Optimal control of some hyperbolic equations with missing data
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Date
2018
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university of Oum- El- Bouaghi
Abstract
The objective of this thesis is to study the optimal control of distributed systems with incompletedata, particularly distributed hyperbolic systems. No-regret control or equivalently Pareto controlare used by J. L. Lions to solve the optimal control problems associated with distributed systemswith incomplete data. Averaged control was introduced recently by Zauazua to control systemsdepending upon an unknown parameter.
We present some distributed systems with missing data, we control them via no-regret controland low-regret control methods, and we obtain some optimality systems that characterize theoptimum.
The main idea in our work is to apply the notions of no-regret control and averaged control to ahyperbolic equation with unknown parameter and a missing boundary condition. The consideredmodel is motivated by an application in biomedicine. We have introduced the notion of averagedno-regret control to control distributed systems with two kinds of incomplete data, on contrarywith previous works, where authors have considered only one kind of missing data. The averagedno-regret control will be characterized by an optimality system.
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Keywords
Optimal control, Pareto control, Hyperbolic equation