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Local null controllability of a fluid-solid interaction problem in dimension 3

Muriel Boulakia, Sergio Guerrero (2013)

Journal of the European Mathematical Society

We are interested by the three-dimensional coupling between an incompressible fluid and a rigid body. The fluid is modeled by the Navier-Stokes equations, while the solid satisfies the Newton's laws. In the main result of the paper we prove that, with the help of a distributed control, we can drive the fluid and structure velocities to zero and the solid to a reference position provided that the initial velocities are small enough and the initial position of the structure is close to the reference...

Maxwell strata in sub-Riemannian problem on the group of motions of a plane

Igor Moiseev, Yuri L. Sachkov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained.

Minimal positive realizations: a survey of recent results and open problems

Luca Benvenuti, Lorenzo Farina (2003)

Kybernetika

In this survey paper some recent results on the minimality problem for positive realizations are discussed. In particular, it is firstly shown, by means of some examples, that the minimal dimension of a positive realization of a given transfer function, may be much “larger” than its McMillan degree. Then, necessary and sufficient conditions for the minimality of a given positive realization in terms of positive factorization of the Hankel matrix are given. Finally, necessary and sufficient conditions...

Nilpotent approximation of a trident snake robot controlling distribution

Jaroslav Hrdina, Radomil Matoušek, Aleš Návrat, Petr Vašík (2017)

Kybernetika

We construct a privileged system of coordinates with respect to the controlling distribution of a trident snake robot and, furthermore, we construct a nilpotent approximation with respect to the given filtration. Note that all constructions are local in the neighbourhood of a particular point. We compare the motions corresponding to the Lie bracket of the original controlling vector fields and their nilpotent approximation.

Nonlinear diagnostic filter design: algebraic and geometric points of view

Alexey Shumsky, Alexey Zhirabok (2006)

International Journal of Applied Mathematics and Computer Science

The problem of diagnostic filter design is studied. Algebraic and geometric approaches to solving this problem are investigated. Some relations between these approaches are established. New definitions of fault detectability and isolability are formulated. On the basis of these definitions, a procedure for diagnostic filter design is given in both algebraic and geometric terms.

On some geometric control properties of active suspensions systems

Domenico Prattichizzo, Paolo Mercorelli (2000)

Kybernetika

The geometric control properties of vehicles with active suspensions are analyzed. A special attention is devoted to the problem of disturbance decoupling. Active suspensions of advanced vehicles allow the active rejection of external disturbances exerted on the sprung mass of the vehicle and caused by road surface irregularity. We focus on the road irregularity disturbances with the purpose of isolating the chassis from vibrations transmitted through suspensions. The paper is aimed at the synthesis...

On the equivalence of control systems on Lie groups

Rory Biggs, Claudiu C. Remsing (2015)

Communications in Mathematics

We consider state space equivalence and feedback equivalence in the context of (full-rank) left-invariant control systems on Lie groups. We prove that two systems are state space equivalent (resp.~detached feedback equivalent) if and only if there exists a Lie group isomorphism relating their parametrization maps (resp. traces). Local analogues of these results, in terms of Lie algebra isomorphisms, are also found. Three illustrative examples are provided.

On the Phase Portrait of the Fast Filtering Algorithms

Yishao Zhou (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Fast filtering algorithms arising from linear filtering and estimation are nonlinear dynamical systems whose initial values are the statistics of the observation process. In this paper, we give a fairly complete description of the phase portrait for such nonlinear dynamical systems, as well as a special type of naturally related matrix Riccati equation.

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