scholarly journals Modified Fletcher-Reeves and Dai-Yuan Conjugate Gradient Methods for Solving Optimal Control Problem of Monodomain Model

2012 ◽  
Vol 03 (08) ◽  
pp. 864-872 ◽  
Author(s):  
Kin Wei Ng ◽  
Ahmad Rohanin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Monodomain Model

scholarly journals Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Kin Wei Ng ◽  
Ahmad Rohanin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conjugate Gradient ◽  
Optimization Problem ◽  
Numerical Solutions ◽  
Gradient Methods ◽  
Parabolic Partial Differential Equation ◽  
Conjugate Gradient Methods ◽  
Monodomain Model

We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY) method and the Liu-Storey-Conjugate-Descent (LS-CD) method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.

scholarly journals Optimal Control of the Cascaded Kainji-Jebba Hydroelectric Power Station Based on Conjugate Gradient

2019 ◽  
Vol 18 (3) ◽  
pp. 1-7
Author(s):  
Olalekan Ogunbiyi ◽  
Cornelius T. Thomas ◽  
Isaac O. A. Omeiza ◽  
Jimoh Akanni ◽  
Benjamin J. Olufeagba
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conjugate Gradient ◽  
Gradient Algorithm ◽  
Hydroelectric Power Station ◽  
Hydroelectric Power ◽  
Power Station ◽  
The Government ◽  
Installed Capacity

Electricity supply in Nigeria has been far below the estimated demand and the installed capacity of the plants. Hence, there has been continuous research on improving the performance of the existing plants, but the government mainly focuses on increasing the installed capacity. This paper presents the determination of the optimal release of water to maximize the energy generation potential of the cascaded Kainji-Jebba hydroelectric power station in Nigeria. The problem was formulated as an optimal control problem with an objective of minimizing the deviation of the head of the Jebba reservoir within a set limit. A conjugate gradient algorithm was then used as a direct solution to the optimal control problem. The computed control law and the resulting state trajectories of 2% error affirm the solution to be genuine and reliable. The algorithm is recommended for use in the design of a real-time optimal controller for the system and a decision guide for the operators.

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