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Parameter influence on passive dynamic walking of a robot with flat feet

Xiangze Lin, Haibo Du, Shihua Li (2013)

Kybernetika

The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased,...

Parametrization and geometric analysis of coordination controllers for multi-agent systems

Xiaoli Wang, Yiguang Hong (2009)

Kybernetika

In this paper, we address distributed control structures for multi-agent systems with linear controlled agent dynamics. We consider the parametrization and related geometric structures of the coordination controllers for multi-agent systems with fixed topologies. Necessary and sufficient conditions to characterize stabilizing consensus controllers are obtained. Then we consider the consensus for the multi-agent systems with switching interaction topologies based on control parametrization.

Parametrization and reliable extraction of proper compensators

Ferdinand Kraffer, Petr Zagalak (2002)

Kybernetika

The polynomial matrix equation X l D r + Y l N r = D k is solved for those X l and Y l that give proper transfer functions X l - 1 Y l characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly...

Passivity based stabilization of non-minimum phase nonlinear systems

Juan C. Travieso-Torres, Manuel A. Duarte-Mermoud, Petr Zagalak (2009)

Kybernetika

A cascade scheme for passivity-based stabilization of a wide class of nonlinear systems is proposed in this paper. Starting from the definitions and basic concepts of passivity-based stabilization via feedback (which are applicable to minimum phase nonlinear systems expressed in their normal forms) a cascade stabilization scheme is proposed for minimum and non-minimum phase nonlinear systems where the constraint of stable zero dynamics imposed by previous stabilization approaches is abandoned. Simulation...

Patchy Vector Fields and Asymptotic Stabilization

Fabio Ancona, Alberto Bressan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on ℝ n . We first introduce a family of discontinuous, piecewise smooth vector fields and derive a number of properties enjoyed by solutions of the corresponding O.D.E's. We then define a class of “patchy feedbacks” which are obtained by patching together a locally finite family of smooth controls. Our main result shows that, if a system is asymptotically controllable at the origin,...

Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control

Y. Kanevsky, A.A. Nepomnyashchy (2010)

Mathematical Modelling of Natural Phenomena

A global feedback control of a system that exhibits a subcritical monotonic instability at a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zero mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero mode. The method based on a variational principle is applied for the derivation of a low-dimensional evolution model. In the framework of this model the investigation of the system’s dynamics...

Positivity and stabilization of 2D linear systems

Tadeusz Kaczorek (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The problem of finding a gain matrix of the state-feedback of 2D linear system such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that the problem can be reduced to suitable linear programming problem. The proposed approach can be extended to 2D linear system described by the 2D Roesser model.

Positivity and stabilization of fractional 2D linear systems described by the Roesser model

Tadeusz Kaczorek, Krzysztof Rogowski (2010)

International Journal of Applied Mathematics and Computer Science

A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation...

Proper feedback compensators for a strictly proper plant by polynomial equations

Frank Callier, Ferdinand Kraffer (2005)

International Journal of Applied Mathematics and Computer Science

We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction...

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