A Projection Operator-Based Discrete-Time Adaptive Architecture for Control of Uncertain Dynamical Systems With Actuator Dynamics

Stability analyses of discrete-time adaptive control algorithms are generally predicated on quadratic Lyapunov-based frameworks that result in unavoidable complexity due to the resulting terms in the Lyapunov difference equations. This prevents generalizations of valuable continuous-time adaptive control results to their discrete-time settings. To this end, one important generalization is the consideration of actuator dynamics, which is present in any uncertain dynamical system. To address this problem, we propose a novel discrete-time adaptive control architecture predicated on the hedging method and a new projection operator. A logarithmic Lyapunov function is used for proving the asymptotic stability of the error between uncertain dynamical system states and hedging-based reference model states. An illustrative numerical example is then presented to demonstrate the efficacy of the proposed architecture.