Elastance-based nonlinear dynamical controller synthesis for the in-vitro cardiovascular circulatory system: A backstepping approach

Abstract

This paper investigates the application of a nonlinear system-dependent and system-independent dynamical backstepping (DBST) controller on a cardiovascular circulatory simulator (CCS) with non-triangular affine dynamics for the first time in literature. That is, this study introduces several novel contributions to the field, including the enhancement of cardiac output and physiological fidelity while addressing the limitations of existing control methods. Additionally, we present a comparative performance evaluation of feedback linearization (FBL) and the developed DBST controller with respect to integral squared error (ISE), integral absolute error (IAE), and integral time absolute error (ITAE), offering new insights into each control technique’s error minimization capabilities and overall system performance effectiveness. Furthermore, we pioneer the use of Monte-Carlo (MC) simulations as a reliable in-vitro alternative to clinical trials for controller performance assessment under intra- and inter-patient parameter variations. This innovative approach overcomes the limitations of in-vivo evaluations, enabling the analysis of crucial factors such as signal energy and reference tracking error value. Our results, supported by both MC simulations, demonstrate the complete superiority of the DBST controller over FBL in terms of error reduction and adaptability due to patient-to-patient variability, thus validating its potential for practical applications in cardiovascular circulatory systems.