Fault Estimation and Control for Unknown Discrete-Time Systems Based on Data-Driven Parameterization Approach

This study investigates the problem of fault estimation and control for unknown discrete-time systems. Such a problem was first formulated as an $H_{infinity}/H_{infinity}$ multiobjective optimization problem. Then, a data-driven parameterization controller design method was proposed to optimize both fault estimation and robust control performances. In terms of the single-objection $H_{infinity}$ control problem, necessary and sufficient conditions for designing the $H_{infinity}$ suboptimal controller were presented, and the $H_{infinity}$ performance index optimized by the developed data-driven method was shown to be consistent with that of the model-based method. In addition, by introducing additional slack variables into the controller design conditions, the conservatism of solving the multiobjective optimization problem was reduced. Furthermore, contrary to the existing data-driven controller design methods, the initial stable controller was not required, and the controller gain was directly parameterized by the collected state and input data in this work. Finally, the effectiveness and advantages of the proposed method are shown in the simulation results.