Tse-Wei Wang

Dynamic Time Delay Models for Load Balancing. Part I: Deterministic Models

Parallel computer architectures utilize a set of computational elements (CE) to achieve performance that is not attainable on a single processor, or CE, computer. A common architecture is the cluster of otherwise independent computers communicating through a shared network. To make use of parallel computing resources, problems must be broken down in to smaller units that can be solved individually by each CE while exchanging information with CEs solving other problems.

Linear time delay model for studying load balancing instabilities in parallel computations

A linear time-delay system is proposed to model load balancing in a cluster of computer nodes used for parallel computations. The linear model is analysed for stability in terms of the delays in the transfer of information between nodes and the gains in the load balancing algorithm. This model is compared with an experimental implementation of the algorithm on a parallel computer network.

Least-Square Deconvolution: A Framework for Interpreting Short Tandem Repeat Mixtures*

ABSTRACT: Interpreting mixture short tandem repeat DNA data is often a laborious process, involving trying different genotype combinations mixed at assumed DNA mass proportions, and assessing whether the resultant is supported well by the relative peak‐height information of the mixture sample. If a clear pattern of major–minor alleles is apparent, it is feasible to identify the major alleles of each locus and form a composite genotype profile for the major contributor. When alleles are shared between the two contributors, and/or heterozygous peak imbalance is present, it becomes complex and difficult to deduce the profile of the minor contributor. The manual trial and error procedures performed by an analyst in the attempt to resolve mixture samples have been formalized in the least‐square deconvolution (LSD) framework reported here for two‐person mixtures, with the allele peak height (or area) information as its only input. LSD operates on the peak‐data information of each locus separately, independent of all other loci, and finds the best‐fit DNA mass proportions and calculates error residual for each possible genotype combination. The LSD mathematical result for all loci is then to be reviewed by a DNA analyst, who will apply a set of heuristic interpretation guidelines in an attempt to form a composite DNA profile for each of the two contributors. Both simulated and forensic peak‐height data were used to support this approach. A set of heuristic guidelines is to be used in forming a composite profile for each of the mixture contributors in analyzing the mathematical results of LSD. The heuristic rules involve the checking of consistency of the best‐fit mass proportion ratios for the top‐ranked genotype combination case among all four‐ and three‐allele loci, and involve assessing the degree of fit of the top‐ranked case relative to the fit of the second‐ranked case. A different set of guidelines is used in reviewing and analyzing the LSD mathematical results for two‐allele loci. Resolution of two‐allele loci is performed with less confidence than for four‐ and three‐allele loci. This paper gives a detailed description of the theory of the LSD methodology, discusses its limitations, and the heuristic guidelines in analyzing the LSD mathematical results. A 13‐loci sample case study is included. The use of the interpretation guidelines in forming composite profiles for each of the two contributors is illustrated. Application of LSD in this case produced correct resolutions at all loci. Information on obtaining access to the LSD software is also given in the paper.

The effect of time delays in the stability of load balancing algorithms for parallel computations

Deterministic dynamic nonlinear time-delay systems are developed to model load balancing in a cluster of computer nodes used for parallel computations. The model is shown to be self consistent in that the queue lengths cannot go negative and the total number of tasks in all the queues are conserved (i.e., load balancing can neither create nor lose tasks). Further, it is shown that using the proposed load balancing algorithms, the system is stable. Experimental results are presented and compared with the predicted results from the analytical model. In particular, simulations of the models are compared with an experimental implementation of the load balancing algorithm on a parallel computer network.

Load balancing instabilities due to time delays in parallel computations

Abstract A deterministic dynamic linear time-delay model is presented to model load balancing in a cluster of nodes used for parallel computations. The model is analyzed for stability in terms of the delays in the transfer of information between nodes and the gains in the load balancing algorithm.

Application of Feedback Linearization to Bioreactor Control

This paper presents the procedures and results of Using the input-output linearization technique in the design of a controller for a generic nonlinear continuous bioreactor. Of special interest is the existence of singular points which renders direct application of the input-output linearization theory infeasible. In this paper, we present a modified scheme which allows us to approximately extend the input-output linearization technique across the singular points. The feasibility and effectiveness of the proposed method are demonstrated through computer simulation. This modified method provides a more intuitive insight into the nonlinear system control.

Optimization approach to controlling constrained nonlinear systems

The authors discuss the results of using the input-output geometric transformation method in the development of an efficient controller for nonlinear systems with constraints, while being easy and intuitive to tune and requiring minimal computational effort. While dynamic matrix control (DMC) and quadratic DMC (QDM-C) have been successfully applied in optimal control of industrial processes, they are restricted to linear/near-linear processes. An approach combining the transformation method with DMC for nonlinear systems with constraints that require low computational effort is reported. Using input-output linearization, a pseudolinear model of the system is derived that is valid for the entire region of operation. DMC is designed on this system, ignoring constraints. The DMC-computed input is checked for constraint violation, and a pointwise optimal feasible input is generated if such violation occurs. The performance of the proposed control scheme is demonstrated via simulation of two processes: a continuous stirred tank bioreactor (CSTBR), and an exothermic continuous stirred tank reactor (CSTR).<<ETX>>

Application of a Robust Multivariable Controller to Nonlinear Bacterial Growth Systems

Abstract This paper presents the simulation results of applying the robust multivariate linear quadratic Gaussian/loop transfer recovery (LQG/LTR) control design methodology to a nonlinear bacterial growth system. The growth system is modeled in state space format containing inde-pendent white noise processes in the system equations. The objective is to design a control system that maintain stable bioreactor operation at a chosen set point in the face of external disturbances and internal modeling uncertainty. The nonlinear system is first linearized around a nominal operating set point. Then, a LQG controller is designed for this linearized system. The control design is carried out by using an expert system called CASCADE, developed at the University of Tennessee. Computer simulations, using the original non-linear system equations in generating the “raw” measurements, demonstrate the closed-loop system is robust . This robustness of the control design approach has wide application potential to industrial scale production of biochemicals using bioreactor systems.

Applying Modern Control Techniques to a Nonlinear Bacterial Growth System

A robust multivariable control design methodology is applied to a nonlinear bacterial growth system. The bacterial system is modeled in the time domain with white noises present in both the state dynamics and the measurement equations. The robust design is based on the properties of linear quadratic Gaussian (LQG) and loop transfer recovery (LTR) techniques. The feasibility of this control design approach is evaluated.