Enhancing statistical performance of data-driven controller tuning via -regularization

Abstract

Noniterative data-driven techniques are design methods that allow optimal feedback control laws to be derived from inputoutput (I/O) data only, without the need of a model of the process. A drawback of these methods is that, in their standard formulation, they are not statistically efficient. In this paper, it is shown that they can be reformulated as L2-regularized optimization problems, by keeping the same assumptions and features, such that their statistical performance can be enhanced using the same identification dataset. A convex optimization method is also introduced to find the regularization matrix. The proposed strategy is finally tested on a benchmark example in digital control system design.

Virtual reference feedback tuning with Bayesian regularization

“…Finally, the bayesian estimate is compared to the regularized approach in [10]. In Figure 7, it is evident that such an approach is outperformed by the approach proposed here.…”

“…The optimal regularization term is derived in Section IV, to obtain the best achievable performance. The regularized methods will be compared to standard VRFT and to the method [10] on the benchmark example [14] in Section V. The paper is ended by some concluding remarks.…”

“…By suitably tuning the L 2 penalty term in the cost function, the quality of the resulting controller can be significantly improved, as L 2 -regularization is very suited to cope with high variance estimation problems [5]. The regularization term of [10] is tuned based on data-driven convex-concave procedures, whereas the a-priori knowledge of the system cannot be exploited.…”

“…Then, the aim of this paper is two-fold: (i) to apply the Bayesian approach in [18] to tune the kernel of regularized VRFT and use priors on the system also for controller identification, (ii) to show that such a Bayesian perspective may outperform the existing regularized VRFT introduced in [10].…”

“…To enhance the statistical performance of the methods, it has been shown in [10] that the VRFT design can be reformulated as an L 2 -regularized optimization problem. By suitably tuning the L 2 penalty term in the cost function, the quality of the resulting controller can be significantly improved, as L 2 -regularization is very suited to cope with high variance estimation problems [5].…”