Application-Based Analysis of Transformations of Uncertain Dynamical Systems Into a Cooperative Form
Résumé
Uncertainty in dynamical system descriptions can have different sources. Whether it be mathematical model simplifications, manufacturing tolerances, and imperfect measurements resulting in parameter uncertainties or be it some kind of time-varying uncertain parameters as an interpretation of state dependencies in quasi-linear state-space representations. On the one hand, uncertainties can be represented as probability distributions in the stochastic case, which can be handled, for example by Monte-Carlo methods. However, those do not allow for the computation of worst-case bounds of the sets of reachable states. On the other hand, interval representations do allow this, which is why we will use those as a bounded error framework in the presented paper. When dealing with interval uncertainty, the rigorous computation of guaranteed state enclosures is a difficult task. Due to conservatism and/or the wrapping effect, overestimation is a common problem. The paper discusses not only a suitable control approach based on LMIs to stabilize an uncertain system but also a cooperativity-enforcing approach, which acts as a countermeasure to the wrapping effect. This simplifies the computation of guaranteed state enclosures in comparison with different methods to get the least conservative hull of the reachable state intervals. This is all done for a boom crane as a real-life application scenario.
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