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Robust delay‐dependent LPV synthesis for blood pressure control with real‐time Bayesian parameter estimation

Mean arterial blood pressure (MAP) dynamics estimation and its automated regulation could benefit the clinical resuscitation of patients in critical conditions. To address the variability and complexity of the MAP response of patients to vasoactive drug infusion, a parameter-varying model with a varying delay is considered to describe such dynamics. The estimation of the varying parameters and delay is performed via a Bayesian-based multiple-model square-root cubature Kalman filtering (MMSRCKF) approach. The estimation results substantiate the effectiveness of the utilized identification method using experimental data. Next, an automated drug delivery scheme to regulate the real-time MAP response of patients is developed via time-delay linear parameter-varying (LPV) control techniques. To this end, a gain-scheduled outputfeedback LPV controller is designed to track a desired reference MAP target and guarantee robustness against norm-bounded uncertainties and disturbances in terms of the closed-loop system induced L 2 -norm. Parameter-dependent Lyapunov–Krasovskii functionals (LKFs) are used to derive sufficient conditions in the convex linear matrix inequality (LMI) constraint framework for the robust stabilization of LPV systems with arbitrarily varying delay. Finally, to evaluate the performance of the proposed MAP regulation approach, closed-loop simulations are conducted, and the results confirm the effectiveness of the proposed method against various simulated clinical scenarios.