Data-Driven Existence and Design of Target Output Controllers

Target output controllers aim at regulating a system's target outputs by placing poles of a suitable subsystem using partial state feedback, where full state controllability is not required. This paper first establishes existence conditions for such controllers using input and partial state data, where the system dynamics are unknown and generically unidentifiable from the available data. Analytical characterizations are provided, ensuring that the resulting closed-loop system satisfies desired performance objectives such as pole placement or stabilization by static partial state feedback. Data-based algorithms are then proposed to design target output controllers directly from data without identifying system parameters, where controllers with the order matching the dimension of target outputs and with minimum-order augmented target outputs are both addressed. Furthermore, a separation principle is revealed, decoupling the design of target output controllers from state observers. This enables the development of data-driven observer-based controllers that integrate estimation and control. Numerical examples validate the theoretical results and demonstrate the efficacy of the proposed approach.