As modern engineered systems grow increasingly complex and access to measurement data becomes ubiquitous, direct data-driven controller synthesis has emerged as a compelling alternative to conventional model-based approaches. This thesis presents a comprehensive data-driven framework for robust controller synthesis that leverages frequency-domain data, eliminating the need for explicit parametric modelling.
A key challenge in robust controller synthesis is the quantification of uncertainty, particularly in multiple-input multiple-output (MIMO) systems. Conventional approaches typically represent uncertainties in the frequency-domain as covering sets using weighting filters and are optimised for the uncertainty radius, but these approaches often yield conservative results in the MIMO context. To address this, a novel size metric for uncertainty sets is introduced, alongside a convex optimisation method to compute the nominal model and its associated uncertainty set from a set of models. Furthermore, the approach can also incorporate statistical uncertainties associated with each model.
Addressing the inherent non-convexity of frequency-domain controller synthesis, an iterative optimisation scheme is devised for fixed-structure controller synthesis for generalised plant models represented in Linear Fractional Representation (LFR) form. This framework enables simultaneous optimisation of multiple performance specifications, including H_2 and H_inf, thereby supporting complex and application-relevant specifications. This leads to a direct data-driven synthesis framework that delivers desired performance without excessive conservatism.
Furthermore, the Integral Quadratic Constraint (IQC) theory is systematically integrated to explicitly account for uncertainties within robust data-driven controller synthesis. Notably, the proposed approach supports both parametric and non-parametric IQC multipliers, allowing for flexible and precise modelling of a wide range of perturbations. In particular, novel non-parametric IQC multipliers have been developed for the representation of multimodel uncertainty sets, uncertain time delays, and slope-bounded nonlinearities, resulting in less conservative uncertainty characterisations. This allows the framework to achieve improved performance while maintaining robustness guarantees.
The efficacy and practicality of the proposed framework are demonstrated through various application case studies, which highlight enhanced robustness, reduced conservatism, and effective trade-offs between performance and uncertainty. Overall, the developed framework offers scalable and practical solutions for the next generation of high-performance control systems operating in uncertain and data-rich environments.
