Optimal control problem for the time-dependent Kirchhoff–Love plate in a domain with rough boundary

2013 ◽  
Vol 81 (3-4) ◽  
pp. 337-355 ◽  
Author(s):  
Ravi Prakash
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Dependent ◽  
Rough Boundary

scholarly journals Optimal control theory with general constraints

1981 ◽  
Vol 23 (2) ◽  
pp. 115-126 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Time Dependent ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
General Constraints ◽  
Elementary Methods ◽  
And Control

AbstractWe consider an optimal control problem with, possibly time-dependent, constraints on state and control variables, jointly. Using only elementary methods, we derive a sufficient condition for optimality. Although phrased in terms reminiscent of the necessary condition of Pontryagin, the sufficient condition is logically independent, as can be shown by a simple example.

scholarly journals POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Maria Strazzullo ◽  
Francesco Ballarin ◽  
Gianluigi Rozza
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Order Reduction ◽  
Time Dependent ◽  
Shallow Waters ◽  
Control Problems ◽  
Reduced Order ◽  
Low Dimensional

Abstract In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by Shallow Waters Equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by Shallow Waters Equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

scholarly journals A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Qingjin Xu ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discontinuous Galerkin ◽  
Mixed Finite Element ◽  
Galerkin Approximation ◽  
Control Variable ◽  
The State ◽  
Time Dependent ◽  
Convection Diffusion

In this paper, we investigate a mixed discontinuous Galerkin approximation of time dependent convection diffusion optimal control problem with control constraints based on the combination of a mixed finite element method for the elliptic part and a discontinuous Galerkin method for the hyperbolic part of the state equation. The control variable is approximated by variational discretization approach. A priori error estimates of the state, adjoint state, and control are derived for both semidiscrete scheme and fully discrete scheme. Numerical example is given to show the effectiveness of the numerical scheme.

scholarly journals Transmission Dynamics and Optimal Control of Malaria in Kenya

2016 ◽  
Vol 2016 ◽  
pp. 1-27 ◽  
Author(s):  
Gabriel Otieno ◽  
Joseph K. Koske ◽  
John M. Mutiso
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Endemic Equilibrium ◽  
Time Dependent ◽  
Transmission Dynamics ◽  
Bed Nets ◽  
Feasible Region ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable

This paper proposes and analyses a mathematical model for the transmission dynamics of malaria with four-time dependent control measures in Kenya: insecticide treated bed nets (ITNs), treatment, indoor residual spray (IRS), and intermittent preventive treatment of malaria in pregnancy (IPTp). We first considered constant control parameters and calculate the basic reproduction number and investigate existence and stability of equilibria as well as stability analysis. We proved that ifR0≤1, the disease-free equilibrium is globally asymptotically stable inD. IfR0>1, the unique endemic equilibrium exists and is globally asymptotically stable. The model also exhibits backward bifurcation atR0=1. IfR0>1, the model admits a unique endemic equilibrium which is globally asymptotically stable in the interior of feasible regionD. The sensitivity results showed that the most sensitive parameters are mosquito death rate and mosquito biting rates. We then consider the time-dependent control case and use Pontryagin’s Maximum Principle to derive the necessary conditions for the optimal control of the disease using the proposed model. The existence of optimal control problem is proved. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that the optimal control strategy for malaria control in endemic areas is the combined use of treatment and IRS; for epidemic prone areas is the use of treatment and IRS; for seasonal areas is the use of treatment; and for low risk areas is the use of ITNs and treatment. Control programs that follow these strategies can effectively reduce the spread of malaria disease in different malaria transmission settings in Kenya.

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