scholarly journals The turnpike property in semilinear control

2021 ◽  
Author(s):  
Dario Pighin
Keyword(s):  
Control Problem ◽  
Numerical Simulations ◽  
Time Evolution ◽  
The State ◽  
Turnpike Property

An exponential turnpike property for a semilinear control problem is proved. The state-target is assumed to be small, whereas the initial datum can be arbitrary.   Turnpike results are also obtained for large targets, requiring that the control acts everywhere. In this case, we prove the convergence of the infimum of the averaged time-evolution functional towards the steady one.   Numerical simulations are performed.

scholarly journals Ana posteriorierror analysis for an optimal control problem with point sources

2018 ◽  
Vol 52 (5) ◽  
pp. 1617-1650 ◽  
Author(s):  
Alejandro Allendes ◽  
Enrique Otárola ◽  
Richard Rankin ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weighted Sobolev Spaces ◽  
Control Variable ◽  
The State ◽  
Point Sources ◽  
Adjoint Equations ◽  
Error Estimator ◽  
A Posteriori

We propose and analyze a reliable and efficienta posteriorierror estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposeda posteriorierror estimator is defined as the sum of two contributions, which are associated with the state and adjoint equations. The estimator associated with the state equation is based on Muckenhoupt weighted Sobolev spaces, while the one associated with the adjoint is in the maximum norm and allows for unbounded right hand sides. The analysis is valid for two and three-dimensional domains. On the basis of the deviseda posteriorierror estimator, we design a simple adaptive strategy that yields optimal rates of convergence for the numerical examples that we perform.

STERILIZATION OF CANNED VISCOUS FOODS: AN OPTIMAL CONTROL APPROACH

2004 ◽  
Vol 14 (03) ◽  
pp. 355-374 ◽  
Author(s):  
L. J. ALVAREZ-VAZQUEZ ◽  
M. MARTA ◽  
A. MARTINEZ
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Nutrient Retention ◽  
Reaction Diffusion ◽  
The State ◽  
Reaction Diffusion Equations ◽  
Boussinesq System ◽  
Temperature Dependent Viscosity ◽  
Control Approach ◽  
Dependent Viscosity

In this paper, we study an optimal control problem with pointwise constraints on state and control, related to sterilization processes involving heat transfer by natural convection. We introduce the mathematical model for the state system, which couples the Boussinesq system for temperature-dependent viscosity and the convection-reaction-diffusion equations, and we set the whole problem as a control problem, assuring the micro-organism reduction, the nutrient retention and the energy saving. The existence and the regularity of the state are studied. Finally, we obtain existence results for the optimal solutions and a first-order optimality condition for their characterization.

scholarly journals Saga of Superfluid Solids

Physics ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 49-66 ◽  
Author(s):  
Vyacheslav I. Yukalov
Keyword(s):  
Numerical Simulations ◽  
State Of The Art ◽  
Theoretical Models ◽  
The State ◽  
Experimental Results ◽  
Standing Problem

The article presents the state of the art and reviews the literature on the long-standing problem of the possibility for a sample to be at the same time solid and superfluid. Theoretical models, numerical simulations, and experimental results are discussed.

Propagation of bursting oscillations

2009 ◽  
Vol 367 (1908) ◽  
pp. 4863-4875 ◽  
Author(s):  
Benjamin Ambrosio ◽  
Jean-Pierre Françoise
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Time Evolution ◽  
Global Attractor ◽  
Reaction Diffusion ◽  
Functional Space ◽  
Excitable Cells ◽  
Diffusion Type ◽  
Bursting Oscillations

We investigate a system of partial differential equations of reaction–diffusion type which displays propagation of bursting oscillations. This system represents the time evolution of an assembly of cells constituted by a small nucleus of bursting cells near the origin immersed in the middle of excitable cells. We show that this system displays a global attractor in an appropriated functional space. Numerical simulations show the existence in this attractor of recurrent solutions which are waves propagating from the central source. The propagation seems possible if the excitability of the neighbouring cells is above some threshold.

Estimating the structure of small dynamical networks from the state time evolution of one node

2013 ◽  
Vol 87 (1) ◽  
Author(s):  
Raffaele Autariello ◽  
Rhonda Dzakpasu ◽  
Francesco Sorrentino
Keyword(s):  
Time Evolution ◽  
The State ◽  
Dynamical Networks ◽  
State Time

Unconstrained and Constrained Control for a Tentacle Manipulator

2004 ◽  
Author(s):  
Mircea Ivanescu
Keyword(s):  
Control Problem ◽  
Numerical Simulations ◽  
Potential Method ◽  
Constrained Control ◽  
Constrained Motion ◽  
Controlled System ◽  
Differential Model

