Search results for "Optimal control"

Opinion dynamics, stubbornness and mean-field games

2014

This paper studies opinion dynamics and stubbornness using mean-field game theory. Assuming an initial exponential density function and affine control policies we analyze under what conditions the Fokker-Planck equation returns an exponential density function over the horizon. Consensus and clusters formation are also studied.

A Nonlinear Circulatory Model for Artificial Heart Studies

1983

Animals with total artificial heart replacement (TAH) have survived for up to 9 months with manually controlled driving systems. A certain physiological control is provided by the animals intact peripheral regulation resulting in pathological venous hemodynamics, expressing the needs for a technical automatic control system, replacing the natural sympathetic stimulation and Starlings Law of the heart. A nonlinear dynamic mathematical model of the human cardiovascular system (CVSM) containing the systemic and pulmonary components was outlined and verified, which is employable to analyse the hemodynamic behaviour under normal and abnormal states. By modifying this model, assuming that cardiac…

CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS

2018

We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…

Digital control circuitry for the p53 dynamics in cancer cell and apoptosis

2010

Abstract Experimental work and theoretical models deduce a “digital” response of the p53 transcription factor when genomic integrity is damaged. The mutual influence of p53 and its antagonist, the Mdm2 oncogene, is closed in a feedback. This paper proposes an aerospace-based architecture for translating the p53/Mdm2/DNA damage network into a digital circuitry in which the optimal control theory is applied for obtaining the requested dynamic evolutions of some considered cell species for repairing a DNA damage. The purpose of this paper is to demonstrate the usefulness of such digital circuitry design to detect and predict the cell species dynamics for shedding light on their inner and mutua…

Casting Robotic end-effectors to reach far objects in space and planetary missions

2006

In this paper we present work aimed at developing a compact robotic device able to reach objects at far distance.The work is based on the idea of casting manipulation, and that allows to deploy an end-effector at large distances from the robot’s base by throwing (casting) it and controlling its ballistic flightusing forces transmitted through a light tether connected to the end-effector itself.

Special Functions for the Study of Economic Dynamics: The Case of the Lucas-Uzawa Model

2004

The special functions are intensively used in mathematical physics to solve differential systems. We argue that they should be most useful in economic dynamics, notably in the assessment of the transition dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of the variables in level. In contrast to the preexisting approaches, our method is global and does not rely on dimension reduction.

Optimal control of the Schrödinger equation with two or three levels

2007

In this paper, we present how techniques of “control theory”, “sub-Riemannian geometry” and “singular Riemannian geometry” can be applied to some classical problems of quantum mechanics and yield improvements to some previous results.

Real-time optimal control of water distribution systems - Models and techniques, including intermittent supply conditions.

2014

Relaxation of a weakly discontinuous functional depending on one control function

2008

The paper considers an optimal control problem of the typewhere the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.