Controlling a polishing system includes receiving from an in-situ monitoring system, for each region of a plurality of regions on a substrate being processed by the polishing system, a sequence of characterizing values for the region. For each region, a polishing rate is determined for the region, and an adjustment is calculated for at least one processing parameter. Calculation of the adjustment includes minimizing a cost function that includes, for each region, a difference between a current characterizing value or an expected characterizing value at an expected endpoint time and a target characterizing value for the region, and optimization of the cost function is subject to at least one constraint.