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Note: The papers on this website may differ from the published versions, both in format and in content.

1. C. T. Abdallah, F. Amato, M. Ariola, P. Dorato and V. Koltchinski, "Finite-Time Control of Uncertain Linear Systems Using Statistical Learning Methods", Accepted, Linear Algebra and its Applications, fourth special issue on Linear Systems and Control, Vol. 11, No. 26, pp. 351-352, 2002. [pdf]    [ps]
   
   Abstract: In this paper we show how some difficult linear algebra problems can be “approximately” solved using statistical learning methods. We illustrate our results by considering the state and output feedback, finite-time robust stabilization problems for linear systems subject to time-varying norm-bounded uncertainties and to unknown disturbances. In the state feedback case, we have obtained in an earlier paper, a sufficient condition for finite-time stabilization in the presence of time-varying disturbances; such condition requires the solution of a Linear Matrix Inequality (LMI) feasibility problem, which is by now a standard application of linear algebraic methods. In the output feedback case, however, we end up with a Bilinear Matrix Inequality (BMI) problem which we attack by resorting to a statistical approach.






2. C. T. Abdallah, M. Ariola, and V. Koltchinski, "Statistical-Learning Control of Multiple-Delay Systems with Applications to ATM Networks", Kybernetica, Special issue on Time-Delay Systems, Vol. 37, No. 3, pp. 355-365, 2001. [pdf]    [ps]
   
   Abstract: Congestion control in the ABR class of ATM network presents interesting challenges due to the presence of multiple uncertain delays. Recently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to challenging control problems. In this paper, using some recent results by the authors, an efficient statistical algorithm is used . Used to design a robust, fixedstructure, controller for a high-speed communication network with multiple uncertain propagation delays.






3. V. Koltchinski, C. T. Abdallah, M. Ariola, and P. Dorato, "Statistical Learning Control of Uncertain Systems: Theory and Algorithms", Applied Mathematics and Computation, Vol. 120/ 1-3 , pp.31-43, April 2001 . [pdf]
   
   Abstract: It has recently become clear that many control problems are too difficult to admit analytic solutions. New results have also emerged to show that the computational complexity of some "solved" control problems is prohibitive. Many of these control problems can be reduced to decidability problems or to optimization questions. Even though such questions may be too difficult to answer analytically, or may not be an­swered exactly given a reasonable amount of computational resources, researchers have shown that we can "approximately" answer these questions "most of the time", and have "high confidence" in the correctness of the answers. .






4. J.A Rohwer, and C. T. Abdallah, "Support Vector Machines for Direction of Arrival Estimation", Accepted, Applied Computational Electromagnetics Society (ACES) Special Issue on Neural Network Applications in Electromagnetics. [pdf]    [ps]
   
   Abstract: Machine learning research has largely been devoted to binary and multiclass problems relating to data mining, text categorization, and pattern/facial recognition. Recently, popular machine learning algorithms have successfully been applied to wireless communication problems, notably spread spectrum receiver design, channel equalization, and adaptive beamforming with direction of arrival estimation (DOA). Various neural network algorithms have been widely applied to these three communication topics. New advanced learning techniques, such as support vector machine (SVM) have been applied, in the binary case, to receiver design and channel equalization. This paper presents a multiclass implementation of SVMs for DOA estimation and adaptive beamforming, an important component of code division multiple access (CDMA) communication systems.






5. V. Blondel, C. T. Abdallah and G.L. Heileman, "Complexity Issues and Decision Methods in Control Systems", Journal of Symbolic Computation, 1995. [pdf]
   
   Abstract: This paper addresses the computational difficulty associated with specific control problems. Using notions from Decision and Computational Complexity theories, it emphasizes the fact that some control problems are undecidable, and that some are decidable but computationally costly.