Fast, large-scale model predictive control by partial enumeration

Partial enumeration (PE) is presented as a method for treating large, linear model predictive control applications that are out of reach with available MPC methods. PE uses both a table storage method and online optimization to achieve this goal. Versions of PE are shown to be closed-loop stable. PE is applied to an industrial example with more than 250 states, 32 inputs, and a 25-sample control horizon. The performance is less than 0.01% suboptimal, with average speedup factors in the range of 80-220, and worst-case speedups in the range of 4.9-39.2, compared to an existing MPC method. Small tables with only 25-200 entries were used to obtain this performance, while full enumeration is intractable for this example.     

Cubic Bézier approximation of a digitized curve

In this paper we present an efficient technique for piecewise cubic Bézier approximation of digitized curve. An adaptive breakpoint detection method divides a digital curve into a number of segments and each segment is approximated by a cubic Bézier curve so that the approximation error is minimized. Initial approximated Bézier control points for each of the segments are obtained by interpolation technique i.e. by the reverse recursion of De Castaljau's algorithm. Two methods, two-dimensional logarithmic search algorithm (TDLSA) and an evolutionary search algorithm (ESA), are introduced to find the best-fit Bézier control points from the approximate interpolated control points. ESA based refinement is proved to be better experimentally. Experimental results show that Bézier approximation of a digitized curve is much more accurate and uses less number of points compared to other approximation techniques.     

Target differentiation with simple infrared sensors using statistical pattern recognition techniques

This study compares the performances of various statistical pattern recognition techniques for the differentiation of commonly encountered features in indoor environments, possibly with different surface properties, using simple infrared (IR) sensors. The intensity measurements obtained from such sensors are highly dependent on the location, geometry, and surface properties of the reflecting feature in a way that cannot be represented by a simple analytical relationship, therefore complicating the differentiation process. We construct feature vectors based on the parameters of angular IR intensity scans from different targets to determine their geometry and/or surface type. Mixture of normals classifier with three components correctly differentiates three types of geometries with different surface properties, resulting in the best performance (100%) in geometry differentiation. Parametric differentiation correctly identifies six different surface types of the same planar geometry, resulting in the best surface differentiation rate (100%). However, this rate is not maintained with the inclusion of more surfaces. The results indicate that the geometrical properties of the targets are more distinctive than their surface properties, and surface recognition is the limiting factor in differentiation. The results demonstrate that simple IR sensors, when coupled with appropriate processing and recognition techniques, can be used to extract substantially more information than such devices are commonly employed for.     

Subspace identification of MIMO LPV systems using a periodic scheduling sequence

A novel subspace identification method is presented which is able to reconstruct the deterministic part of a multivariable state-space LPV system with affine parameter dependence, in the presence of process and output noise. It is assumed that the identification data is generated with the scheduling variable varying periodically during the course of the identification experiment. This allows to use methods from LTI subspace identification to determine the column space of the time-varying observability matrices. It is shown that the crucial step in determining the original LPV system is to ensure the obtained observability matrices are defined with respect to the same state basis. Once the LPV model has been identified, it is valid for other nonperiodic scheduling sequences as well.     

Generalized adaptive notch filters with frequency debiasing for tracking of polynomial phase systems

Generalized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. For general patterns of frequency variation the generalized adaptive notch filtering algorithms yield biased frequency estimates. We show that when system frequencies change slowly in a smooth way, the estimation bias can be substantially reduced by means of post-filtering of the frequency estimates. The modified (debiased) algorithm has better tracking capabilities than the original algorithm.     

The S-kernel: A measure of symmetry of objects

In this paper we introduce a new symmetry feature named “symmetry kernel” (SK) to support a measure of symmetry. Given any symmetry transform S, SK of a pattern P is the maximal included symmetric sub-set of P for all directions and shifts. We provide a first algorithm to exhibit this kernel where the centre of symmetry is assumed to be the centre of mass. Then we prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its symmetric version. That leads to a second algorithm. The associated symmetry measure is a modified difference between the respective surfaces of a pattern and its kernel. A series of experiments supports the actual algorithm validation.     

Robust control of polytopic systems by convex optimization

Robust control synthesis of linear time-invariant SISO polytopic systems is investigated using the polynomial approach. A convex set of all stabilizing controllers for a polytopic system is given over an infinite-dimensional space. A finite-dimensional approximation of this set is obtained using the orthonormal basis functions and represented by a set of LMIs thanks to the KYP lemma. Then, an LMI based convex optimization problem for robust pole placement with sensitivity function shaping in two- and infinity-norm is proposed. The simulation results show the effectiveness of the proposed method.     

Information cut for clustering using a gradient descent approach

We introduce a new graph cut for clustering which we call the Information Cut. It is derived using Parzen windowing to estimate an information theoretic distance measure between probability density functions. We propose to optimize the Information Cut using a gradient descent-based approach. Our algorithm has several advantages compared to many other graph-based methods in terms of determining an appropriate affinity measure, computational complexity, memory requirements and coping with different data scales. We show that our method may produce clustering and image segmentation results comparable or better than the state-of-the art graph-based methods.