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Motion planning and boundary control for a class of linear PDEs with constant coefficients is presented. With the proposed method transitions from rest to rest can be achieved in a prescribed finite time. When parameterizing the system by a flat output, the system trajectories can be calculated from the flat output trajectory by evaluating definite convolution integrals. The compact kernels of the integrals can be calculated using infinite series. Explicit formulae are derived employing Mikusiński’s...
Motion planning and boundary control for a class of linear PDEs with
constant coefficients is presented. With the proposed method transitions
from rest to rest can be achieved in a prescribed finite time. When
parameterizing the system by a flat output, the system trajectories can be
calculated from the flat output trajectory by evaluating definite
convolution integrals. The compact kernels of the integrals can be
calculated using infinite series. Explicit formulae are derived employing
...
In this paper we consider a free boundary problem for a nonlinear parabolic partial differential equation. In particular, we are concerned with the inverse problem, which means we know the behavior of the free boundary a priori and would like a solution, e.g. a convergent series, in order to determine what the trajectories of the system should be for steady-state to steady-state boundary control. In this paper we combine two issues: the free boundary (Stefan) problem with a quadratic nonlinearity....
In this paper we consider a free boundary problem for a nonlinear
parabolic partial differential equation. In particular, we are
concerned with the inverse problem, which means we know the
behavior of the free boundary a priori and would like a solution,
e.g. a convergent series, in order to determine what the
trajectories of the system should be for steady-state to
steady-state boundary control. In this paper we combine two
issues: the free boundary (Stefan) problem with a quadratic
nonlinearity....
In this paper, an extension of the Lafferriere-Sussmann algorithm of motion planning for driftless nilpotent control systems is analyzed. It is aimed at making more numerous admissible representations of motion in the algorithm. The representations allow designing a shape of trajectories joining the initial and final configuration of the motion planning task. This feature is especially important in motion planning in a cluttered environment. Some natural functions are introduced to measure the shape...
In this paper, we introduce several system theoretic problems brought forward by recent studies on neural models of motor control. We focus our attention on three topics: (i) the cerebellum and adaptive control, (ii) reinforcement learning and the basal ganglia, and (iii) modular control with multiple models. We discuss these subjects from both neuroscience and systems theory viewpoints with the aim of promoting interplay between the two research communities.
The problem of designing realistic decentralized controller to solve a servomechanism problem in the framework of “large scale systems” is considered in this paper. As any large scale system is built by expanding construction of one subsystem being connected to the existing system. In particular, it is desired to find a local stabilizing controller in terms of a free parameter (belonging to the ring of proper stable transfer functions) so that desirable properties of the controlled system, such...
In this work, we propose a methodology for the expression of necessary and
sufficient Lyapunov-like conditions for the existence of stabilizing
feedback laws. The methodology is an extension of the well-known Control
Lyapunov Function (CLF) method and can be applied to very general nonlinear
time-varying systems with disturbance and control inputs, including both
finite and infinite-dimensional systems. The generality of the proposed
methodology is also reflected upon by the fact that partial...
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