A finite dimensional optimal control problem in inverse acoustics applications

2002 ◽  
Author(s):  
G. Crosta
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Finite Dimensional

scholarly journals OptiDose: Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control

2021 ◽  
Author(s):  
Freya Bachmann ◽  
Gilbert Koch ◽  
Marc Pfister ◽  
Gabor Szinnai ◽  
Johannes Schropp
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Disease Progression ◽  
Dosing Regimen ◽  
Reference Function ◽  
Cost Functional ◽  
Finite Dimensional ◽  
Optimal Dosing ◽  
The Cost

AbstractProviding the optimal dosing strategy of a drug for an individual patient is an important task in pharmaceutical sciences and daily clinical application. We developed and validated an optimal dosing algorithm (OptiDose) that computes the optimal individualized dosing regimen for pharmacokinetic–pharmacodynamic models in substantially different scenarios with various routes of administration by solving an optimal control problem. The aim is to compute a control that brings the underlying system as closely as possible to a desired reference function by minimizing a cost functional. In pharmacokinetic–pharmacodynamic modeling, the controls are the administered doses and the reference function can be the disease progression. Drug administration at certain time points provides a finite number of discrete controls, the drug doses, determining the drug concentration and its effect on the disease progression. Consequently, rewriting the cost functional gives a finite-dimensional optimal control problem depending only on the doses. Adjoint techniques allow to compute the gradient of the cost functional efficiently. This admits to solve the optimal control problem with robust algorithms such as quasi-Newton methods from finite-dimensional optimization. OptiDose is applied to three relevant but substantially different pharmacokinetic–pharmacodynamic examples.

An Improved DMOC Method with Gradient Penalty Term

2014 ◽  
Vol 945-949 ◽  
pp. 2784-2787
Author(s):  
Lei Gao ◽  
Jie Yu Ding
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Control ◽  
Penalty Term ◽  
Cost Functional ◽  
Finite Dimensional ◽  
Total Gradient ◽  
Control Forces ◽  
Stable Control

An efficient method aimed at smooth and stable control forces for optimal control problem is described. Based on the native discrete mechanics and optimal control (DMOC) method, which focus mainly on the minimization of the total control forces, a gradient penalty term is introduced to cost functional to smooth the control forces. Then vibration of control forces is overcome by limiting the total gradient of the discrete control forces. With suitable discrete cost functional and constraints, the continuous optimal control problem is transformed to an equally finite dimensional form, which can be easily solved by standard algorithms. Finally, the numerical example of orbit transferring shows the effectiveness of the improved method.

scholarly journals Resolution of a Linear-quadratic Optimal Control Problem Based on Finite-dimensional Models

2021 ◽  
Vol 37 ◽  
pp. 3-16
Author(s):  
V.A. Srochko ◽  
◽  
E.V. Aksenyushkina ◽  
V.G. Antonik ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Regularization Parameter ◽  
Convexity Property ◽  
Dimensional Model ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Finite Dimensional ◽  
Quadratic Optimal Control

We consider a linear-quadratic optimal control problem with indefinite matrices and the interval control constraint. The problem also has a regularizationparameter in the functional. The approximate solution of the problem is carried out on subsets of admissible controls, which are formed using linear combinations of special functions with an orientation to the optimal control structure due to the maximum principle. As a result of this procedure, a finite-dimensional quadratic optimization problem with the interval constraint on variables is obtained. The following relations between the variational problem and its finite-dimensional model are established: the convexity property of the optimal control problem is preserved for finite-dimensional model; a nonconvex optimal control problem under a certain condition on the regularization parameter (estimate from below) is approximated by a convex quadratic problem, which is solved in a finite number of operations;a special non-convex optimal control problem with an upper bound on the regularization parameter passes into the problem of minimizing a concave function on a finite set of points. A special case of a non-convex optimal control problem for the maximum of the norm of the final state is distinguished. Two procedures for improving the extreme points of finite-dimensional model are constructed, which reduce the computational costs for the global solution of the problem within the framework of the linearization method.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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