Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

2 2001

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: infinite dimensional control systems

Sortuj według:

Ogranicz wyniki do:

Motion Planning, Equivalence, Infinite Dimensional Systems

Rouchon P.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 1

165-188

Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al., 1995; 1999a), motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function y, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems on Monge equations and equivalence investigated by Hilbert and Cartan. The study of several examples (the car with n-trailers and the non-holonomic snake, pendulums in series and the heavy chain, the heat equation and the Euler-Bernoulli flexible beam) indicates that the notion of flatness and its underlying explicit description can be extended to infinite-dimensional systems. As in the finite-dimensional case, this property yields simple motion planning algorithms via operators of compact support. For the non-holonomic snake, such operators involve non-linear delays. For the heavy chain, they are defined via distributed delays. For heat and Euler-Bernoulli systems, their supports are reduced to a point and their definition domain coincides with the set of Gevrey functions of order 2.

Circle criterion and boundary control systems in factor form: input-output approach

Grabowski P., Callier F. M.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 6

1387-1403

A circle criterion is obtained for a SISO Lur'e feedback control system consisting of a nonlinear static sector-type controller and a linear boundary control system in factor form on an infinite-dimensional Hilbert state space H previously introduced by the authors (Grabowski and Callier, 1999). It is assumed for the latter that (a) the observation functional is infinite-time admissible, (b) the factor control vector satisfies a compatibility condition, and (c) the transfer function belongs to Hinfty(Pi+) and satisfies a frequency-domain inequality of the circle criterion type. We also require that the closed-loop system be well-posed, i.e. for any initial state x0in H the truncated input and output signals uT, yT belong to L2(0,T) for any T>0. The technique of the proof adapts Desoer-Vidyasagar's circle criterion method (Desoer and Vidyasagar, 1975, Ch.3, Secs.1 and 2, pp.37-43, Ch.5, Sec.2, pp.139-142 and Ch.6, Secs.3 and 4, pp.172-174]), and uses the input-output map developed by the authors (Grabowski and Callier, 2001). The results are illustrated by two transmission line examples: (a) that of the loaded distortionless RLCG type, and (b) that of the unloaded RC type. The conclusion contains a discussion on improving the results by the loop-transformation technique.