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A posteriori error estimation for nonlinear parabolic boundary control

A posteriori error estimation for nonlinear parabolic bounda...

引用

international conference on methods and models in automation and robotics (mmar)

作者： Eileen Kammann Fredi Tröltzsch Technische Universitt Berlin Institut für Mathematik Berlin Germany

We consider the following problem of error estimation for the optimal control of nonlinear parabolic partial differential equations: Let an arbitrary control function be given. How far is it from the next locally optimal control? Under natural assumptions including a second order sufficient optimality condition for the (unknown) locally optimal control, we are able to estimate the distance between the two controls. To do this, we need some information on the lowest eigenvalue of the reduced Hessian. We apply this technique to a model reduced optimal control problem obtained by proper orthogonal decomposition (POD). the distance between a (suboptimal) local solution of the reduced problem to a local solution of the original problem is estimated.

关键词： Optimal control Mathematical model Equations Optimization Moment methods Coercive force Estimation

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Generating Chen-Fliess-Sussmann equation via Campbell-Baker-Hausdorff-Dynkin formula

Generating Chen-Fliess-Sussmann equation via Campbell-Baker-...

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international conference on methods and models in automation and robotics (mmar)

作者： Ignacy Duleba Jacek Jagodziński Institute of Computer Engng. Control and Robotics Wroclaw Univ. of Technology Wroclaw Poland

Generating and solving the Chen-Fliess-Sussmann (CFS) equation for a given representation of motion is a crucial step in deriving controls to steer nilpotent nonholonomic systems using the Lafferriere-Sussmann method. the equation can be quite complicated, and its derivation differs substantially from one representation to another. therefore instead to derive CFS for a given hard-to-compute representation we propose to derive it for any easy-to-compute representation and then to transform it to the given representation. For this purpose the Campbell-Baker-Hausdorff-Dynkin formula is applied. this approach is illustrated on generating and solving CFS for forward, backward and canonical representations.

关键词： Equations Mathematical model Algebra Robots Planning Generators Control systems

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Dynamic modeling and simulation of rowing with a robotics formalism

Dynamic modeling and simulation of rowing with a robotics fo...

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international conference on methods and models in automation and robotics (mmar)

作者： François Rongère Wisama Khalil Jean-Michel Kobus Laboratoire de Mécanique des Fluides (LMF) Nantes France Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN) Nantes France

this paper presents a robotics framework intended to be used for rowing simulation. It provides kinematic and inverse dynamic models for the system composed of boat, rowers and oars. the inverse dynamic model is based on the Recursive Newton-Euler Algorithm with free-floating base dealing with tree-structured systems with kinematic loops. Examples of simulations of a rowing-like model are given along with external force models. It is composed of a total of 6 links for the rower and the oars, the floating boat, and 7 joints. It presents a branched structure with one loop enabling to test the ability of the framework regarding its goals.

关键词： Boats Joints Mathematical model Computational modeling Acceleration Dynamics Heuristic algorithms

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On-line data registration in OUTDOOR environment

On-line data registration in OUTDOOR environment

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international conference on methods and models in automation and robotics (mmar)

作者： Janusz Bedkowski Andrzej Masłowski Institute of Automation and Robotics Warsaw University of Technology Warsaw Poland

In the paper an algorithm of 3D data registration based on CUDA implementation is shown. the research is related to the problem of collecting 3D data with laser measurement system mounted on rotated head, to be used in mobile robot applications. Assumed performance of data registration algorithm is achieved, therefore it can used as On-line. the ICP (Iterative Closest Point) approach is chosen as registration method. Computation is based on massively parallel architecture of NVIDIA CUDA. the presented concept of 3D data matching is based on parallel computation used for fast nearest neighbor search. Nearest neighbor search procedure is using 3D space decomposition into cubic buckets, therefore the time of matching is deterministic.

关键词： three dimensional displays Iterative closest point algorithm Graphics processing unit Mobile robots Lasers Mobile communication

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Innovative, reconfigurable simulator of mobile robots to support anti-crisis operations

Innovative, reconfigurable simulator of mobile robots to sup...

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international conference on methods and models in automation and robotics (mmar)

作者： Maciej Zasuwa Janusz Narkiewicz Jakub Bartoszek The Institute of Aeronautics and Applied Mechanics Warsaw University of Technology Warsaw Poland Industrial Research Institute for Automation and Measurements PIAP Warsaw Poland

the paper presents innovative, reconfigurable simulator of mobile robots included in anti-crisis operations system. the simulator development is a part of the PROTEUS project. Along the whole anti-crisis system is developed, the simulator of mobile robots is constructed. Majority of the simulators developed worldwide are intended for specific vehicles and used for various applications of particular robots. this approach does not satisfy developers from Poland because the anti-crisis operations system has an open architecture and allows to introduce different mobile robots into action. In the paper the requirements and architecture of the simulator are described. Its integration with training system of all parts of anti-crisis operations is discussed. the paper shows the novelty of the solution (both in hardware and software).

