achieving a balanced level of control performance in reductions of either floor accelerations or base displacements. Many theoretical papers have been written by researchers regarding active base isolation. A few experiments have been performed to verify these theories; however, challenges in appropriately scaling the structural system and modeling the complex nature of control–structure interaction (CSI) have limited the applicability of these results. This paper presents the development and experimental verification of an active base isolation system for a seismically excited building. First, the general problem formulation and control design procedure are provided. Subsequently, the experimental setup is described; unique features include low‐friction pendular bearings and custom‐manufactured low‐force hydraulic actuators. A new system identification procedure that can effectively capture the phenomena of CSI is then presented and used to realize control‐oriented models of the system. H 2/LQG control strategies employing different performance objectives are developed and experimentally evaluated on a six degree‐of‐freedom shake table in the Smart Structures Technology Laboratory at the University of Illinois at Urbana‐Champaign. The proposed control strategies are shown to perform effectively for a wide range of seismic excitations. Copyright © 2010 John Wiley & Sons, Ltd.

Coordinated Motion Design on Lie Groups

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3) , SE(2) and SE(3) .

Discriminating between rival biochemical network models: three approaches to optimal experiment design

BackgroundThe success of molecular systems biology hinges on the ability to use computational models to design predictive experiments, and ultimately unravel underlying biological mechanisms. A problem commonly encountered in the computational modelling of biological networks is that alternative, structurally different models of similar complexity fit a set of experimental data equally well. In this case, more than one molecular mechanism can explain available data. In order to rule out the incorrect mechanisms, one needs to invalidate incorrect models. At this point, new experiments maximizing the difference between the measured values of alternative models should be proposed and conducted. Such experiments should be optimally designed to produce data that are most likely to invalidate incorrect model structures.ResultsIn this paper we develop methodologies for the optimal design of experiments with the aim of discriminating between different mathematical models of the same biological system. The first approach determines the 'best' initial condition that maximizes the L2 (energy) distance between the outputs of the rival models. In the second approach, we maximize the L2-distance of the outputs by designing the optimal external stimulus (input) profile of unit L2-norm. Our third method uses optimized structural changes (corresponding, for example, to parameter value changes reflecting gene knock-outs) to achieve the same goal. The numerical implementation of each method is considered in an example, signal processing in starving Dictyostelium amœbæ.ConclusionsModel-based design of experiments improves both the reliability and the efficiency of biochemical network model discrimination. This opens the way to model invalidation, which can be used to perfect our understanding of biochemical networks. Our general problem formulation together with the three proposed experiment design methods give the practitioner new tools for a systems biology approach to experiment design.

Variational problems on the contact of heterogeneous phases

The variational formulation of general problems of capillary surface equilibrium (problems on a drop on a solid surface, drop on the surface of a drop of another liquid, partly faceted capillary surface) is considered. For the problem of a partly faceted capillary surface, the Legendre transformation between the equilibrium form and surface energy density is used.

The elucidation of metabolic pathways and their improvements using stable optimization of large-scale kinetic models of cellular systems

Metabolic engineering of cellular systems to maximize reaction fluxes or metabolite concentrations still presents a significant challenge by encountering unpredictable instabilities that can be caused by simultaneous or consecutive enhancements of many reaction steps. It can therefore be important to select carefully small subsets of key enzymes for their subsequent stable modification compatible with cell physiology. To address this important problem, we introduce a general mixed integer non-linear problem (MINLP) formulation to compute automatically which enzyme levels should be modulated and which enzyme regulatory structures should be altered to achieve the given optimization goal using non-linear kinetic models of relevant cellular systems. The developed MINLP formulation directly employs a stability analysis constraint and also includes non-linear biophysical constraints to describe homeostasis conditions for metabolite concentrations and protein machinery without any preliminary model simplification (e.g. linlog kinetics approximation). The framework is demonstrated on a well-established large-scale kinetic model of the Escherichia coli central metabolism used for the optimization of the glucose uptake through the phosphotransferase transport system (PTS) and serine biosynthesis. Computational results show that substantial stable improvements can be predicted by manipulating only small subsets of enzyme levels and regulatory structures. This means that while more efforts can be required to elucidate larger stable optimal enzyme level/regulation choices, no further significant increase in the optimized fluxes can be obtained and, therefore, such choices may not be worth the effort due to the potential loss of stability properties. The source for instability through saddle-node and Hopf bifurcations is identified, and all results are contrasted with predictions from metabolic control analysis.

A general real-time formulation for multi-rate mass transfer problems

Abstract. Many flow and transport phenomena, ranging from delayed storage in pumping tests to tailing in river or aquifer tracer breakthrough curves or slow kinetics in reactive transport, display non-equilibrium (NE) behavior. These phenomena are usually modeled by non-local in time formulations, such as multi-porosity, multiple processes non equilibrium, continuous time random walk, memory functions, integro-differential equations, fractional derivatives or multi-rate mass transfer (MRMT), among others. We present a MRMT formulation that can be used to represent all these models of non equilibrium. The formulation can be extended to non-linear phenomena. Here, we develop an algorithm for linear mass transfer, which is accurate, computationally inexpensive and easy to implement in existing groundwater or river flow and transport codes. We illustrate this approach by application to published data involving NE groundwater flow and solute transport in rivers and aquifers.

