634 research outputs found
Optimal trajectory tracking
This thesis investigates optimal trajectory tracking of nonlinear dynamical
systems with affine controls. The control task is to enforce the system state
to follow a prescribed desired trajectory as closely as possible. The concept
of so-called exactly realizable trajectories is proposed. For exactly
realizable desired trajectories exists a control signal which enforces the
state to exactly follow the desired trajectory. For a given affine control
system, these trajectories are characterized by the so-called constraint
equation. This approach does not only yield an explicit expression for the
control signal in terms of the desired trajectory, but also identifies a
particularly simple class of nonlinear control systems. Based on that insight,
the regularization parameter is used as the small parameter for a perturbation
expansion. This results in a reinterpretation of affine optimal control
problems with small regularization term as singularly perturbed differential
equations. The small parameter originates from the formulation of the control
problem and does not involve simplifying assumptions about the system dynamics.
Combining this approach with the linearizing assumption, approximate and partly
linear equations for the optimal trajectory tracking of arbitrary desired
trajectories are derived. For vanishing regularization parameter, the state
trajectory becomes discontinuous and the control signal diverges. On the other
hand, the analytical treatment becomes exact and the solutions are exclusively
governed by linear differential equations. Thus, the possibility of linear
structures underlying nonlinear optimal control is revealed. This fact enables
the derivation of exact analytical solutions to an entire class of nonlinear
trajectory tracking problems with affine controls. This class comprises
mechanical control systems in one spatial dimension and the FitzHugh-Nagumo
model.Comment: 240 pages, 36 figures, PhD thesi
Oscillatory motion of a droplet in an active poroelastic two-phase model
We investigate flow-driven amoeboid motility as exhibited by microplasmodia
of Physarum polycephalum. A poroelastic two-phase model with rigid boundaries
is extended to the case of free boundaries and substrate friction. The
cytoskeleton is modeled as an active viscoelastic solid permeated by a fluid
phase describing the cytosol. A feedback loop between a chemical regulator,
active mechanical deformations, and induced flows gives rise to oscillatory and
irregular motion accompanied by spatio-temporal contraction patterns. We cover
extended parameter regimes of active tension and substrate friction by
numerical simulations in one spatial dimension and reproduce experimentally
observed oscillation periods and amplitudes. In line with experiments, the
model predicts alternating forward and backward ectoplasmatic flow at the
boundaries with reversed flow in the center. However, for all cases of periodic
and irregular motion, we observe practically no net motion. A simple
theoretical argument shows that directed motion is not possible with a
spatially independent substrate friction
Establishing user requirements for a mobile learning environment
This paper presents the rationale, challenges, successes and results of activities to establish the requirements for a mobile learning environment. The effort is part of a European-funded research and development project investigating context-sensitive approaches to informal, problem-based and workplace learning by using key advances in mobile technologies. The techniques used include user observation, participatory design workshops and questionnaires. Analytic techniques include UML and the Volere shell and template
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