A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

TL;DR

This paper presents a convex optimization-based data-driven method for designing robust multivariable controllers that can handle uncertainties and noise, applicable to both continuous and discrete systems, with demonstrated effectiveness on real gyroscope data.

Contribution

It introduces a unified convex optimization framework for robust control design using frequency-domain data, accommodating various controller structures and performance specifications.

Findings

Method achieves monotonic convergence to local optima.

Compared favorably with fixed-structure and full-order controllers in simulations.

Successfully applied to real gyroscope data for practical validation.

Abstract

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like $H_2$, $H_\infty$ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex-concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimal solution in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controllers using non-smooth optimization and with full-order optimal controllers via simulation examples. Finally, the experimental data of a gyroscope is used to design a data-driven controller that is successfully applied on the real system.