Multilevel control by duality

Umberto Biccari, Enrique ZuazuaMultilevel control by duality (2023) Systems & Control Letters, Vol. 175, 105-502,

Abstract. We discuss the multilevel control problem for linear dynamical systems, consisting in designing a piece-wise constant control function taking values in a finite-dimensional set. In particular, we provide a complete characterization of multilevel controls through a duality approach, based on the minimization of a suitable cost functional. In this manner we build optimal multi-level controls and characterize the time needed for a given ensemble of levels to assure the controllability of the system. Moreover, this method leads to efficient numerical algorithms for computing multilevel controls.

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arxiv: 2109.02346