Control-Oriented Identification Via Stochastic Optimization

Data-driven control benefits from rich datasets, but constructing such datasets becomes challenging when gathering data is limited. We consider an offline experiment design approach to gathering data where we design a control input to collect data that will most improve the performance of a feedback controller. We consider a setting in which the dynamics are modeled parametrically and formulate a control-oriented identification procedure by way of a stochastic optimization problem that explicitly optimizes the post-experiment closed-loop control performance. We propose solving this problem via stochastic gradient descent by first constructing a gradient estimator of our stochastic objective. We then focus on a particular setting with linear dynamics and quadratic objective, which benefits from a numerically tractable gradient estimator. We show our formulation numerically outperforms an A-and L-optimal experiment design approach, illustrate the effects of scaling the system state and input dimensions, and compare against a recent robust dual control approach.