A Tractable Class of Maximal Hedging Policies in Multi-Part Manufacturing Systems

The flow control problem in multi-part failure prone manufacturing systems is considered. While computationnaly attractive, the near optimal controllers of Caramanis and Sharifnia, suffer from the drawback that the production capacity set must be approximated via a very restricted set of inscribed hypercubes, namely those for which a componentwise feasibility requirement is satisfied. Also, due to the completely decoupled nature of production along each component, utilization of the restricted capacity set is suboptimal. A class of capacity set incribed hypercube policies called simple maximal hedging (SMH) policies is introduced. In SMH policies production levels along the various components of the capacity set are coupled, the componentwise feasibility requirement is lifted, and there is no underutilization of production capacity if needed. In a p part types manufacturing system, for partwise additive cost functionals, it is shown that performance evaluation of a given SMH policy reduces to the analysis of p decoupled (fictitious) semi-Markovian machines. The machines are Markovianized via first passage-time analysis and a Padé approximants technique. Numerical optimization over the class of SMH policies in a sample manufacturing system indicates that their performance can come close to that of the optimal control.     

H ∞ model reduction for discrete-time Markov jump linear systems with partially known transition probabilities

In this article, the H _∞ model reduction problem for a class of discrete-time Markov jump linear systems (MJLS) with partially known transition probabilities is investigated. The proposed systems are more general, relaxing the traditional assumption in Markov jump systems that all the transition probabilities must be completely known. A reduced-order model is constructed and the LMI-based sufficient conditions of its existence are derived such that the corresponding model error system is internally stochastically stable and has a guaranteed H _∞ performance index. A numerical example is given to illustrate the effectiveness and potential of the developed theoretical results.     

Data validation and missing data reconstruction using self-organizing map for water treatment

Applications in the water treatment domain generally rely on complex sensors located at remote sites. The processing of the corresponding measurements for generating higher-level information such as optimization of coagulation dosing must therefore account for possible sensor failures and imperfect input data. In this paper, self-organizing map (SOM)-based methods are applied to multiparameter data validation and missing data reconstruction in a drinking water treatment. The SOM is a special kind of artificial neural networks that can be used for analysis and visualization of large high-dimensional data sets. It performs both in a nonlinear mapping from a high-dimensional data space to a low-dimensional space aiming to preserve the most important topological and metric relationships of the original data elements and, thus, inherently clusters the data. Combining the SOM results with those obtained by a fuzzy technique that uses marginal adequacy concept to identify the functional states (normal or abnormal), the SOM performances of validation and reconstruction process are tested successfully on the experimental data stemming from a coagulation process involved in drinking water treatment.     

Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty

This paper studies, via a linear matrix inequality approach, the problem of Hinfinity control for discrete time-delay linear systems with parametric uncertainty. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and time delay in the state. First, the problem of robust stability of the underlying system is investigated. Next, we address the problem of robust Hinfinity state feedback control in which both robust stability and a prescribed Hinfinity performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a linear matrix inequality has a symmetric positive definite solution.