Analysis of Multiple Orientations

Estimation of local orientations in multivariate signals is an important problem in image processing and computer vision. This general problem formulation also covers optical flow estimation, which can be regarded as orientation estimation in space-time-volumes. Modelling a signal using only a single orientation, however, is often too restrictive, since occlusions and transparencies occur frequently, thus necessitating the modelling and analysis of multiple orientations. We, therefore, develop a unifying mathematical model for multiple orientations: Beyond describing an arbitrary number of orientations in scalar- and vector-valued image data such as color image sequences, it allows the unified treatment of additively and occludingly superimposed oriented structures as well as of combinations of these. Based on this model, we describe estimation schemes for an arbitrary number of additively or occludingly superimposed orientations in images. We confirm the performance of our framework on both synthetic and real image data.

Breakthrough of attenuating contaminant plumes in pumping wells: Analytical model and implications for integral pumping tests

Monitoring of contaminant plumes and predicting their future fate are essential for effective management of groundwater contaminants. Solute breakthrough curves from operating pumping wells can provide information on the water quality in relatively large aquifer regions, which may be unavailable to instrumentation and direct measurement for practical and/or economical reasons. Relations between spatially varying aquifer concentrations C0(x, y) initially surrounding a well and temporally varying concentrations of subsequently extracted well water, Cp(t), then need to be quantified. However, limited applicability of analytical expressions and numerical inaccuracies related to solving transport equations for converging flow fields hamper such quantifications even in homogeneous aquifers. We use a stream‐tube approach and provide a general problem formulation that accounts for first‐order degradation and linear, instantaneous, sorption/retardation in heterogeneous aquifers. An analytical expression is obtained for homogeneous aquifer conditions (in the well vicinity), relating any given initial C0(x, y) function and the subsequent contaminant breakthrough Cp(t) in the well. Results for wide plumes subject to first‐order degradation show that concentrations at the extraction well will increase as a function of pumping time. This increase is despite the fact that late‐time data reflect longer transport paths (to the well), along which mass is removed through degradation. We also derive unique solutions for the inverse problem, in particular considering how the average contaminant concentration Cav (averaged along a control plane through the well within its capture zone, perpendicular to the mean groundwater flow direction) depends on the measurable Cp(t). The solutions demonstrate that the longer the pumping time, the more sensitive the solutions for Cav become to degradation rate constants, which if needed can be determined in situ using multiple control planes.

A control-volume finite-element method for three-dimensional multiphase basin modeling

In this paper we describe a 3D control-volume finite-element method to solve numerically the coupled partial differential equations (PDEs) governing geological processes involved in the evolution of sedimentary basins. These processes include sediment deposition and deformation, hydrocarbon generation, multiphase fluid flow, and heat transfer in deforming porous media. These integrated processes possess a wide range of time-scales, indicating the need for implicit methods. In addition, sedimentary basins are geometrically complex environments, requiring unstructured tetrahedral meshes to adequately represent the problem realistically without the need for an excessive number of mesh elements. Here, we also present a general formulation for problems involving back-oil, thermal, or compositional models using overall component mass concentrations, and an arbitrary Lagrangian–Eulerian (ALE) formulation to deal with salt motion conservatively. The Newton method is used to solve the sparse Jacobian systems resulting from the linearization of the coupled non-linear PDEs for multiphase flow and energy transfer. These systems are solved with the generalized minimal residual method (GMRES) method with an incomplete lower–upper (ILU) preconditioner for faster inner iteration convergence rates. We applied this model to a sedimentary basin and we describe the results for this basin.

Pareto optimization of analog circuits considering variability

AbstractThe trade‐off between competing design objectives is often decided at the beginning of the analog sizing process by assigning weights to the design objectives. Architectural design, however, requires the knowledge of all possible optimal trade‐offs of a building block. Methods for Pareto optimization provide the set of all optimal trade‐offs, the so‐called Pareto front. The next generation of analog Pareto optimization tools additionally has to consider the manufacturing variations. This paper describes an approach to this challenging problem. First, analog Pareto optimization will be developed as a set of specific nonlinear programming problems that provide a discretization of the Pareto front of competing performance features. Second, a general problem formulation to consider manufacturing variations and operating ranges of circuit parameters in analog Pareto optimization will be presented. Third, an efficient solution approach to the resulting tolerance Pareto optimization problem will be described. It is based on a combination of nominal Pareto optimization and realistic worst‐case analysis on discrete Pareto points. It provides high efficiency at acceptable loss in accuracy. Copyright © 2008 John Wiley & Sons, Ltd.

Water reservoir control under economic, social and environmental constraints

Although great progress has been made in the last 40 years, efficient operation of water reservoir systems still remains a very active research area. The combination of multiple water uses, non-linearities in the model and in the objectives, strong uncertainties in inputs and high dimensional state make the problem challenging and intriguing. The purpose of this paper is to review, in a strict Control Theory perspective, recent and significant advances in designing management policies for water reservoir networks, under economic, social and environmental constraints. A general and thorough problem formulation is provided, along with a description of traditional solution techniques, their limitations and possible alternative approaches.

A general finite element formulation for fractional variational problems

This paper presents a general finite element formulation for a class of Fractional Variational Problems (FVPs). The fractional derivative is defined in the Riemann–Liouville sense. For FVPs the Euler–Lagrange and the transversality conditions are developed. In the Fractional Finite Element Formulation (FFEF) presented here, the domain of the equations is divided into several elements, and the functional is approximated in terms of nodal variables. Minimization of this functional leads to a set of algebraic equations which are solved using a numerical scheme. Three examples are considered to show the performance of the algorithm. Results show that as the number of discretization is increased, the numerical solutions approach the analytical solutions, and as the order of the derivative approaches an integer value, the solution for the integer order system is recovered. For unspecified boundary conditions, the numerical solutions satisfy the transversality conditions. This indicates that for the class of problems considered, the numerical solutions can be obtained directly from the functional, and there is no need to solve the fractional Euler–Lagrange equations. Thus, the formulation extends the traditional finite element approach to FVPs.