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Guaranteed parameter estimation and dual control

Guaranteed parameter and state estimation

The quality of the results of model-based optimization strongly depends on the accuracy of the models that are employed. It is essential that the predictions of variables that are considered in the optimization problem, e.g. product quality parameters, are accurate. The quality of the models can be increased by online adaptation of crucial parameters by robust state and parameter estimation schemes.
In this respect, we pursue a guaranteed parameter estimation approach to obtain robust estimates of uncertain parameters while avoiding unreliable approximations that are associated with classical estimation approaches. The guaranteed estimation approach seeks to find the set of all possible parameter values such that the predicted outputs match the corresponding measurements within prescribed error bounds.

Guaranteed parameter and state estimationS10_1
The solution of the guaranteed parameter and state estimation problems is found by the application of set inversion via interval analysis. We have developed a computationally efficient approach based on improved bounding techniques for parametric ordinary differential equations, and optimization-based domain and CPU-time reduction techniques.


Paulen, R., Villanueva, M., Chachuat, B.: Guaranteed parameter estimation of non-linear dynamic systems using high-order bounding techniques with domain and CPU-time reduction strategies. IMA J Math Control, 2015.

Robust dual nonlinear model-predictive control

Dual control is a technique that seeks to solve the trade-off between probing control actions, which result in more precise estimation of unknown model parameters, and the optimal operation of a nonlinear dynamic system under parametric uncertainty.
We study robust approaches to dual control based on the mul-ti-stage NMPC formulation that lead to a dual control formulation by taking explicitly into account the reduction of the uncertainty that future probing actions will provide over the prediction horizon. Using this formulation, our approach does not require any a priori heuristic decision on the relative importance of the probing actions with respect to the optimal performance of the controlled system, as proposed in some recent approaches, but takes this effect into account exactly.

The novel dual robust NMPC formulation which is based on multi-stage NMPC reduces the conservatism of the robust control actions since it considers that future control inputs can be adapted to future observations and it predicts the future reduction of the uncertainty. The results show the advantage of using a dual robust NMPC over the classical adaptive control approaches, i.e. the sequential use of parameter estimation and optimization.


Thangavel, S., Lucia, S., Paulen, R., Engell, S.: Towards Dual Robust Nonlinear Model Predictive Control: A Multi-stage Approach. In: Proc. American Control Conference, Chicago, 2015, 428–433.