Approximate adjoint-based iterative learning control

Abstract

This paper characterises stochastic convergence properties of adjoint-based (gradient-based) iterative learning control (ILC) applied to systems with load disturbances, when provided only with approximate gradient information and noisy measurements. Specifically, conditions are discussed under which the approximations will result in a scheme which converges to an optimal control input. Both the cases of time-invariant step sizes and cases of decreasing step sizes (as in stochastic approximation) are discussed. These theoretical results are supplemented with an application on a sequencing batch reactor for wastewater treatment plants, where approximate gradient information is available. It is found that for such case adjoint-based ILC outperforms inverse-based ILC and model-free P-type ILC, both in terms of convergence rate and measurement noise tolerance.

Keywords:

• iterative learning control
• stochastic convergence analysis
• stochastic approximation
• approximate gradients
• sequencing batch reactor

Acknowledgements

This work was supported by the Swedish Foundation for Strategic Research (SSF), project number RIT08-0065.