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 Stochastic differential equations in infinite dimensional Hilbert space and its optimal control problem with Lévy processes

2021 ◽  
Vol 7 (2) ◽  
pp. 2427-2455
Author(s):  
Meijiao Wang ◽  
◽  
Qiuhong Shi ◽  
Maoning Tang ◽  
Qingxin Meng ◽  
...  
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
Teugels Martingales

<abstract><p>The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugels martingales which are more general processes and the corresponding optimal control problems. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see Nualart and Schoutens <sup>[<xref ref-type="bibr" rid="b21">21</xref>]</sup>). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classic convex variation method and dual techniques. The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.</p></abstract>

Optimal Control Of A Bilinear System Subjected To A Quadratic Cost Function Using Lie Algebra

1987 ◽  
pp. 49-55
Author(s):  
Hishamuddin Jamaluddin
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Lie Algebra ◽  
Bilinear System ◽  
System Matrice ◽  
Cost Functional ◽  
Quadratic Cost ◽  
Quadratic Cost Function

Optimal control for a Biliner System subjected to a quadratic cost functional was derived by applying Lie Algerbra. Interesting results were obtained when the system matrice commute and when the Lie sub-algebra generated by the system matrices is nilpotent.

An Optimal Control Problem with a Mixed Cost Function

1993 ◽  
Vol 31 (3) ◽  
pp. 624-645 ◽  
Author(s):  
V. I. Korobov ◽  
V. I. Krutin’ ◽  
G. M. Sklyar
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cost Function

scholarly journals The Dubovitskii and Milyutin Methodology Applied to an Optimal Control Problem Originating in an Ecological System

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 479
Author(s):  
Aníbal Coronel ◽  
Fernando Huancas ◽  
Esperanza Lozada ◽  
Marko Rojas-Medar
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Cost Function ◽  
Ecological Model ◽  
Control Function ◽  
Semigroup Theory ◽  
Reaction Diffusion ◽  
Functional Responses ◽  
Adjoint State

We research a control problem for an ecological model given by a reaction–diffusion system. The ecological model is given by a nonlinear parabolic PDE system of three equations modelling the interaction of three species by considering the standard Lotka-Volterra assumptions. The optimal control problem consists of the determination of a coefficient such that the population density of predator decreases. We reformulate the control problem as an optimal control problem by introducing an appropriate cost function. Then, we introduce and prove three types of results. A first contribution of the paper is the well-posedness framework of the mathematical model by considering that the interaction of the species is given by a general functional responses. Second, we study the differentiability properties of a cost function. The third result is the existence of optimal solutions, the existence of an adjoint state, and a characterization of the control function. The first result is proved by the application of semigroup theory and the second and third result are proved by the application of Dubovitskii and Milyutin formalism.

scholarly journals EFFECT OF RISK-SENSITIVE STOCHASTIC OPTIMAL CONTROL WITH TRACKING IN AN EVAPORATOR

2022 ◽  
Vol 11 (1) ◽  
pp. [12 P]-[12 P]
Author(s):  
María Aracelia Alcorta García ◽  
SANTOS MENDEZ DIAZ ◽  
JOSE ARMANDO SAENZ ESQUEDA ◽  
GERARDO MAXIMILIANO MENDEZ DIAZ ◽  
NORA ELIZONDO VILLAREAL ◽  
...  
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
State Equation ◽  
The State ◽  
Quadratic Cost ◽  
Risk Sensitive ◽  
Stochastic Nonlinear System ◽  
Expansion Valve ◽  
Risk Sensitive Control ◽  
Quadratic Cost Function

This work presents an application of the Risk-Sensitive (R-S) control with tracking applied to a stochastic nonlinear system which models the operation of an electronic expansion valve (EEV) in a conventional evaporator. A novel dynamical stochastic equation represents the mathematical model of the evaporator system. The R-S stochastic optimal problem consists of the design of an optimal control u(t) such that the state reaches setpoint values (SP) and minimizes the exponential quadratic cost function. The presence of disturbances and errors in the sensor measurements is represented by Gauss white noise in the state equation, with the coefficient v(e/(2?^2 )) . One novel characteristic in this proposal is that the coefficient of the control into the state equation contains the state term. The error and exponential quadratic cost function show that the R-S control has a better performance versus the classical PID (Proportional, Integral Derivative) control. Key Words: Optimal Risk-Sensitive control with tracking, modelling of the evaporator.

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