Comments on ‘ Dynamic feedback methodology for interconnected control systems ’ and ‘ Dynamic multilevel optimization for a class of non-linear systems ’

The paper considers the Kalman-Bucy filter for a linear system when the measurement noise covariance matrix is singular. It is shown that the problem of infimizing the square of a linear functional of the state estimation error is the dual of the optimal singular linear regulator problem. Furthermore there is an optimal reduced-order Kalman-Bucy filter for minimization of the trace of the state error covariance matrix, when all extremal controls for a dual regulator have finite order of singularity, and no Luenberger observer is needed. The proof is constructive. Necessary and sufficient conditions for the existence of a reduced-order optimal estimator are derived.     

Method for 3D fibre reconstruction on a microrobotic platform

Automated handling of a natural fibrous object requires a method for acquiring the three‐dimensional geometry of the object, because its dimensions cannot be known beforehand. This paper presents a method for calculating the three‐dimensional reconstruction of a paper fibre on a microrobotic platform that contains two microscope cameras. The method is based on detecting curvature changes in the fibre centreline, and using them as the corresponding points between the different views of the images. We test the developed method with four fibre samples and compare the results with the references measured with an X‐ray microtomography device. We rotate the samples through 16 different orientations on the platform and calculate the three‐dimensional reconstruction to test the repeatability of the algorithm and its sensitivity to the orientation of the sample. We also test the noise sensitivity of the algorithm, and record the mismatch rate of the correspondences provided. We use the iterative closest point algorithm to align the measured three‐dimensional reconstructions with the references. The average point‐to‐point distances between the reconstructed fibre centrelines and the references are 20–30 μm, and the mismatch rate is low. Given the manipulation tolerance, this shows that the method is well suited to automated fibre grasping. This has also been demonstrated with actual grasping experiments.     

A hierarchical approach to state space constrained optimization problems

A class of hierarchical prediction-type methods for solving state space constrained optimization problems is studied. The approach is a generalization of the balance-type methods suggested by the authors in earlier papers, where the state space constrained optimization problem was converted into a two-level problem with control constrained first-level problems by using the multiplier method of Hestenes. The use of a prediction-type approach allows simpler first-level optimization problems via decomposition and/or simplification of the constraints.     

On coordination strategies for the interaction prediction principle using gradient and multiplier methods

This paper deals with supremal level coordination strategies for the interaction (input) prediction principle. The decision-making problem of thoe supremal level (the coordinator) is to find a saddle point of a dual function of the coordination variables. The differentiability properties of the dual function are studied and explicit formulae for the gradients are derived. Application of the multiplier method of Hestenes results in a heuristical coordination strategy. The proposed algorithm is tested by two numerical examples.     

TEXTURE PREDICTION WITH A MODEL SYSTEM

In a texturization process a desired texture is obtained by applying processing operations to a selected set of raw materials. The objective of the present study was to construct a simple model to predict the textural parameters of a product from a texturization process. The variables studied included both ingredients and processing parameters. The system studied was the mixture in which gelatinization of wheat flour takes place in a sugar solution with limited concentration of water. The gelatinization was facilitated by heating and mixing, as in the candy licorice process. A modified Brabender amylograph was employed for cooking. An Instron Universal testing machine with a specially designed extruder-conveyor was used for the extrusion of the cooked mass. This machine, in a normal setup, was used for the textural measurements. In texture measurements the deformation speeds were 1, 5, and 10 cm/min. Statistically significant (at 1% level) second-order polynomial models with high multiple correlation coefficients, and statistically nonsignificant (at 5% level) lack of fit were obtained for the texture parameters studied. Several second-order terms, indicating nonlinearity, and cross-products, indicating interactions of the variables, were included in the models. Different sets of variables, or of variable cross-products, also were included at different deformation speeds. Under certain conditions differences between flour and flouringredient experiments were apparent.