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In this paper, we consider advanced image processing and artificial intelligence based techniques for design of fiber optic statistical mode sensors. Output from an optical fiber exhibits a speckle pattern when projected on a flat surface, and intensity, size, and location of these speckles do change with external effects like pressure, temperature, vibration, etc. Statistical mode sensors reported in the literature use global image differencing or global correlation like approaches for sensor design. Namely, lots of localized information in the image is not taken into account, instead global difference and/or correlation are used for sensor construction. We propose the use of localized information with image processing techniques; generate more features, and analysis of these via artificial intelligence based methods. In this way, we can capture more information from the speckle pattern distribution, and hence design a better sensor.

In this note, we study the conservatism of structured singular value computation by a randomized algorithm. It is proved that, if the maximization problem µ (M) = max ρ(MΔ) is solved by generating polynomial number of random Δ samples and then taking the maximum of the function at these sample points, for any fixed lower bound on the confidence level, conservatism of the resulting estimate grows faster than any polynomial function of the logarithm of the matrix size. This result holds for purely complex, mixed, and purely real cases with no repeated blocks. However, it is shown to be not true if the number of samples exceeds some exponential function for the purely complex version of the problem. Although the estimate obtained by polynomial number of samples can be used to find an exact robustness margin with a high confidence level, for all except for a small relative volume of the uncertainty set, it has high conservatism for the worst-case robustness analysis, no matter how small the confidence level lower bound may be. The results of this note imply that conservatism will be large for certain classes of matrices. However, this does not eliminate the possibility of existence of other classes of matrices for which the conservatism is small. [ABSTRACT FROM AUTHOR]

Presents a study on the complexity of computation and related problems in multidimensional systems. Details on study conducted; Indication of findings; Discussion on results.

In this paper, it is shown that the problem of checking robust stability of linear parameter varying (LPV) systems is NP-hard, and therefore it is rather unlikely to find polynomial time solution procedures for this problem. In the frequency domain structured uncertainty case, it is known that the robust stability problem is NP-hard [19,20,15,14,2], but allowing the uncertain blocks to be time varying gives a computationally tractable problem [17,16], which can be solved by convex optimization techniques. In the parameteric uncertainty case, NP-hardness of the robust stability problem has been shown in [15,14]. The results of this paper show that, allowing the uncertain parameters to be time varying, does not give a computationally simplier problem, i.e. it remains .NP-hard, and hence it is rather unlikely to find computationally tractable solution procedures for this problem. On the other hand, as far as the existence of an algorithm is considered, there is still no known (non-polynomial time) algorithm for the robust stability problem of linear parameter varying systems [13], and the well known Tarski's theorem [18] does not provide a solution procedure [12]. Recently, there has been some developments in the direction of constructing non-polynomial time algorithms for a related problem, called the joint spectral radius (JSR) computation problem [13]. We also comment on the use of these results for developing a non-polynomial time algorithm for testing robust stability of linear parameter varying systems.

Abstract: In this paper the following stability problems concerning linear delay-differential systems are shown to beN P-hard: (i) asymptotic stability independent of delay, and (ii) robust asymptotic stability, when each delay is known to lie in an interval. The main results are based on theN P-hardness of complex bilinear programming over the polydisk MediaObjects/2005_498_BF01211858_f1.jpg n which also shows that the purely complexμ computation, analysis/synthesis problems areN P-hard even if there are no repeated blocks. Another side result of the paper is that checking robust nonsingularity, robust Hurwitz stability, and robust Schur stability of a disk matrix areN P-hard problems.

In this paper, it is shown that the problem of checking the stability of discrete event systems, is algorithmically unsolvable. Namely, it is impossible to design an algorithm that can be used to test the stability of such systems. In particular, two stability problems, SP1and SP2, are defined, and shown to be algorithmically unsolvable for the class of discrete event systems of the form x(k+1) =Af(u(k), g(x(k)))x(k), where g(·) is a simple threshold function. Therefore, the above stability problems for general discrete event systems are algorithmically unsolvable. The results of this paper imply that, there is no algorithm (i.e. there is no Turing machine) that can be used to solve these stability problems for discrete event systems. In particular, these stability problems are rationally undecidable, and there is no polynomial time or non-polynomial time algorithm that solves these problems. Furthermore, it is also shown that, some reachability problems for asynchronous iterative processes are algoritlunically unsolvable too.

In this work, we consider optimal design of Modal Power Distribution (MPD) based fiber optic sensors and compare power-meter and CCD camera based techniques for strain measurements. To the best of authors' knowledge, majority of the power-meter based MPD sensors use a single photo detector, and there is only one known work where two photodetectors are used with no optimization on photo-detector locations. Optimal measurement location selection problem and comparison of power-meter and CCD camera based sensor measurements were both addressed in this work. Based on our experimental data, more than 100% increased sensitivity is observed in the newly designed optimal strain sensor. It was also shown that there is a fixed nonlinear relationship between CCD based and power-meter based fiber optic sensor measurements. This allows estimation of power-meter measurements utilizing CCD camera images, which in turn simplifies the optimal detector location selection problem.