Multiple objective optimization approach to adaptive and learning control

Abstract

This paper formulates a new approach to the classical learning/adaptive control. problem. Our approach is based on two key observations: (1(the inherent conflict between control and identification as they compete for the only available resource, namely the input to the plant; (2) when designing and optimizing the performance of a control system the current task, as well as the repertoire of other typical future tasks which the system may encounter during its life time, should be considered. Our approach is formulated for a general nonlinear time-varying plant; thus, unlike existing adaptive control theory, the theory for a linear time-invariant system evolves as a special case of the general case. The design for the full lifetime of the system creates a methodology that specifies what current actions should be taken in addition to the tracking of the current reference trajectory, at the expense of some performance degradation in the current task, so as to improve the performance of future tasks: this is the learning trade off. The conflicting objectives, namely, tracking versus learning and current task versus future tasks, are most naturally posed and partially solved in the domain of ‘multiple objective optimization theory’. We demonstrate for linear time-invariant plants with quadratic cost, that Pareto optimal learning adaptive controllers may be obtained by simple ‘out of loop’ mixing, where a scalar controls the tracking versus learning trade off in a reliable way. © 1992 Taylor & Francis Group, LLC.