Dynamic extremum control

Extremum control (EC) deals with steady-state optimisation of noisy nonlinear systems and this work is concerned with the use of self-tuning EC methods to control system dynamic behaviour. Previous research has shown the robustness of self-tuning EC to unmodelled nonlinearities. The possibility of having a similar kind of robustness when dealing with dynamic control provided motivation for the development of dynamic extremum control (DEC). There are also computational advantages to be gained, especially in relation to multi-stage cost methods like generalized predictive control (GPC). This work represents a step towards these aims by showing the viability of DEC and providing new results regarding the convergence properties in the single-stage case. We consider GMV control because it is a fairly general strategy in the context of single-stage optimal control.