A MODEL REFERENCE ADAPTIVE CONTROL FRAMEWORK FOR UNCERTAIN DYNAMICAL SYSTEMS WITH HIGH-ORDER ACTUATOR DYNAMICS AND UNKNOWN ACTUATOR OUTPUTS

摘要

As it is well-known, the stability properties of model reference adaptive controllers can be seriously affected by the presence of actuator dynamics. To this end, the authors recently proposed linear matrix inequalities-based hedging approaches to compute the stability limits of model reference adaptive controllers in the presence of a) scalar actuator dynamics with known outputs, b) scalar actuator dynamics with unknown outputs, and c) high-order (linear time-invariant) actuator dynamics with known outputs. The common denominator of these approaches is that they have the capability to rigorously characterize the fundamental stability interplay between the system uncertainties and the necessary bandwidth of the actuator dynamics. Building on these results, the purpose of this paper is to extend the recent work by the authors to the general case, where there exist high-order actuator dynamics with unknown outputs in the closed-loop model reference adaptive control systems. For this purpose, we propose an observer architecture to estimate the unknown output of the actuator dynamics and use the estimated actuator output to design the linear matrix inequalities-based hedging framework. Remarkably, with the proposed observer, the sufficient stability condition in this case of unknown actuator outputs is identical to the case with known actuator outputs that was established in the prior work by the authors. Therefore, a control designer can utilize the proposed framework for practical applications when the output of the actuator dynamics is not measurable, and hence, unknown (e.g., in hypersonic vehicle applications). An illustrative numerical example complements the proposed theoretical contribution.