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Motion planning for a nonlinear Stefan problem

William B. Dunbar, Nicolas Petit, Pierre Rouchon, Philippe Martin (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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....

Motion Planning for a nonlinear Stefan Problem

William B. Dunbar, Nicolas Petit, Pierre Rouchon, Philippe Martin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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....

Motion representations for the Lafferriere-Sussmann algorithm for nilpotent control systems

Ignacy Dulęba, Jacek Jagodziński (2011)

International Journal of Applied Mathematics and Computer Science

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...

Motor control neural models and systems theory

Kenji Doya, Hidenori Kimura, Aiko Miyamura (2001)

International Journal of Applied Mathematics and Computer Science

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.

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