We present a formulation for both implicit and explicit dual model predictive control with chance constraints. The formulation is applicable to systems that are affine in the state and disturbances, but possibly nonlinear in the controls. Awareness of uncertainty and dual control effect is achieved by including the covariance of a Kalman Filter state estimate in the predictions. For numerical stability, these predictions are obtained from a square-root Kalman filter update based on a QR decomposition. In the implicit formulation, the incentive for uncertainty reduction is given indirectly via the impact of active constraints on the objective, as large uncertainty leads to large safety backoffs from the constraint set boundary. The explicit formulation additionally uses a heuristic cost term on uncertainty to encourage its active exploration. We evaluate the methods based on numerical simulation of a simplified but representative industrial steel recycling problem. Here, new steel needs to be produced by choosing a combination of several different steel scraps with unknown pollutant content. The pollutant content can only be measured after a scrap combination is molten, allowing for inference on the pollutants in the different scrap heaps. The cost should be minimized while ensuring high quality of the product through constraining the maximum amount of pollutant. The numerical simulations demonstrate the superiority of the two dual formulations with respect to a robustified but non-dual formulation. Specifically we achieve lower cost for the closed-loop trajectories while ensuring constraint satisfaction with a given probability.
IntroductionPituitary metastases are very rare in cancer patients and often originate from lung or breast tumors. They usually occur in patients with known metastatic disease, but rarely may be the first presentation of the primary tumor.MethodsWe present the case of a 58 years-old-man who reported a three-month history of polyuria-polydipsia syndrome, generalized asthenia, panhypopituitarism and bitemporal hemianopsia. Brain-MRI showed a voluminous pituitary mass causing posterior sellar enlargement and compression of the surrounding structures including pituitary stalk, optic chiasm, and optic nerves.ResultsThe patient underwent neurosurgical removal of the mass. Histological examination revealed a poorly differentiated adenocarcinoma of uncertain origin. A total body CT scan showed a mass in the left kidney that was subsequently removed. Histological features were consistent with a clear cell carcinoma. However, endoscopic examination of the digestive tract revealed an ulcerating and infiltrating adenocarcinoma of the gastric cardia. Total body PET/CT scan with 18F-FDG confirmed an isolated area of accumulation in the gastric cardia, with no hyperaccumulation at other sites.ConclusionTo the best of our knowledge, there are no reports of pituitary metastases from gastric cardia adenocarcinoma. Our patient presented with symptoms of sellar involvement and without evidence of other body metastases. Therefore, sudden onset of diabetes insipidus and visual deterioration should lead to the suspicion of a rapidly growing pituitary mass, which may be the presenting manifestation of a primary extracranial adenocarcinoma. Histological investigation of the pituitary mass can guide the diagnostic workup, which must however be complete.
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