A stable strain feedback control design is proposed for a flexible two-link manipulator using a model with partial differential equations directly. Stability is established using a Lyapunov-based design.

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The partial differential equations of a flexible two-link manipulator are derived using the Hamilton’s Principle. The model is validated by simulation as well as experimental studies using a two-link setup in the laboratory.

The regulation of the G2/M transition for the mammalian cell cycle has been modeled using 19 states to investigate the G2 checkpoint dynamics in response to oxidative stress. A detailed network model of G2/M regulation is presented and then a “core” subsystem is extracted from the full network. An existing model of Mitosis control is extended by adding two important pathways regulating G2/M transition in response to DNA damage induced by oxidative stress. Model predictions indicate that the p53 dependent pathway is not required for initial G2 arrest as the Chk1/Cdc25C pathway can arrest the cell in G2 right after DNA damage. However, p53 and p21 expression is important for a more sustained G2 arrest by inhibiting the Thr161 phosphorylation by CAK. By eliminating the phosphorylation effect of Chk1 on p53, two completely independent pathways are obtained and it is shown that it does not affect the G2 arrest much. So the p53/p21 pathway makes an important, independent contribution to G2 arrest in response to oxidative stress, and any defect in this pathway may lead to genomic instability and predisposition to cancer. Such strict control mechanisms probably provide protection for survival in the face of various environmental changes. The controversial issue related to the mechanism of inactivation of Cdc2 by p21 is addressed and simulation predictions indicate that G2 arrest would not be affected much by considering the direct binding of p21 to Cdc2/Cyclin B given that the inhibition of CAK by p21 is already present if the binding efficiency is within a certain range. Lastly, we show that the G2 arrest time in response to oxidative stress is sensitive to the p53 synthesis rate.