Data-Driven Finite-Time Control for Discrete-Time Linear Time-Invariant Systems

This paper studies the data-driven finite-time control (FTC) problem of unknown discrete-time linear time-invariant (LTI) systems with unknown and bounded noise. The proposed FTC aims to guarantee that the state of such a system does not exceed a given bound over a finite time interval under bounded initial conditions. Data-dependent representations are built for the unknown system without and with noise from pre-collected input/state data, based on which a finite-time controller is designed. Sufficient conditions of finite-time stability/boundness of the closed-loop system without/with noise are derived. Compared with model-based FTC methods that strongly depend on some accurate system models, the proposed method is model-free and only relies on pre-collected data. Numerical simulations are performed to illustrate the effectiveness of the proposed scheme.