All approaches to optimal experiment design for control have so far focused on deriving an input signal (or input signal spectrum) that minimizes some control-oriented measure of plant/model mismatch between the nominal closed loop system and the actual closed loop system, typically under a constraint on the total input power. In practical terms, this amounts to finding the (constrained) input signal that minimizes a measure of a control-oriented model uncertainty set. Here we address the experiment design problem from a "dual" point of view and in a closed-loop setting: given a maximum allowable controloriented model uncertainty measure compatible with our robust control specifications, what is the cheapest identification experiment that will give us an uncertainty set that is within the required bounds? The identification cost can be measured by either the experiment time, the performance degradation during experimentation due to the added excitation signal, or a combination of both. Our results are presented for the situation where the control objective is disturbance rejection only.

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International audienceIn this paper, we investigate the prediction of the cell composition of bacteria with respect to their medium. By modeling the bacterium as an interconnection of subsystems, the problem is written as a nonsmooth convex optimization problem equivalent to a Linear Programming feasibility problem. We then obtain a new method, called Resource Balance Analysis (RBA), predicting the distribution of the available resources in the medium among the various cellular subsystems. Beyond its predictive capability, the proposed approach grasps some fundamental aspects of the bacterium physiology by including a refined model. This method reveals the existence of an intrinsic bottleneck in the system resource distribution of the bacterium, leading to the existence of a structural limitation of its growth rate which can be predicted. RBA is also able to predict the configuration of the metabolic network for a given medium at steadystate regimen which nicely fits the available experimental results for the gram-positive model bacterium Bacillus subtilis