Robust adaptive control system with fixed compensator attaining robust positive realness

This paper presents a new control design for a single input, single output, continuous time linear time invariant plant in the presence of deterministic disturbances and unmodeled dynamics. A novel robust model reference adaptive control scheme is based on the concept of dynamic certainty equivalence (DyCE) and incorporates the design of a fixed compensator in the error feedback loop. The fixed compensator is used to attenuate the effect of disturbances on the tracking error and achieve the robust stability in the presence of unmodeled dynamics by ensuring strict positive realness of the error transfer function. The key feature of our control design are: (1) use of H_∞ design for the fixed compensator, and (2) use of a robust high-order estimator with σ-modification.