Analyzing very large time series using suffix arrays

Suffix arrays form a powerful data structure for pattern detection and matching. In a previous work, we presented a novel algorithm (COV) which is the only algorithm that allows the detection of all repeated patterns in a time series by using the actual suffix array. However, the requirements for storing the actual suffix strings even on external media makes the use of suffix arrays impossible for very large time series. We have already proved that using the concept of Longest Expected Repeated Pattern (LERP) allows the actual suffices to be stored in linear capacity O(n) on external media. The repeated pattern detection using LERP has analogous time complexity, and thus makes the analysis of large time series feasible and limited only to the size of the external media and not memory. Yet, there are cases when hardware limitations might be an obstacle for the analysis of very larger time series of size comparable to hard disk capacity. With the Moving LERP (MLERP) method introduced in this paper, it is possible to analyze very large time series (of size tens or hundreds thousands times larger than what the LERP can analyze) by maximal utilization of the available hardware. Further, when empirical knowledge related to the distribution of repeated pattern’s length is available, the proposed method (MLERP) can achieve better time performance compared to the standard LERP method and definitely much better than using any other pattern matching algorithm and applying brute force techniques which are unfeasible in logical (human) time frame. Thus, we may argue that MLERP is a very useful tool for detecting all repeated patterns in a time series regardless of its size and hardware limitations.     

On finite-time and infinite-time cost improvement of economic model predictive control for nonlinear systems

A novel two-layer economic model predictive control (EMPC) structure that addresses provable finite-time and infinite-time closed-loop economic performance of nonlinear systems in closed-loop with EMPC is presented. In the upper layer, a Lyapunov-based EMPC (LEMPC) scheme is formulated with performance constraints by taking advantage of an auxiliary Lyapunov-based model predictive control (LMPC) problem solution formulated with a quadratic cost function. The lower layer LEMPC uses a shorter prediction horizon and smaller sampling period than the upper layer LEMPC and involves explicit performance-based constraints computed by the upper layer LEMPC. Thus, the two-layer architecture allows for dividing dynamic optimization and control tasks into two layers for a computationally manageable control scheme at the feedback control (lower) layer. A chemical process example is used to demonstrate the performance and stability properties of the two-layer LEMPC structure.     

Evaluation of atmospheric correction to airborne hyperspectral data relying on radiative transfer concepts

Physically based atmospheric correction is one of the most important but also perilous radiometric corrections in remote-sensing imagery. The main objective of this work was to evaluate the efficiency of atmospheric correction algorithms, based not only on quantification of the changes induced but also on a step-by-step interpretation of the results, in association with the radiative transfer (RT) processes that occur in the atmosphere and on Earth. A four-level atmospheric correction scheme was applied to airborne hyperspectral visible/near-infrared (VNIR) imagery and the performance was evaluated. Each atmospheric correction level was more numerous than the previous following adjunctive assessment of the following parameters: (1) atmospheric influence, (2) the adjacency effect, (3) cast shadows, and (4) effects induced by the Earth’s surface reflectance anisotropy. Performance assessment showed that, even though a more complex atmospheric correction scheme resembles in greater detail the conditions under which the image acquisition was carried out, it is more sensitive to restrictions that arise from either the sensor’s characteristics or the algorithms and data used. Moreover, it was shown that evaluating atmospheric correction results using criteria based on RT concepts can considerably assist in the evaluation process.     

Robust near-optimal output feedback control of non-linear systems

This work proposes a robust near-optimal non-linear output feedback controller design for a broad class of non-linear systems with time-varying bounded uncertain variables. Both vanishing and non-vanishing uncertainties are considered. Under the assumptions of input-to-state stable (ISS) inverse dynamics and vanishing uncertainty, a robust dynamic output feedback controller is constructed through combination of a high-gain observer with a robust optimal state feedback controller synthesized via Lyapunov's direct method and the inverse optimal approach. The controller enforces exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of the uncertain variables on the output of the closed-loop system, for initial conditions and uncertainty in arbitrarily large compact sets, provided that the observer gain is sufficiently large. Utilizing the inverse optimal control approach and singular perturbation techniques, the controller is shown to be near-optimal in the sense that its performance can be made arbitrarily close to the optimal performance of the robust optimal state feedback controller on the infinite time-interval by selecting the observer gain to be sufficiently large. For systems with non-vanishing uncertainties, the same controller is shown to ensure boundedness of the states, uncertainty attenuation and near-optimality on a finite time-interval. The developed controller is successfully applied to a chemical reactor example.     

