Control of positive systems with an unknown state-dependent power law input delay and input saturation

Nonlinear dynamic modeling and model predictive control of thrombin generation to treat trauma‐induced coagulopathy

“…The coagulation process is subject to characteristic nonlinearities that must be compensated for, including input saturation and an unknown state-dependent power law input delay 𝜏 that is a function of TF (state x 1 in (3)), 27 Figure 9:…”

“…Elsewhere, we designed a satisfactory positive system controller, Figure 10A-C, using a Lyapunov analysis. 27 We now compare the performance of our designed MPC schemes from Sections 3 and 4 to this state-of-the-art nonlinear controller for the system dynamics of Trauma Patient 1. We perform MPC simulations from the same initial conditions as Figure 10A-C where the initial thrombin level is elevated at 300 nM, a condition that is commonly observed in patients with hyper-coagulability.…”

“…31 Both features are important for the application in this article because: (1) the coagulation cascade is an example of a positive dynamical system, with states that are confined to the positive orthant of R n , which is denoted in this article by R + ; and (2) the coagulation process is subject to characteristic nonlinearities that must be compensated for, including an unknown state-dependent power law input delay and input saturation. 27 When coupled with MPC's potential to adapt to uncertainty, 32 such as that arising from patient variability, the technique represents a promising process control approach for TIC treatment. Moreover, MPC use can be extended to coagulopathy disorders beyond TIC, for example, hemophilia, factor V Leiden, von Willebrand disease, pulmonary embolism, deep vein thrombosis, stroke, sickle cell disease, and coagulation factor deficiencies.…”

“…In the few studies that mathematically generate the concentration time‐history of thrombin from measured coagulation factor concentrations, either the models are linear with states that are not experimentally measurable, 25 or their computational loads are high, 26 which precludes model use in urgent care settings. Since we have previously shown that coagulation factor concentration modulation approaches have merit, 24 and that it is possible to compensate for unique coagulation nonlinearities when tracking a desired reference concentration of thrombin, 27 what remains is the development of a viable process control strategy that harnesses an accurate nonlinear model of experimentally measurable states. This will enable future experimental validation.…”

“…I G U R E 10 SISO and MISO MPC performance comparison with a state-of-the-art positive system controller in the presence of an unknown state-dependent power law input delay27 for the system dynamics of Trauma Patient 1. (A) TF signal from the controller in the literature 27. (B) The input time delay associated with the signal in panel (A) is between 1 and 2 min.…”