Optimal Control for Problems with a Quadratic Cost Functional on the Therapeutic Agents

2015 ◽  
pp. 141-170
Author(s):  
Heinz Schättler ◽  
Urszula Ledzewicz
Keyword(s):  
Optimal Control ◽  
Therapeutic Agents ◽  
Cost Functional ◽  
Quadratic Cost

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.

BILINEAR OPTIMAL CONTROL FOR A WAVE EQUATION

1999 ◽  
Vol 09 (01) ◽  
pp. 45-68 ◽  
Author(s):  
MIN LIANG
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Optimality System ◽  
Cost Functional ◽  
Quadratic Cost ◽  
Uniqueness Of The Solution ◽  
Initial Boundary Value ◽  
The Cost

We consider the problem of optimal control of a wave equation. A bilinear control is used to bring the state solutions close to a desired profile under a quadratic cost of control. We establish the existence of solutions of the underlying initial boundary-value problem and of an optimal control that minimizes the cost functional. We derive an optimality system by formally differentiating the cost functional with respect to the control and evaluating the result at an optimal control. We establish existence and uniqueness of the solution of the optimality system and thus determine the unique optimal control in terms of the solution of the optimality system.

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