A system of linear recurrence equations for determinant of pentadiagonal matrix

Borowska, Jolanta; Łacińska, Lena; Rychlewska, Jowita

doi:10.17512/jamcm.2014.2.01

Cited by 5 publications

(7 citation statements)

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“…In order to obtain the determinant n W we adapt the approach proposed in [4]. After repeated use of the theorem of Laplace expansion we finally obtain a system of three linear recurrence equations n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n In order to obtain value of determinant n W we must take into account the system of equations (4) together with initial conditions of the form …”

Section: The Main Resultsmentioning

confidence: 99%

Recurrence form for determinant of a heptadiagonal symmetric Toeplitz matrix

Borowska¹,

Łacińska²

2014

J. Appl. Math. Comput. Mech.

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Section: The Main Resultsmentioning

confidence: 99%

Recurrence form for determinant of a heptadiagonal symmetric Toeplitz matrix

Borowska¹,

Łacińska²

2014

J. Appl. Math. Comput. Mech.

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“…The robot dynamics is described by (2), where M i = diag(m i , J i ), m i and J i are the vehicle mass and mass moment of inertia about the vertical axis, respectively, D i ∈ R 2×2 is the constant damping matrix, and u i ∈ R 2 represents the force-/torque-level control input provided by the drivetrain actuators.…”

Section: System Modelmentioning

confidence: 99%

“…The information exchange between robots is modeled by graph T (V, E ), which should be a spanning tree of the complete graph K n . (2) The spanning tree guarantees that the least number of control links (edges) between the robots in the graph is used to meet the control objective. The spanning tree is also motivated by our proposed collaboration protocol for the robots, which includes three categories of agents.…”

Section: Problem Statementmentioning

confidence: 99%

A formation maneuvering controller for multiple non-holonomic robotic vehicles

Khaledyan¹,

Queiroz²

2018

Robotica

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SUMMARYIn this paper, we present a new leader–follower type solution to the translational maneuvering problem for formations of multiple, non-holonomic wheeled mobile robots. The solution is based on the graph that models the coordination among the robots being a spanning tree. Our control law incorporates two types of position errors: individual tracking errors and coordination errors for leader–follower pairs in the spanning tree. The control ensures that the robots globally acquire a given planar formation while the formation as a whole globally tracks a desired trajectory, both with uniformly ultimately bounded errors. The control law is first designed at the kinematic level and then extended to the dynamic level. In the latter, we consider that parametric uncertainty exists in the equations of motion. These uncertainties are accounted for by employing an adaptive control scheme. The main contributions of this work are that the proposed control scheme minimizes the number of control links and global position measurements, and accounts for the uncertain vehicle dynamics. The proposed formation maneuvering controls are demonstrated experimentally and numerically.

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“…Secondly we are to show that every determinant n W , 4 > n , given by relationships (10) and (11) satisfies recurrence equation (2). Substituting n = 2k -1 into (2) we have…”

Section: Introductionmentioning

confidence: 99%