Fault-tolerant control subject to Markov fault model: Direct data-driven strategy

In this work, a direct data-driven control (DDC) scheme for linear systems under stochastic sensor faults is proposed. First, a fault model obeying Markov chain is constructed to reflect the random occurrence of various possible sensor faults. In the case that the controller cannot accurately obtain the actual fault mode, a detected mode-dependent controller is designed, accordingly, a model-based stability condition is established. And then, a data-based representation of the closed-loop system is constructed by introducing a new parameterization relation to solve the unknown fault matrix and stochastic detected modes, based on which the above model-based controller and stability conditions are converted into data-based forms. Unlike traditional model-based methods, the proposed DDC strategy only utilizes the pre-collected input/state data for controller design without explicit knowledge of system matrices. Finally, the effectiveness of the proposed DDC strategy is verified via a numerical example.