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.

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 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.

scholarly journals A Monge–Ampère Problem with Non-quadratic Cost Function to Compute Freeform Lens Surfaces

2019 ◽  
Vol 80 (1) ◽  
pp. 475-499 ◽  
Author(s):  
N. K. Yadav ◽  
J. H. M. ten Thije Boonkkamp ◽  
W. L. IJzerman
Keyword(s):  
Cost Function ◽  
Quadratic Cost ◽  
Monge Ampere ◽  
Quadratic Cost Function ◽  
Freeform Lens
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