Multiple Objective Approach to Adaptive Control of Linear Systems

This paper applies a new approach to the classical adaptive control problem. The approach is based on the inherent conflict between control and identification as they are competing for the only available resource, namely the input to the plant. The theory developed for general nonlinear time varying systems is applied to linear time-invariant system. The conflicting objective, namely, tracking vs. identification is most naturally posed and partially solved in the domain of Multiple Objective Optimization Theory. The control objective here is minimization of a standard quadratic criterion. The identification criterion is maximization of the Fisher information matrix. The Multiple Objective criterion is the simultaneous minimization of the quadratic criterion and maximization of the information matrix. We demonstrate, for linear time invariant plants with quadratic cost, that Pareto optimal adaptive controller may be obtained where a scalars control the tracking vs. identification tradeoff.