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With commercial supercomputers and homogeneous clusters of PCs, static load balancing is accomplished by assigning equal tasks to each processor. With heterogeneous clusters, the system designers have the option of quickly adding newer hardware that is more powerful than the existing hardware. When this is done, the assignment of equal tasks to each processor results in suboptimal performance. This research addresses techniques by which the size of the task assigned to a processor is a suitable match. Thus, the more powerful processors do more work and the less powerful processors perform less work. We find that when the range of processing power is narrow, some benefit can be achieved with asymmetric load balancing. When the range of processing power is broad, dramatic improvements in performance are realized — our experiments have shown up to 92% improvement when asymmetrically load balancing a modified version of the computationally intensive NAS Parallel Benchmarks’ LU application on a heterogeneous cluster of Linux-powered PCs.

During the past few years there has developed a widespread interest in Horowitz’s Quantitative Feedback Theory (QFT) because of its potential for solving complex real-world control problems. In particular, QFT focuses on achieving the desired system performance despite plant models with parameter uncertainly and additive disturbances. The design of a QFT robust controller requires the formulation of quantitative factors representing acceptable input-output models, a set of plant models due to parameter uncertainity and graphical composition. To accomplished this task requires considerable numerical and symbolic manipulation and therefore implies that an extensive educational environment be provided. The intent of this paper is to present such an educational environment in which extensive student design projects can be accomplished. Both the multi-input single-output (MISO) and the multiple-input multiple-output (MIMO) models are depicted in the classroom along with discussion of various CAD packages. The QFT MIMO controller development is approached by converting the MIMO model into a number of MISO models. Both the continuous and discrete QFT design procedures are elements of the educational program. Discussion of appropriate prerequisites for the various models is included in the paper as an integral element of a control engineer’s education. The major educational emphasis is on the development of a student’s ability to apply the unified QFT method. Various aspects of the QFT educational CAD capabilities exist under various computer operating system environments.

The estimation of states in noisy dynamical systems is a problem whose solution is of significant importance in various scientific disciplines. Algorithms for filtering, smoothing and prediction estimates of lumped parameter system states have been derived by Kalman and Bucy [5], Bryson and Frazier [l], Cox [3], and Detchmendy and Sridhar [4]. The techniques utilized for generating these algorithms include orthogonal projection theory [5], maximum likelihood estimate [3], and the classical least squares error criterion combined with an invariant embedding technique [4]. The class of problems considered in these investigations were dynamical systems described by ordinary differential equations with additive disturbances. Also, statistical assumptions concerning the characteristics of the input disturbances were an integral part of the algorithm derivations in most cases. Many dynamical systems are distributed in space as well as time and are defined as distributed parameter systems. A general class of such systems are those defined by partial differential equations. Estimation algorithms for partial differential systems have been generated by Tzafestas and Nightingale [ll], Thau [lo], and Seinfeld [9]. Seinfeld [9] utilized the least squares estimation criterion and an approximation to the minimum value of the error criterion to generate an approximation to the optimal estimate for nonlinear partial differential equation systems.