Adaptive design and control
Seminar Room 1, Newton Institute
There exist strong relations between experimental design and control, for instance in situations where optimal inputs are constructed in order to obtain precise parameter estimation in dynamical systems or when suitably designed perturbations are introduced in adaptive control to force enough excitation into the system. The presentation will focus on adaptive design when the construction of an optimal experiment requires the knowledge of the model parameters and current estimated values are substituted for unknown true values. This adaptation to estimated values creates dependency among observations and makes the investigation of the asymptotic behaviors of the design and estimator a much more complicated issue than when the design is specified independently of the observations. Also, even if the system considered is static, this adaptation introduces some feedback and the adaptive-design mechanism can be considered as a particular adaptive-control scheme. The role of experimental design in the asymptotic properties of estimators will be emphasized. The assumption that the set of experimental variables (design points) is finite facilitates the study of the asymptotic properties of estimators (strong consistency and asymptotic normality) in stochastic regression models. Two situations will be considered: adaptive D-optimal design and adaptive design with a cost constraint where the design should make a compromise between maximizing an information criterion (D-optimality) and minimizing a cost (function optimization). The case when the weight given to cost minimization asymptotically dominates will be considered in detail in connection with self-tuning regulation and self-tuning optimization problems.