The control problem of the spatial tentacle manipulator is presented. In order to avoid the difficulties generated by the complexity of the nonlinear integral - differential model, the control problem is based by the artificial potential method. It is shown that the control of a tentacle robot to a desired position it is possible if the artificial potential is a potential functional whose point of minimum is attractor of this dissipative controlled system. Then, the method is used for constrained motion in an environment with obstacles. Numerical simulations for spatial and planar tentacle models are presented in order to illustrate the efficiency of the method.

scholarly journals Dynamic Analysis of a Two-Language Competitive Model with Control Strategies

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Lin-Fei Nie ◽  
Zhi-Dong Teng ◽  
Juan J. Nieto ◽  
Il Hyo Jung
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Positive Order ◽  
State Dependent ◽  
Competitive Model ◽  
The Impact

The dynamic behavior of a two-language competitive model is analyzed systemically in this paper. By the linearization and the Bendixson-Dulac theorem on dynamical system, some sufficient conditions on the globally asymptotical stability of the trivial equilibria and the existence and the stability of the positive equilibrium of this model are presented. Nextly, in order to protect the endangered language, an optimal control problem relative to this model is explored. We derive some necessary conditions to solve the optimal control problem and present some numerical simulations using a Runge-Kutta fourth-order method. Finally, the languages competitive model is extended to this model assessing the impact of state-dependent pulse control strategy. Using the Poincaré map, differential inequality, and method of qualitative analysis, we prove the existence and stability of positive order-1 periodic solution for this control model. Numerical simulations are carried out to illustrate the main results and the feasibility of state-dependent impulsive control strategy.

Steady-State Optimal State and Input Observer for Discrete Stochastic Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Y. Park ◽  
J. L. Stein
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Stochastic Systems ◽  
Linear Time ◽  
The State ◽  
Optimal State ◽  
Unknown Inputs ◽  
Linear Time Invariant ◽  
Error Covariance ◽  
Time Invariant

Model-based machine diagnostics techniques require the modeled states and machine inputs to be measured. Because measurement of all the states and inputs is not always possible or practical, a simultaneous state and input observer is required. Previous work has developed this type of acausal observer and shown it is susceptible to noise. This paper develops a steady-state optimal observer that minimizes the trace of the steady-state error covariance of the state and input estimates for discrete, linear, time-invariant, stochastic systems with unknown inputs. In addition, a method to distinguish the best measurement set among the available measurement sets is developed. Results from numerical simulations show that the optimal observer can greatly improve estimation results in some cases.

COLLAPSE AND REVIVAL EFFECT IN A MESOSCOPIC LC CIRCUIT

2004 ◽  
Vol 18 (08) ◽  
pp. 1217-1224 ◽  
Author(s):  
HAI-MEI LUO ◽  
YING-HUA JI ◽  
JIE LIU
Keyword(s):  
Time Evolution ◽  
Dynamic Behavior ◽  
Quantum State ◽  
Tunnel Junction ◽  
Coherent States ◽  
The State ◽  
Quantum States ◽  
Quantum Superposition ◽  
Coupling Energy ◽  
Lc Circuit

This paper studied the time evolution of quantum state in a mesoscopic LC circuit with the coupling energy caused by mesoscopic capacitor acting as a tunnel junction. It indicates that the state of the junction evolves into the quantum superposition of two coherent states and, in the state, nonclassical squeezing properties of the circuit appear. It also indicates that the dynamic behavior of the current shows collapse and revival phenomenon. The research in the paper will be helpful to miniaturize integrate circuits and electric components. It will be also important for the utilization of mesoscopic circuits to evolve the quantum states, which work as information carriers.

scholarly journals Simulation of a high-brightness, hard X-ray source based on high-intensity interaction of ultra-short laser pulses with high-Z targets

1997 ◽  
Vol 15 (1) ◽  
pp. 139-143
Author(s):  
V.A. Lykov ◽  
V.E. Chernyakov ◽  
Ya.Z. Kandiev ◽  
I.A. Litvinenko ◽  
V.G. Nikolaev
Keyword(s):  
Angular Distribution ◽  
Numerical Simulations ◽  
Electromagnetic Fields ◽  
High Intensity ◽  
Laser Pulses ◽  
The State ◽  
High Brightness ◽  
Fast Electrons ◽  
X Ray ◽  
Short Laser Pulses

The results of numerical simulations of fast electrons interaction with matter, calculated yield and angular distribution of bremsstrahlung and fluorescence K-α X-ray radiation and generation of electromagnetic fields, carried out by ERA, PM2D, and PRIZMA codes for the state of experiments on interaction of ultra-short laser pulses with high-Z targets at intensity of 1016−1018 W/cm2 are presented. Spherical targets with conical hollows and conical targets of high-Z matter are proposed for experiments with picosecond lasers to increase the brightness of hard X-ray sources.

Sign in / Sign up

Export Citation Format

Share Document