Optimizing adaptive control allocation with actuator dynamics

In this work we address the optimizing control allocation problem for an over-actuated nonlinear time-varying system with actuator dynamic where parameters affine in the actuator and effector model may be assumed unknown. Instead of optimizing the control allocation at each time instant, a dynamic approach is considered by constructing actuator reference update-laws that represent an asymptotically optimal allocation search. By using Lyapunov analysis for cascaded set- stable systems, uniform global/local asymptotic stability is guaranteed for the optimal equilibrium sets described by the system, the control allocation update-law and the adaptive update-law, if some persistence of exitation condition holds. Simulations of a scaled-model ship, manoeuvred at low-speed, demonstrate the performance of the proposed allocation scheme.