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. ... Read more

It might surprise you that networks play a role in biology, but networks are ubiquitous. All living things have DNA within their cells. This DNA contains the building blocks of an organism. The process of creating such a building block requires mRNA and proteins. The concentration of a certain mRNA molecule plays a part in the making of these proteins. In biology these processes are called transcription and translation. These interacting processes can be transformed into a mathematical model, a network. This network is a collection of nodes and edges, which represent the interactions between different mRNA concentrations. Since these interactions are unknown, random matrix theory is used to model these interactions. It is interesting how the concentrations of mRNA molecules evolve over time. A system of differential equations can be used to model these changes of concentrations over time. This report aims to discover the properties of the model of interacting organisms. For this a linear model is found, which is a system of differential equations linearised around a given equilibrium. A system can be written as a matrix, to model multiple organisms this results in a block matrix. Each block can then be envisioned to model a certain gene pool that corresponds to an organism. Interactions between these gene pools can be modelled by adding an interaction block to the off diagonal blocks of the block matrix. Later on this linear model is improved with a non-­negative constraint, concentrations are after all non-­negative, which results in a new nonlinear model. Properties of both models are found by studying the distribution of the eigenvalues. Girko’s law and Wigner’s law are two important laws from random matrix theory, that help with the determination of the eigenvalues of a random interaction matrix. For the linear model it was found that the distribution of the eigenvalues is influenced by the entries of the block matrix and by the strength of the connection between the block matrices. Once the eigenvalues and the corresponding eigenvectors are found, the solution is deterministic. For the nonlinear model it was found that the distribution of the eigenvalues are influenced in a similar way as the linear model. But due the non­negative constraint, the stability of the system is not deterministic. The system can be partly asymptotically stable, partly stable and partly unstable for different time windows. It is living on the ‘edge of chaos’. ... Read more