An optimal control problem with piecewise quadratic cost functional containing a ‘dead-zone’

1980 ◽  
Vol 1 (4) ◽  
pp. 361-372 ◽  
Author(s):  
Mahmut Parlar ◽  
R. G. Vickson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Dead Zone ◽  
Cost Functional ◽  
Quadratic Cost

scholarly journals Optimal problem of cost function for the linear neutral systems

2001 ◽  
Vol 25 (12) ◽  
pp. 777-785
Author(s):  
Jong Yeoul Park ◽  
Yong Han Kang
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cost Function ◽  
Optimal Condition ◽  
Neutral Type ◽  
Neutral Systems ◽  
Quadratic Cost ◽  
Quadratic Cost Function

We study the optimal control problem of a system governed by linear neutral type in Hilbert spaceX. We investigate optimal condition for quadratic cost function and as applications, we give some examples.

scholarly journals Solution to an Optimal Control Problem via Canonical Dual Method

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Jinghao Zhu ◽  
Jiani Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Analytic Solution ◽  
Dual Method ◽  
Cost Functional ◽  
Nonconvex Problem ◽  
Pontryagin Principle ◽  
Dual Variables ◽  
The Cost

The analytic solution to an optimal control problem is investigated using the canonical dual method. By means of the Pontryagin principle and a transformation of the cost functional, the optimal control of a nonconvex problem is obtained. It turns out that the optimal control can be expressed by the costate via canonical dual variables. Some examples are illustrated.

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.

Convexity of the cost functional in an optimal control problem for a class of positive switched systems

Automatica ◽  
2014 ◽  
Vol 50 (4) ◽  
pp. 1227-1234 ◽  
Author(s):  
Patrizio Colaneri ◽  
Richard H. Middleton ◽  
Zhiyong Chen ◽  
Danilo Caporale ◽  
Franco Blanchini
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Switched Systems ◽  
Cost Functional ◽  
Positive Switched Systems ◽  
The Cost

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.

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