Stability Analysis of Discrete Adaptive Control With Adaptive Control Allocation for Uncertain Systems

ABSTRACT An over‐actuated system is a control system in which the number of available independent actuators exceeds the number of independent control variables required to achieve the desired system behavior. This redundancy allows multiple actuator combinations to generate the same control effect, enabling flexibility in allocation strategies. Yet, unknown actuator degradation in over‐actuated systems presents a challenge in controlling uncertain systems. Systems with unknown actuator degradation require designing an adaptive dynamic control allocation method. Also, the presence of uncertain dynamics introduces an additional difficulty to the controlled system's stability. This article presents a discrete‐time adaptive solution for uncertain systems with unknown actuator degradation since discrete‐time control design has advantages over continuous ones (e.g., naturally suited for digital hardware implementation, and avoids quantization issues and stability margin loss by eliminating discretization). A comprehensive Lyapunov stability analysis is provided to prove closed‐loop stability and reference model tracking for the considered system. Numerical results of the simulation on both hexacopter rotational and Aero‐Data Model in Research Environment (ADMIRE) dynamics are provided to illustrate the effectiveness of the proposed control architecture.