Stabilization, pole placement, and regular implementability

In this paper, we study control by interconnection of linear differential systems. We give necessary and sufficient conditions for. regular implementability of a given linear differential system. We formulate the problems of stabilization and pole placement as problems of finding a suitable, regularly implementable sub-behavior of the manifest plant behavior. The problem formulations and their resolutions are completely representation free, and specified only in terms of the system dynamics. Control is viewed as regular interconnection. A controller is a system that constrains the plant behavior through a distinguished set of variables, namely, the control variables. The issue of implementation of a controller in the feedback configuration and its relation to regularity of interconnection is addressed. Freedom of disturbances in a plant and regular interconnection with a controller also turn out to be inter-related     

Monitoring of multivariable dynamic processes and sensor auditing

Industrial continuous processes are usually operated under closed-loop control, yielding process measurements that are autocorrelated, cross correlated, and collinear. A statistical process monitoring (SPM) method based on state variables is introduced to monitor such processes. The statistical model that describes the in-control variability is based on a canonical variate (CV) state space model. The CV state variables are linear combinations of the past process measurements which explain the variability of the future measurements the most, and they are regarded as the principal dynamic dimensions. A T² statistic based on the CV state variables is utilized for developing the SPM procedure. The CV state variables are also used for monitoring sensor reliability. An experimental application to a high temperature short time (HTST) pasteurization process illustrates the proposed methodology.     

Numerical solution of a Newtonian jet emanating from a converging channel

A theoretical analysis has been carried out to find the shape and final thickness of a Newtonian jet emanating from a converging channel. The gravitational force is neglected but the surface tension effect is included in the present analysis. There are four variables, i.e. the contraction ratio L, the converging angle θ, the Reynolds number Re and the capillary number Ca, that completely determine the flow field. The effects of these four variables on the motion of the jet are examined. The mathematical problem of the jet is formulated with stream function and vorticity as dependent variables. The boundary-fitted coordinate transformation method developed by Thompson et al. is adopted to map the flow geometry into a regular domain for numerical integration, and the finite difference method is applied to solve the flow equations in the transformed plane. We have found that the final thickness of the jet will reach its frozen value as L > 15. As Re > 50, the jet contraction coefficient is very close to that of a potential Helmholtz jet. Surface tension is only important if Re is small. The jet contraction coefficients as functions of Re and θ are presented. We have also found that a vortex may exist in the converging channel if the converging angle θ > 75°.     

Neural networks and response surface polynomials for design of vehicle joints

Typically, design of a complex system starts by setting targets for its performance characteristics. Then, design engineers cascade these targets to the components and design the components to meet these targets. It is important to have efficient tools that check if a set of performance targets for a component corresponds to a feasible design and determine the dimensions and mass of this design. This paper describes a method to develop tools that relate response parameters that describe the performance of a component to the physical design variables that specify its geometry. Neural networks and response surface polynomials are used to rapidly predict the performance characteristics of the components given the component dimensions. The method is demonstrated on design of an automotive joint. The paper compares neural networks and response surface polynomials and shows that they are almost equally accurate for the problem considered.     

Equivalence of rational representations of behaviors

This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel representations are called equivalent if they represent one and the same behavior. For kernel representations defined by polynomial matrices, necessary and sufficient conditions for equivalence are well known. In this paper, we deal with the equivalence of rational representations, i. e. kernel and image representations that are defined in terms of rational matrices. As the first main result of this paper, we will derive a new condition for the equivalence of rational kernel representations of possibly noncontrollable behaviors. Secondly we will derive conditions for the equivalence of rational representations of a given behavior in terms of the polynomial modules generated by the rows of the rational matrices. We will also establish conditions for the equivalence of rational image representations. Finally, we will derive conditions under which a given rational kernel representation is equivalent to a given rational image representation.     

