Data-Driven Control

Abstract

The field of control engineering has evolved significantly in response to the increasing complexity and uncertainty of modern technological systems. Traditional control methods, which rely on precise analytical models derived from first principles, often encounter limitations when applied to systems with unknown dynamics, time-varying parameters, or unmeasured disturbances. These challenges have motivated the development of data-driven control methodologies, which utilise the growing availability of input-output data to learn a control law directly from data, without the need for an explicit model.

Among the various data-driven approaches, Subspace Predictive Control (SPC) integrates subspace identification with Model Predictive Control (MPC) into a unified data-driven framework. The classical SPC formulation is based on an AutoRegressive with eXogenous input (ARX) model, which restricts its ability to capture coloured noise and complex stochastic dynamics.

This thesis investigates whether SPC can be extended to AutoRegressive Moving Average with eXogenous input (ARMAX) models to enhance noise modelling and control performance. The research addresses two key questions: from a theoretical perspective, how ARMAX models can be integrated into the SPC framework to achieve improved noise representation; and from a practical perspective, how ARMAX-based SPC can be applied to a real-life system exhibiting an anti-resonance.

The proposed framework reformulates the SPC data and prediction equations to include the ARMAX structure and employs Extended Recursive Least Squares for online identification. Both simulation studies and laboratory experiments on an inertia-spring-damping system were conducted to evaluate reference tracking, computational cost, and numerical robustness.

The results demonstrate that lower-order ARMAX models outperform ARX models, achieving substantially lower Integral Absolute Error (IAE), Integral Squared Error (ISE), and Input Energy (InEn) while producing smoother control actions. For higher-order models, however, both methods show comparable control performance, as the deterministic part of the system dynamics becomes well identified. Importantly, the computational cost of the ARMAX-based SPC remains of the same order as the ARX formulation for an equivalent number of parameters, confirming its feasibility for real-time implementation. These findings provide a foundation for future research on multi-input multi-output (MIMO) systems, hybrid SPC formulations, and stochastic predictive control frameworks.

Keywords – Data-Driven Control, Subspace Predictive Control, Model Predictive Control, System Identification, Recursive Least Squares, ARX, ARMAX, Markov Parameters.