Feedback control of uncertain systems: robustness with respect to neglected actuator and sensor dynamics†

Abstract

Feedback control of a class of imperfectly known dynamical systems is considered. On the basis of known functional properties and bounds relating to the uncertain elements in the generic system, and initially neglecting control actuator and state sensor dynamics, a feedback structure is determined (using established techniques) which guarantees uniform ultimate boundedness of all motions of the system. The effects on performance of the introduction of (i) uncertain actuator dynamics, and (ii) uncertain sensor dynamics, with respective parameters μ_s≥ 0 and μ_s≥ 0 which (inversely) reflect the ‘fastness’ of these dynamics, are subsequently investigated, with main emphasis on case (i). Under appropriate assumptions, in case (i) the existence of a calculable threshold value μ_s∗ > 0 is established such that the property of global uniform ultimate boundedness is retained by the system for all parameter values μ_a ε (0, μ_s∗). Finally, additional conditions are imposed on the sensor structure which enable the results of case (i) to be applied directly to establish the existence of a corresponding calculable threshold value μ_s∗s > 0 in case (ii).