Embedded visual behaviors for navigation

The implementation of a set of visually based behaviors for navigation is presented. The approach, which has been inspired by insect's behaviors, is aimed at building a “library” of embedded visually guided behaviors coping with the most common situations encountered during navigation in an indoor environment. Following this approach, the main goal is no longer how to characterize the environment, but how to embed in each behavior the perceptual processes necessary to understand the aspects of the environment required to generate a purposeful motor output.

The approach relies on the purposive definition of the task to be solved by each of the behaviors and it is based on the possibility of computing visual information during the action. All the implemented behaviors share the same input process (partial information of the image flow field) and the same control variables (heading direction and velocity) to demonstrate both the generality of the approach as well as its efficient use of the computational resources. The controlled mobile base is supposed to move on a flat surface but virtually no calibration is required of the intrinsic and extrinsic parameters of the two cameras and no attempt is made at building a 2D or 3D map of the environment: the only output of the perceptual processes is a motor command.

The first behavior, the centering reflex allows a robot to be easily controlled to navigate along corridors or following walls of a given scene structure. The second behavior extends the system capabilities to the detection of obstacles lying on the pavement in front of the mobile robot. Finally docking behaviors to control the robot to a given position in the environment, with controlled speed and orientation, are presented.

Besides the long-term goal of building a completely autonomous system, these behaviors can have very short-term applications in the area of semi-autonomous systems by taking care of the continuous, tedious control required during routine navigation.     

Stabilization of discrete 2D behaviors by regular partial interconnection

In this work, we consider linear, shift-invariant and complete two-dimensional (2D) discrete systems from a behavioral point of view. In particular, we examine behaviors with two types of variables: the variables that we are interested to control (the to-be-controlled variables) and the variables on which we are allowed to enforce restrictions (the control variables). The main purpose of this contribution is to derive necessary and sufficient conditions for the stabilization of the to-be-controlled variables by ‘attaching’ a controller to the control variables. This problem turns out to be related to the decomposition of a given behavior into the sum of two sub-behaviors. Moreover, we show that under certain conditions, it is possible to obtain a constructive solution and characterize the structure of the to-be-controlled behavior.     

Equivalence conditions for behaviors and the Kronecker canonical form

In this paper we explore equivalence conditions and invariants for behaviors given in kernel representations. In case the kernel representation is given in terms of a linear matrix pencil, the invariants for strict equivalence are given by the Kronecker canonical form which, in turn, we interpret in geometric control terms. If the behavior is given in a kernel representation by a higher order rectangular polynomial matrix, the natural equivalence concept is behavior equivalence. These notions are closely related to the Morse group that incorporates state space similarity transformations, state feedback, and output injection. A simple canonical form for behavioral equivalence is given that clearly exhibits the reachable and autonomous parts of the behavior. Using polynomial models we also present a unified approach to pencil equivalence that elucidates the close connections between classification problems from linear algebra, geometric control theory, and behavior theory. We also indicate how to derive the invariants under behavior equivalence from the Kronecker invariants.     

On flat systems behaviors and observable image representations

In this short paper we propose a definition of flatness for systems not necessarily given in input/state/output representation. A flat system is a system for which there exists a mapping such that the manifest system behavior is equal to the image of this mapping, and such that the latent variable appearing in this image representation can be written as a function of the manifest variable and its derivatives up to some order. For linear differential systems, flatness is equivalent to controllability. We will generalize the main theorem of Levine and Nguyen (Systems Control Lett. 48 (2003) 69) to general linear differential systems.     

