Linear Parameter Varying Control of Uncertain Time-Delay Systems with Applications to Automated Blood Pressure Regulation



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This dissertation examines the problem of real-time estimation and automated control of mean arterial blood pressure (MAP) response of a critical patient subject to the vasoactive drug infusion in emergency resuscitation scenarios. The proposed methodologies rely on the wealth of the system identification and feedback control theory and can provide reliable and efficient patient resuscitation tools via computerized drug administration. Therefore, such advanced resuscitation methods can reduce emergency care costs and significantly increase the survival chances by improving the patient's MAP regulation in an intensive care unit. In order to derive an appropriate mathematical description, a dynamic first-order linear time-varying model structure with varying parameters and time delay is employed to characterize the patient's complex physiological MAP response dynamics. In the first part of the dissertation, real-time estimation of the varying model 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, two classical frequency-domain control design methods, namely, IMC-PID and parameter-varying loop-shaping approaches, are proposed and implemented to achieve desired MAP regulation in various simulation scenarios. The second part of the dissertation is devoted to the analysis and control synthesis of time-delayed linear parameter-varying (LPV) systems with norm-bounded parametric and/or time-delay uncertainties. LPV time-delay systems are linear dynamical systems whose dynamic characteristics rely on a measurable scheduling parameter vector, where the scheduling parameter vector is used systematically to capture the dynamics of time-varying and nonlinear systems. In order to reduce the design conservatism and handle the varying delay uncertainties, a Lyapunov-Krasovskii based approach is exercised, and by utilizing an improved parameter-dependent Lyapunov Krasovskii functional (LKF) candidate and applying an efficient cross-term bounding technique, the affine Jensen's inequality, sufficient stability and performance conditions are derived and formulated in terms of convex linear matrix inequality (LMI) framework. The final relaxed synthesis conditions are obtained to design a robust delay-dependent gain-scheduled controller, which guarantees closed-loop stability and minimizes disturbance amplification in terms of the induced L2-norm performance specification. The effectiveness of the proposed control design algorithms is assessed through the automated MAP regulation task, and the results are compared with the conventional control approaches in the literature. The final closed-loop simulation results confirm the potential and superiority of the adopted LPV methodologies.



Linear parameter-varying (LPV) time-delay systems, Lyapunov-Krasovskii functionals (LKFs), robust control, scaled small-gain theorem, time-delay uncertainty, induced L2-norm performance, Bayesian estimation, cubature Kalman filter (CKF), real-time parameter estimation, input delay estimation, pharmacological variability, linear matrix inequalities (LMIs), mean arterial blood pressure (MAP) regulation and control


Portions of this document appear in: Tasoujian, Shahin, Saeed Salavati, Karolos Grigoriadis, and Matthew Franchek. "Real-time cubature Kalman filter parameter estimation of blood pressure response characteristics under vasoactive drugs administration." In 2020 American Control Conference (ACC), pp. 3355-3362. IEEE, 2020.; Tasoujian, Shahin, Saeed Salavati, Matthew Franchek, and Karolos Grigoriadis. "Robust IMC-PID and parameter-varying control strategies for automated blood pressure regulation." International Journal of Control, Automation and Systems 17, no. 7 (2019): 1803-1813.; Tasoujian, Shahin, Karolos Grigoriadis, and Matthew Franchek. "Delay-dependent output-feedback control for blood pressure regulation using LPV techniques." In Dynamic Systems and Control Conference, vol. 59162, p. V003T16A011. American Society of Mechanical Engineers, 2019.; Tasoujian, Shahin, Saeed Salavati, Matthew A. Franchek, and Karolos M. Grigoriadis. "Robust delay-dependent LPV synthesis for blood pressure control with real-time Bayesian parameter estimation." IET Control Theory & Applications 14, no. 10 (2020): 1334-1345.