Adaptive Loop Transfer Recovery

DAPTIVE control is an attractive approach in nonlinear systems theory due to its ability to cope with system uncertainties and failures. Adaptive controllers can be classified as either indirect or direct. This paper focuses on improving the robustness of a direct adaptive control design. The method is arrived at by examining the loop transfer properties of an adaptive system when linearized about an equilibrium condition. The design approach modifiesanadaptivelawwiththegoalofpreservingthelooptransfer propertiesofareferencemodelassociatedwithanonadaptivecontrol design. The aim is to achieve an adaptive system that preserves the stability margins of a nonadaptive design, while at the same time providing the benefits of adaptation to modeling error. Many modification terms are reported in the literature [1–11]. Included among these, � modification [1] adds a pure damping term to the adaptive law, whereas e modification [2] adds a variable damping term that depends on the error signal. These terms are introduced to ensure that the adapted weights remain bounded. Backgroundlearning[3–5]usescurrentandpastdataconcurrentlyin the adaptation process. It allows the adaptation law to continually train in the background based on past data, while still being responsivetodynamicchangesbasedonthecurrentdata.Inthisway, background learning incorporates long-term learning. Q modification [6–8] is similar in spirit to background learning in its intent to improve adaptation performance by using a moving window of the integrated system uncertainty. There is an optimal control theory based modification term that improves adaptation in the presence of large adaptive gain [9]. More recently, a Kalman filter modification approach[10]hasbeenintroducedasamodificationterminadaptive control.Kalman filtermodificationleadstoalternativeformsforwell