An Approximation of Minimax Control using Random Sampling and Symbolic Computation
Résumé
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.
