On Set-Theoretic Model Reference Adaptive Control of Uncertain Dynamical Systems Subject to Actuator Dynamics

摘要

In applications where the bandwidth of the actuator dynamics is not sufficiently high, the stability of model reference adaptive controllers can be degraded drastically as it is well known. To this end, one of the effective approaches for tackling the challenge of limited actuator bandwidth is the hedging method in which using a "modified" reference model, the adaptation becomes "excluded" from the actuator dynamics. With this approach, however, the performance bounds between the uncertain dynamical system trajectories and the "ideal" reference model trajectories can be conservative and depend on the bounds on the system uncertainties; therefore, no "practical" performance guarantees exist. To address this challenge, we generalize a recently developed set-theoretic model reference adaptive control architecture, which has the capability to achieve "practical" (i.e., user-defined) performance guarantees, for uncertain dynamical systems subject to actuator dynamics. Specifically, we first show that the proposed architecture keeps the performance bounds between the uncertain dynamical system trajectories and the "modified" reference model trajectories within an a-priori, user-defined bound. We next show that the error bounds between the "ideal" reference model trajectories and the uncertain dynamical system trajectories is characterized by this user-defined bound as well as the actuator bandwidth limit, and hence, is "computable" using a given set of adaptive control design parameters. Finally, as a byproduct, our illustrative numerical example shows that the time rate of change of the actual control signal (i.e.. the output of the actuator dynamics) becomes less in magnitude as compared with the the set-theoretic model reference adaptive control case without actuator dynamics.