Thesis
A novel approximation algorithm for the solution and control of nonlinear and coupled systems
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2026
- Thesis identifier
- T18003
- Person Identifier (Local)
- 202068978
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- This thesis develops and assesses the “approximation via dual auxiliary problems” (ADAP) method, a novel algorithm for solving nonlinear, coupled dynamical systems. Many existing approximation techniques use simplified initial guesses that are augmented through the use of calibrated corrections – this is the foundational principle of the ADAP method. Departing from existing methods, the ADAP method is designed to enhance the performance of linear model-predictive control (MPC) algorithms, forming the ADAP-MPC strategy - a generalised architecture for the ADAP method’s integration with MPC, introduced in the second half of this thesis. The method is assessed through solving the governing dynamics of a large-scale, high-precision industrial manipulator. This manipulator is then considered as a further case study for the ADAP-MPC strategy. The ADAP methodology demonstrates improved accuracy and computational efficiency. In the examples and case study considered in the first half of this thesis, the observed absolute error is generally lower than the Lindstedt-Poincar´e technique to which it is compared. In quantifying the computational burden associated with both algorithms, the ADAP approach is shown to have a reduced cost. In the second half of this thesis, the ADAP-MPC strategy achieves similar performance improvements in the control domain compared to a commonly-used approach. The transient and steady-state errors of the studied systems are generally improved with the ADAP-MPC strategy. Furthermore, the resulting control effort is shown to be either reduced or consistent with that of the feedback linearisation strategies considered. The significance of this work is the introduction of a novel approximation algorithm which permits the use of linear MPC while simultaneously improving accuracy and reducing computational burden in controlling complex nonlinear systems.
- Advisor / supervisor
- Cartmell, Matthew, 1958-
- Wynne, Brad
- Resource Type
- DOI
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PDF of Thesis T18003 | 2026-07-15 | Public | Download |