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An Approximation of Minimax Control using Random Sampling and Symbolic Computation

Jawher Jerray 1 Laurent Fribourg 2 Étienne André 3, 4 
3 MOSEL - Proof-oriented development of computer-based systems
LORIA - FM - Department of Formal Methods
4 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : We aim at the synthesis of an approximate minimax control for a system dynamic given in the form x.(t) = f(x(t),u(t),d(t)) where x represents the state, u the control (or input) and d a disturbance (or perturbation). The disturbance d(t) is prescribed to a compact domain D on which it can take any value (bounded uncertainty). Our method makes use of symbolic computation to enclose the solutions corresponding to all possible disturbance d. in D, together with a simple algorithm of random sampling to select the minimum control u*. We illustrate the interest of this approximate minimax control on an example of a biochemical reactor.
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Contributor : Étienne André Connect in order to contact the contributor
Submitted on : Tuesday, September 14, 2021 - 8:13:33 AM
Last modification on : Friday, August 5, 2022 - 2:58:08 PM

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Jawher Jerray, Laurent Fribourg, Étienne André. An Approximation of Minimax Control using Random Sampling and Symbolic Computation. IFAC-PapersOnLine, Elsevier, 2021, Proceedings of the 7th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS 2021), 54 (5), pp.265-270. ⟨10.1016/j.ifacol.2021.08.509⟩. ⟨hal-03343147⟩

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