LMIs in Control/Applications/LMIforPiecewiseLinearHinfControllerSynthesisInIncentoryControl
This problem dealt with the inventory control problem for a deterministic production system with given deterministic demand rate plus an unknown fluctuating demand rate with finite energy whose bound is known.
The System edit
Given a state-space representation of a system and an initial estimate of reduced order model .
Where .
The Data edit
The full order state matrices .
The Optimization Problem edit
This problem has been modeled as a control problem of a switched (PWA) system and it has been solved using new results on piecewise-linear control theory.
The LMI: edit
Objective: .
Subject to::
where
for
Conclusion: edit
The resulting matrices allow us to construct a state feedback controller that forces the stock level to be kept close to zero (sometimes called a just-in-time policy), even when there are fluctuations in the demand of the product.
Implementation: edit
- [1] - example
External Links edit
A list of references documenting and validating the LMI.
- [2] Rodrigues, Boukas. “Piecewise-Linear H ∞ Controller Synthesis with Applications to Inventory Control of Switched Production Systems.” Automatica (Oxford), vol. 42, no. 8, Elsevier Ltd, 2006, pp. 1245–54, doi:10.1016/j.automatica.2006.04.004.