Finite-horizon optimisation and control of dynamic systems with uncertainty

Abstract

This dissertation addresses the optimisation and control of dynamic systems operating over finite time horizons under uncertainty. The work proposes a methodology for deriving time-dependent feedback controllers from known optimal feedforward strategies. This approach is intended to retain the performance of classical finite-horizon solutions, while improving robustness to model mismatches, parametric deviations, and structural uncertainties.

The proposed framework is applied to a range of systems from both economic and physical domains. In economic modelling, the focus is on a three-sector macroeconomic system with dynamic labour and investment allocation. The finite-horizon optimisation problem is solved numerically using a finite-difference approach with piecewise-constant control parametrisation. In the absence of analytical solutions, this method achieves optimal control trajectories but does not support feedback synthesis in the same way as in mechanical systems.

For physical systems, including a point mass, a gravity pendulum, a cart-pendulum, and an electromechanical linear precision motion levitating platform, the dissertation develops explicit time-dependent feedback controllers derived from analytical feedforward solutions. These controllers are shown to maintain quasi-optimality while compensating for uncertainties. Hybrid control strategies are also introduced, combining finite- and infinite-horizon methods to manage the growth of the control effort close to terminal times and to improve robustness in practical scenarios.

The main contributions of thiswork include demonstrating that finite-horizon optimization can be systematically applied across domains, introducing a method to convert analytical open-loop controls into real-time feedback laws, and developing hybrid schemes that reduce computational complexity and enable practical implementation. The findings suggest that finite-horizon control, when paired with feedback synthesis, offers a powerful tool for managing dynamic systems where both optimality and robustness are critical.