Approximate closed-form solutions to finite-horizon optimal control of nonlinear systems

2012 ◽  
Author(s):  
A. Heydari ◽  
S. N. Balakrishnan
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Closed Form ◽  
Finite Horizon ◽  
Closed Form Solutions

scholarly journals Optimal Control of Nonsmooth Production Systems with Deteriorating Items, Stock-Dependent Demand, with or without Backorders

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 183
Author(s):  
Messaoud Bounkhel ◽  
Lotfi Tadj ◽  
Yacine Benhadid ◽  
Ramdane Hedjar
Keyword(s):  
Optimal Control ◽  
Dynamic System ◽  
Closed Form ◽  
Production Systems ◽  
Necessary Optimality Conditions ◽  
Optimal Production ◽  
Closed Form Solutions ◽  
Stock Dependent Demand ◽  
The Cost ◽  
Dependent Demand

We propose a nonsmooth dynamic system integrating production and inventory where the items may deteriorate and the demand is stock-dependent. We aim to derive the optimal production rate. In our first model, backorders are not allowed, while in the second model they are. Using optimal control, necessary optimality conditions are obtained for general forms of the cost, demand, and deterioration rates and closed form solutions are derived for specific forms of these rates. Numerical simulations are presented and sensitivity of the solutions are examined.

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