Identification for control: adaptive input design using convex optimization

An optimal experiment design for system identification is studied. The main contribution is the development of an adaptive method for the direct design of FIR filters for the input spectrum design problem. The accuracy of the identified model is measured in terms of the closed-loop performance of the system using the controller designed from the model. Under the assumption that the identified parameters are sufficiently close to their true values, we show that this problem may be formulated as a convex optimization problem with linear matrix inequality constraints. Thus, a global solution (if feasible) is guaranteed and the solution may further achieve any demanded accuracy. The problem formulation is particularly suited for a practical implementation, thus the extension of the experiment design problem into an iterative/adaptive identification-experiment design framework is straight forward. The adaptive approach is further studied in a simulation example, where the rapid convergence of the method is noted, and the superior result compared to an arbitrary experiment design is clear. The example support the use of the approximations taken in the theoretical approach.