Laboratoire d’analyse et d’architecture des systèmes

17395

31/10/2017

Y.ARIBA, D.ARZELIER

MAC, ROC

Rapport LAAS N°17395, Octobre 2017, 32p.

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141372 17393

24/10/2017

C.GAZZINO, D.ARZELIER, L.CERRI, D.LOSA, C.LOUEMBET, C.PITTET-MECHIN

MAC, ROC, CNES, Thalès Alenia Space

Rapport LAAS N°17393, Octobre 2017, 8p.

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141334 17110

24/10/2017

C.GAZZINO, D.ARZELIER, L.CERRI, D.LOSA, C.LOUEMBET, C.PITTET-MECHIN

MAC, ROC, CNES, Thalès Alenia Space

Revue Scientifique : Transactions of the Japan Society for Aeronautical and Space Sciences, 8p., Octobre 2017, To appear , N° 17110

Lien : https://hal.laas.fr/hal-01609252

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In this paper, a fuel optimal rendezvous problem is tackled in the Hill-Clohessy-Wiltshire framework with several operational constraints as bounds on the thrust, non linear non convex and disjunctive operational constraints (on-off profile of the thrusters, minimum elapsed time between two consecutive firings...). An indirect method and a decomposition technique have already been combined in order to solve this kind of optimal control problem with such constraints. Due to a great number of parameters to tune, satisfactory results are hard to obtain and are sensitive to the initial condition. Assuming that no singular arc exists, it can be shown that the optimal control exhibits a bang-bang structure whose optimal switching times are to be found. Noticing that a system with a bang-bang control profile can be considered as two subsystems switching from one with control on to with control off, and vice-versa, a technique coming from the switching systems theory is used in order to optimise the switching times.

17389

23/10/2017

C.ALBEA SANCHEZ, G.GARCIA, S.HADJERAS, W.P.M.H.HEEMELS, L.ZACCARIAN

MAC, Eindhoven

Rapport LAAS N°17389, Octobre 2017, 8p.

Lien : https://hal.archives-ouvertes.fr/hal-01617999

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The paper deals with the problem of practical stabilisation of operating points for switched affine systems, ensuring a dwell-time associated with an LQR performance level during the transient response and an admissible chattering around the operating point. In this paper we propose a solution to this problem in which the formal guarantees are established using recent tools from hybrid dynamical systems theory. We also include insights on the quadratic performance of the proposed switching strategies.

17378

20/10/2017

L.BURLION, L.ZACCARIAN, H.DE PLINVAL, S.TARBOURIECH

ONERA, MAC

Rapport LAAS N°17378, Octobre 2017, 4p.

Lien : https://hal.inria.fr/hal-01593178

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141292 16426

05/10/2017

O.MOKRENKO, C.ALBEA SANCHEZ, S.LESECQ, L.ZACCARIAN

CEA-LETI, MAC

Revue Scientifique : 12p., Octobre 2017 , N° 16426

Lien : https://hal.archives-ouvertes.fr/hal-01402876

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Energy is a key resource in Wireless Sensor Networks (WSNs), especially when sensor nodes are powered by batteries. This work investigates how to save energy of the whole WSN, thanks to control strategies, in real time and in a dynamic way. The energy management strategy is based on a Hybrid Dynamical System (HDS) approach. This choice is motivated by the hybrid inherent nature of the WSN system when energy management is considered. The hybrid nature basically comes from the combination of continuous physical processes, namely, the charge/discharge of the node batteries; while the discrete part is related to the change in the functioning modes and an Unreachable condition of the nodes. This approach provides a decentralized controller with low computational load that reduces the number of switching as compared to existing approaches. The proposed strategy is evaluated and compared in simulation on a realistic test-case. Lastly, they have been implemented on a real test-bench and the obtained results have been discussed.

17349

03/10/2017

C.JOSZ, D.MOLZAHN

MAC, ANL

Rapport LAAS N°17349, Octobre 2017, 30p.

Lien : https://hal.laas.fr/hal-01592093

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We propose general notions to deal with large scale polynomial optimization problems and demonstrate their efficiency on a key industrial problem of the twenty first century, namely the optimal power flow problem. These notions enable us to find global minimizers on instances with up to 4,500 variables and 14,500 constraints. First, we generalize the Lasserre hierarchy from real to complex to numbers in order to enhance its tractability when dealing with complex polynomial optimization. Complex numbers are typically used to represent oscillatory phenomena, which are omnipresent in physical systems. Using the notion of hyponormality in operator theory, we provide a finite convergence criterion which generalizes the Curto-Fialkow conditions of the real Lasserre hierarchy. Second, we introduce the multi-ordered Lasserre hierarchy in order to exploit sparsity in polynomial optimization problems (in real or complex variables) while preserving global convergence. It is based on two ideas: 1) to use a different relaxation order for each constraint, and 2) to iteratively seek a closest measure to the truncated moment data until a measure matches the truncated data. Third and last, we exhibit a block diagonal structure of the Lasserre hierarchy in the presence of commonly encountered symmetries.

17345

03/10/2017

C.JOSZ

MAC

Rapport LAAS N°17345, Octobre 2017, 9p.

Lien : https://hal.archives-ouvertes.fr/hal-01592101

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We consider the problem of solving a linear system of equations which involves complex variables and their conjugates. We characterize when it reduces to a complex linear system, that is, a system involving only complex variables (and not their conjugates). In that case, we show how to construct the complex linear system. Interestingly, this provides a new insight on the relationship between real and complex linear systems. In particular, any real symmetric linear system of equations can be solved via a complex linear system of equations. Numerical illustrations are provided. The mathematics in this manuscript constitute an exciting interplay between Schur's complement, Cholesky's factorization, and Cauchy's interlace theorem.

17346

03/10/2017

C.JOSZ

MAC

Rapport LAAS N°17346, Octobre 2017, 32p.

Lien : https://hal.archives-ouvertes.fr/hal-01592106

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On one hand, consider the problem of finding global solutions to a polynomial optimization problem and, on the other hand, consider the problem of interpolating a set of points with a complex exponential function. This paper proposes a single algorithm to address both problems. It draws on the notion of hyponormality in operator theory. Concerning optimization, it seems to be the first algorithm that is capable of extracting global solutions from a polynomial optimization problem where the variables and data are complex numbers. It also applies to real polynomial optimization, a special case of complex polynomial optimization, and thus extends the work of Henrion and Lasserre implemented in GloptiPoly. Concerning interpolation, the algorithm provides an alternative to Prony's method based on the Autonne-Takagi factorization and it avoids solving a Vandermonde system. The algorithm and its proof are based exclusively on linear algebra. They are devoid of notions from algebraic geometry, contrary to existing methods for interpolation. The algorithm is tested on a series of examples, each illustrating a different facet of the approach. One of the examples demonstrates that hyponormality can be enforced numerically to strenghten a convex relaxation and to force its solution to have rank one.

17340

03/10/2017

J.P.LAUMOND, N.MANSARD, J.B.LASSERRE

GEPETTO, MAC

Ouvrage (éditeur) : Geometric and Numerical Foundations of Movements, Springer, N°ISBN 978-3-319-51546-5, Octobre 2017, 425p. , N° 17340

Lien : https://hal.laas.fr/hal-01590779

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This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.

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