Non-linear feedback control of parabolic partial differential difference equation systems

This paper proposes a general method for the synthesis of non-linear output feedback controllers for single-input singleoutput quasi-linear parabolic partial differential difference equation (PDDE) systems, for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Initially, a non-linear model reduction scheme which is based on combination of Galerkin's method with the concept of approximate inertial manifold is employed for the derivation of differential difference equation (DDE) systems that describe the dominant dynamics of the PDDE system. Then, these DDE systems are used as the basis for the explicit construction of non-linear output feedback controllers through combination of geometric and Lyapunov techniques. The controllers guarantee stability and enforce output tracking in the closed-loop parabolic PDDE system independently of the size of the state delay, provided that the separation of the slow and fast eigenvalues of the spatial differential operator is sufficiently large and an appropriate matrix is positive definite. The methodology is successfully employed to stabilize the temperature profile of a tubular reactor with recycle at a spatially non-uniform unstable steadystate.     

Improved component mode synthesis and variants

This survey focuses on the two known model order reduction schemes being widely integrated in various commercial finite element packages, namely, the static and dynamic condensation methods. The advantages as well as the corresponding drawbacks have been extensively analyzed in several papers throughout the last decades. Based on combining the beneficial properties of the aforementioned methods, several alternative reduction methodologies are outlined in this paper, i.e., the generalized improved reduction system method, the generalized component mode synthesis and the improved component mode synthesis with its generalized version, which incorporate in a more efficient way the system’s inertia terms. Therefore, the associated error regarding higher frequency ranges of interest is better controlled. Basis of these methodologies is the so-called master and slave degrees of freedom partitioning, the right selection of which highly influences the reduced order model’s dynamics. The methods are tested and verified on a rather small three-dimensional bar structure and on the lever part of a turbocharger’s variable turbine geometry. Several reduced order models are generated by varying both the number of Craig–Bampton modes and the selection of the required master degrees of freedom. A comparison is conducted based on the modal criterion of the corresponding eigenvectors and the associated computation time required.     

Convex parametric piecewise quadratic optimization: Theory and algorithms

In this paper we study the problem of parametric minimization of convex piecewise quadratic functions. Our study provides a unifying framework for convex parametric quadratic and linear programs. Furthermore, it extends parametric optimization algorithms to problems with piecewise quadratic cost functions, paving the way for new applications of parametric optimization in explicit dynamic programming and optimal control with quadratic stage cost.     

A Unified Framework for Providing Recommendations in Social Tagging Systems Based on Ternary Semantic Analysis

Social Tagging is the process by which many users add metadata in the form of keywords, to annotate and categorize items (songs, pictures, Web links, products, etc.). Social tagging systems (STSs) can provide three different types of recommendations: They can recommend 1) tags to users, based on what tags other users have used for the same items, 2) items to users, based on tags they have in common with other similar users, and 3) users with common social interest, based on common tags on similar items. However, users may have different interests for an item, and items may have multiple facets. In contrast to the current recommendation algorithms, our approach develops a unified framework to model the three types of entities that exist in a social tagging system: users, items, and tags. These data are modeled by a 3-order tensor, on which multiway latent semantic analysis and dimensionality reduction is performed using both the Higher Order Singular Value Decomposition (HOSVD) method and the Kernel-SVD smoothing technique. We perform experimental comparison of the proposed method against state-of-the-art recommendation algorithms with two real data sets (Last.fm and BibSonomy). Our results show significant improvements in terms of effectiveness measured through recall/precision.     

A biomimetic approach to inverse kinematics for a redundant robot arm

Redundant robots have received increased attention during the last decades, since they provide solutions to problems investigated for years in the robotic community, e.g. task-space tracking, obstacle avoidance etc. However, robot redundancy may arise problems of kinematic control, since robot joint motion is not uniquely determined. In this paper, a biomimetic approach is proposed for solving the problem of redundancy resolution. First, the kinematics of the human upper limb while performing random arm motion are investigated and modeled. The dependencies among the human joint angles are described using a Bayesian network. Then, an objective function, built using this model, is used in a closed-loop inverse kinematic algorithm for a redundant robot arm. Using this algorithm, the robot arm end-effector can be positioned in the three dimensional (3D) space using human-like joint configurations. Through real experiments using an anthropomorphic robot arm, it is proved that the proposed algorithm is computationally fast, while it results to human-like configurations compared to previously proposed inverse kinematics algorithms. The latter makes the proposed algorithm a strong candidate for applications where anthropomorphism is required, e.g. in humanoids or generally in cases where robotic arms interact with humans.