Data-Driven Existence and Design of Target Output Controllers

Abstract: 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 establishes existence conditions for such controllers using input and partial state data, where the system dynamics are unknown. The approach bypasses traditional system identification steps and leverages the intrinsic structure of historical data to certify controller existence and synthesize a suitable feedback gain. Analytical characterizations are provided, ensuring that the resulting closed-loop system satisfies desired performance objectives such as pole placement or stabilization. Data-driven algorithms are then proposed to design target output controllers directly from data without identifying system parameters, where controllers with the order matching the number 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.