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Monomial subdigraphs of reachable and controllable positive discrete-time systems

Rafael Bru, Louis Caccetta, Ventsi Rumchev (2005)

International Journal of Applied Mathematics and Computer Science

A generic structure of reachable and controllable positive linear systems is given in terms of some characteristic components (monomial subdigraphs) of the digraph of a non-negative a pair. The properties of monomial subdigraphs are examined and used to derive reachability and controllability criteria in a digraph form for the general case when the system matrix may contain zero columns. The graph-theoretic nature of these criteria makes them computationally more efficient than their known equivalents....

Monotone optimal policies in discounted Markov decision processes with transition probabilities independent of the current state: existence and approximation

Rosa María Flores-Hernández (2013)

Kybernetika

In this paper there are considered Markov decision processes (MDPs) that have the discounted cost as the objective function, state and decision spaces that are subsets of the real line but are not necessarily finite or denumerable. The considered MDPs have a cost function that is possibly unbounded, and dynamic independent of the current state. The considered decision sets are possibly non-compact. In the context described, conditions to obtain either an increasing or decreasing optimal stationary...

Monotonicity of minimizers in optimization problems with applications to Markov control processes

Rosa M. Flores–Hernández, Raúl Montes-de-Oca (2007)

Kybernetika

Firstly, in this paper there is considered a certain class of possibly unbounded optimization problems on Euclidean spaces, for which conditions that permit to obtain monotone minimizers are given. Secondly, the theory developed in the first part of the paper is applied to Markov control processes (MCPs) on real spaces with possibly unbounded cost function, and with possibly noncompact control sets, considering both the discounted and the average cost as optimality criterion. In the context described,...

Motion planning and feedback control for a unicycle in a way point following task: The VFO approach

Maciej Michałek, Krzysztof Kozłowski (2009)

International Journal of Applied Mathematics and Computer Science

This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization stage are considered. The way point following task is determined by the user-defined sequence of waypoints which have to be passed by the unicycle with the assumed finite precision. This sequence will take the vehicle from the initial state to the target state in finite time. The motion planning strategy proposed in the paper does not involve any interpolation...

Motion planning, equivalence, infinite dimensional systems

Pierre Rouchon (2001)

International Journal of Applied Mathematics and Computer Science

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, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems...

Motion planning for a class of boundary controlled linear hyperbolic PDE’s involving finite distributed delays

Frank Woittennek, Joachim Rudolph (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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 for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays

Frank Woittennek, Joachim Rudolph (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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 ...

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.

Multiphase and Multiscale Trends in Cancer Modelling

L. Preziosi, A. Tosin (2009)

Mathematical Modelling of Natural Phenomena

While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models.

Currently displaying 121 – 140 of 148