Synthesis of dissipative systems using quadratic differentialforms: part II

For pt.1 see ibid., p.53-69 (2002). The authors discuss several important special cases of the problem solved in Part I. These are: disturbance attenuation and passivation, the full information case, the filtering problem, and the case that the to-be-controlled plant is given in input-state-output representation. An interesting aspect is the notion of full information, which we define in terms of the observability of the to-be-controlled variables from the control variables. When the system is given in state space form, we obtain conditions for the existence of a controller that renders a system dissipative in terms of two coupled algebraic Riccati inequalities. The controller turns out to be a feedback system with a transfer function that is proper, but, in general, not strictly proper. Another issue that we study in this paper is feedback implementability. We find conditions under which, in the context of synthesis of dissipative systems, a controlled behavior can implemented by a feedback controller     

Non-homothetic granulometric mixing theory with application to blood cell counting

A granulometry is a family of morphological openings by scaled structuring elements. As the scale increases, increasing image area is removed. Normalizing removed area by the total area yields the pattern spectrum of the image. The pattern spectrum is a probability distribution function and its moments are known as granulometric moments. Modeling the image as a random set, the pattern spectrum is a random function and its moments are random variables. The original granulometric mixing theory provides closed-form representation of the granulometric moments, shows that the distributions of the moments are asymptotically normal, and gives asymptotic expressions for the means and variances of the granulometric moments. The theory applies to random-set models formed as disjoint unions of randomly scaled image primitives (grains). The scaled grains are known as homothetics. The theory can be used in a method-of-moments fashion to estimate the parameters governing the random scaling factors and mixture proportions. Application is limited by the homothetic assumption. This paper drops the homothetic requirement and provides a mixing theory for a disjoint union of fully randomized primitives. Whereas the original asymptotic theory gives expressions for the moments themselves and is applied by taking expectations afterwards, the non-homothetic theory involves the granulometric size density, which is the mean of the original size distribution prior to normalization. Hence, the representation concerns expectations, not random variables. Nonetheless, a similar method-of-moments approach can be used to estimate mixture proportions. A large part of the paper is devoted to estimate blood cell proportions that correspond to cell-age categories. Each cell class is represented by a random grain, and the problem is to estimate the proportions of cells occurring in the various age categories. The random behavior of the cells in each category makes the non-homothetic theory appropriate. Because the estimation strategy leads to a system of nonlinear equations whose solution presents computational difficulties, the estimation is accomplished via a divide-and-conquer strategy in which the full mixture problem is partitioned into smaller problems, and the solutions of these problems are joined to solve the full problem.     

Multivariate feed back control: an application in a productive process

The main purpose of this research is to implement a multivariate feedback adjustment proportional to the last deviation from the target, in the set of variables wandering around the target. To apply the controller equation it will be necessary to study the exponentially weighted moving average (EWMA) statistic, in order to determine the behavior of the target disturbances. To determine the forecast values of the variables we will use Seemingly Unrelated Regression (SUR), which is necessary since there is a relationship between the variables and between the errors. In this manner, multivariate feedback adjustment can be reached based on scientific grounds.     

Shaping robot behavior using principles from instrumental conditioning

Shaping by successive approximations is an important animal training technique in which behavior is gradually adjusted in response to strategically timed reinforcements. We describe a computational model of this shaping process and its implementation on a mobile robot. Innate behaviors in our model are sequences of actions and enabling conditions, and shaping is a behavior editing process realized by multiple editing mechanisms. The model replicates some fundamental phenomena associated with instrumental learning in animals, and allows an RWI B21 robot to learn several distinct tasks derived from the same innate behavior.     

k-Anonymization with Minimal Loss of Information

The technique of k-anonymization allows the releasing of databases that contain personal information while ensuring some degree of individual privacy. Anonymization is usually performed by generalizing database entries. We formally study the concept of generalization, and propose three information-theoretic measures for capturing the amount of information that is lost during the anonymization process. The proposed measures are more general and more accurate than those that were proposed by Meyerson and Williams and Aggarwal et al. We study the problem of achieving k-anonymity with minimal loss of information. We prove that it is NP-hard and study polynomial approximations for the optimal solution. Our first algorithm gives an approximation guarantee of O(ln k) for two of our measures as well as for the previously studied measures. This improves the best-known O(k)-approximation in. While the previous approximation algorithms relied on the graph representation framework, our algorithm relies on a novel hypergraph representation that enables the improvement in the approximation ratio from O(k) to O(ln k). As the running time of the algorithm is O(n^2k}), we also show how to adapt the algorithm in in order to obtain an O(k)-approximation algorithm that is polynomial in both n and k.     