关键词： Solid modeling Software Mobile robots Training Vehicles Computational modeling

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An optimal sequence of tasks for autonomous learning systems

An optimal sequence of tasks for autonomous learning systems

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international conference on methods and models in automation and robotics (mmar)

作者： Radoslaw Rudek Agnieszka Rudek Piotr Skworcow Wroclaw University of Economics Wroclaw Poland De Montfort University Water Software Systems Leicester UK

In this paper, we consider an optimal sequence of tasks for systems that improve their performances due to autonomous learning (learning-by-doing). In particular, we focus on a problem of determining sequence of performed tasks for the autonomous learning systems to minimize the total weighted completion times of tasks. Fundamental for the presented approach is that schedule (a sequence of tasks) allows to efficiently utilize learning abilities of the system to optimize its objective, but it does not affect the system itself. To solve the problem, we prove an eliminating property that is used to construct a branch and bound algorithm and present some fast heuristic and metaheuristic methods. An extensive analysis of the efficiency of the proposed algorithms is also provided.

关键词： Algorithm design and analysis Approximation algorithms Upper bound Schedules Heuristic algorithms Approximation methods Learning systems

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Optimal control of non-homogeneous wave equation

Optimal control of non-homogeneous wave equation

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international conference on methods and models in automation and robotics (mmar)

作者： Grigory M. Sklyar Grzegorz Szkibiel Institute of Mathematics Szczecin University Szczecin Poland

While studying vibrations of non-homogeneous strings or chains a trigonometric non-Fourier moment problems arise. the existence of solutions of such problems is still researched by many authors. In current note, a particular solution, called optimal, i.e. the one with the least L 2 -norm is searched for. Proposed is an algorithm that allows to change an infinite system of equations into the linear one with only a finite number of equations. the mentioned algorithm is based on the fact, that in the case of a Fourier moment problem, the optimal solution is periodic and easy to construct. the optimal solution of a non-Fourier moment problem close to a Fourier one is approximated by a sequence of solutions with periodicity disturbed in a finite number of equations. It is proved that this sequence of approximations converges to the solution sought for. the note is concluded with the application of proposed algorithm.

关键词： Equations Approximation methods Approximation algorithms Boundary conditions Optimal control Eigenvalues and eigenfunctions Propagation

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On the rational approximation of fractional order systems

On the rational approximation of fractional order systems

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international conference on methods and models in automation and robotics (mmar)

作者： Wiesław Krajewski Umberto Viaro Systems Research Institute Polish Academy of Sciences Warsaw Poland Dipartimento di Ingegneria Elettrica Università degli Studi di Udine Udine Italy

this paper is concerned with the finite-dimensional approximation of a fractional-order system represented in state-space form. To this purpose, resort is made to the Oustaloup method for approximating a fractional-order integrator by a rational filter. By applying this method to the RHS of the state equation of the fractional-order system, a matrix differential equation is obtained. this equation is then realized in a state-space form whose state matrix exhibits a (sparse) block-companion structure. To reduce the dimension of this integer-order model, an efficient method for L 2 approximation can profitably be applied. Numerical simulations show that the suggested approach compares favourably with alternative techniques recently presented in the literature to the same purpose.

关键词： Mathematical model Approximation methods Reduced order systems Solid modeling Equations Differential equations Signal processing

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Model-based control of solenoid actuators using flux channel reluctance models

Model-based control of solenoid actuators using flux channel...

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international conference on methods and models in automation and robotics (mmar)

作者： Johannes Reuter Matthias Jäkle Felix Prauße Felix Rey Institute of System Dynamics University of Applied Sciences Konstanz Konstanz Germany Hochschule Konstanz Technik Wirtschaft und Gestaltung Konstanz Baden-WÃ¼rttemberg DE Karlsruhe Institute of Technology Karlsruhe Germany

Control-oriented magnetic models for solenoid actuators are analyzed and evaluated subject to their capabilities to reflect important features of the magnetic properties. Moreover, it is shown that undesired tuning requirements can be omitted by use of flux channel models. the focus here is put on the modeling of eddy currents since the accurate calculation of eddy current losses is a requirement for control strategies that are designed to minimize these losses. It is shown that flux channel models provide good results while the computational burden is low in comparison to finite element models. However, flux channel models require an additional step when used in flatness-based optimization schemes. this step is called state-decomposition and is explained in the second part of this paper.

关键词： Mathematical model Equations Eddy currents Magnetic cores Channel models Actuators Saturation magnetization

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Feature selection for pattern recognition by LASSO and thresholding methods - a comparison

Feature selection for pattern recognition by LASSO and thres...

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international conference on methods and models in automation and robotics (mmar)

作者： Urszula Libal Control and Robotics Wroclaw University of Technology Wroclaw Poland

For high-dimensional data processing, like pattern recognition, it seems desirable to precede with a reduction of the number of describing features. Our aim is a comparison of various feature selection methods for pattern recognition. We consider two-class supervised classification problem for signals decomposed in wavelet bases. We test kNN classification rule with soft and hard thresholding, performed in two stages: (1) wavelet detail coefficient thresholding (noise reduction) and (2) searching for the most differentiating coefficients between classes (selection of discriminating coefficients). We present a new classification rule based on LARS/LASSO. We compare criteria for L1-norm regularization of wavelet coefficients: AIC, BIC and the thresh derived for kNN rule. there were performed simulations for noisy signals with SNR in the range from 0 to 22 [dB], approximated for all possible wavelet resolutions. the quality of pattern recognition for the presented algorithms was measured by the estimated recognition risk and the size of reduced model.

关键词： Pattern recognition Signal to noise ratio Noise measurement Signal resolution Noise level Noise reduction

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