Nonlinear Adaptive Control of Fluid Flow Dynamic Systems Under Actuator Uncertainty

A Lyapunov-based adaptive control law is applied to a reduced-order model for a fluid flow dynamic system, which contains parametric uncertainty in both the plant dynamic model and the actuator model. The reduced-order model is derived using a proper orthogonal decomposition (POD) technique. To generate a control-oriented reduced-order model for the actuated flow dynamics, the POD decomposition is performed using both actuated and unactuated modes. This results in a reduced-order flow dynamic model that is in a non-standard mathematical form. This challenge is mitigated through innovative algebraic manipulation in the regulation error system development along with a Lyapunov-based adaptive control law. To the best of the authors' knowledge, this is the first result to apply a nonlinear, Lyapunov-based adaptive control law to the complete actuated POD-based reduced-order flow dynamics to formally compensate for input-multiplicative parametric uncertainty. To achieve the result, a rigorous error system development is presented along with a Lyapunov-based stability analysis. To complement the theoretical development, detailed numerical simulation results are also provided, which show the control design trade-off between the adaptive control law and a standard non-adaptive control law.