A characterization theorem of multivariate splines in blossoming form

It is known that polynomials in m variables of total degree n are equivalent to symmetric polynomials in n variables that are linear in each single variable. This principle, called the blossoming principle, has applied to the study of multivariate splines in this paper. For any spline on a simplicial partition Δ, a smoothness condition on its polynomial pieces on any two simplices of Δ which may not be adjacent is given. This smoothness condition presented in blossoming form generalizes the well-known smoothness conditions in B-form.     

Dead beat observer synthesis

In the paper the observer design problem is investigated in the context of linear left shift invariant discrete behaviors, whose trajectories have support on the positive axis. Observability and reconstructibility properties of certain manifest variables from certain others, in the presence of latent variables, are defined and fully characterized. Necessary and sufficient conditions for the existence of either a dead-beat or an exact observer are introduced, and a complete parametrization of all dead-beat observers is given.     

t-Spanners for metric space searching

The problem of Proximity Searching in Metric Spaces consists in finding the elements of a set which are close to a given query under some similarity criterion. In this paper we present a new methodology to solve this problem, which uses a t-spanner G′(V, E) as the representation of the metric database. A t-spanner is a subgraph G′(V, E) of a graph G(V, A), such that E  A and G′ approximates the shortest path costs over G within a precision factor t.

Our key idea is to regard the t-spanner as an approximation to the complete graph of distances among the objects, and to use it as a compact device to simulate the large matrix of distances required by successful search algorithms such as AESA. The t-spanner properties imply that we can use shortest paths over G′ to estimate any distance with bounded-error factor t.

For this sake, several t-spanner construction, updating, and search algorithms are proposed and experimentally evaluated. We show that our technique is competitive against current approaches. For example, in a metric space of documents our search time is only 9% over AESA, yet we need just 4% of its space requirement. Similar results are obtained in other metric spaces.

Finally, we conjecture that the essential metric space property to obtain good t-spanner performance is the existence of clusters of elements, and enough empirical evidence is given to support this claim. This property holds in most real-world metric spaces, so we expect that t-spanners will display good behavior in most practical applications. Furthermore, we show that t-spanners have a great potential for improvements.     

A parametrization for dissipative behaviors

The behavioral equivalent of single input single output (SISO) systems are behaviors with two manifest variables. Passive SISO systems can, therefore, be viewed as J-dissipative behaviors with two manifest variables. Here the special matrix J defines a QDF that captures the passivity property of SISO systems. In this paper, we investigate more general QDFs Q_Φs induced by some operator Φ. These QDFs define some relation between the input, the output and their derivatives of a SISO system. We characterize all behaviors that are dissipative with respect to the prescribed QDF Q_Φ. In fact, we parametrize all the behaviors dissipative with respect to Q_Φ in terms of those dissipative with respect to the special QDF Q_J induced by the matrix J. Similar results can also be given for lossless systems.     

H∞ control in a behavioral context: the fullinformation case

The authors formulate the H_∞-control problem in a behavioral setting. Given a mathematical model, say a set of higher order differential equations together with some static equations, the vector of manifest variables is partitioned into yet to be controlled variables, unknown exogenous variables, and interconnection variables. The interconnection variables are available for interconnection, in the sense that they can be made to obey certain differential or static equations, to be specified by the designer. Such a system of differential equations and static equations is called a controller. The design problem that we consider is to find controllers such that the size of the to be controlled variables is less than a given tolerance, for all disturbances in the unit ball, and such that the interconnection is a stable system. We find necessary and sufficient conditions for the existence of suitable controllers, under the hypothesis that we have a full information problem. These conditions involve indefinite factorizations of polynomial matrices and a test on a given Pick matrix