Stability analysis of iterative optimal control algorithms modelled as linear unit memory repetitive processes

Abstract

The theory of unit memory repetitive processes is used to investigate local convergence and stability properties of algorithms for the solution of discrete optimal control problems. In particular, the properties are addressed of a method for finding the correct solution of an optimal control problem where the model used for optimisation is different from reality. Limit profile and stability concepts of unit memory linear repetitive process theory are employed to demonstrate optimality and to obtain necessary and sufficient conditions for convergence. Two main stability theorems are obtained from different approaches and their equivalence is proved. The theoretical results are verified through simulation and numerical analysis, and it is demonstrated that repetitive process theory provides a useful tool for the analysis of iterative algorithms for the solution of dynamic optimal control problems.