Supervised learning-based explicit nonlinear model predictive control and unknown input estimation in biomedical systems

Ankush Chakrabarty, Purdue University

Abstract

Application of nonlinear control theory to biomedical systems involves tackling some unique and challenging problems. The mathematical models that describe biomedical systems are typically large and nonlinear. In addition, biological systems exhibit dynamics which are not reflected in the model (so-called 'un-modeled dynamics') and hard constraints on the states and control actions, which exacerbate the difficulties in designing model-based controllers or observers. This thesis investigates the design of scalable fast explicit nonlinear model predictive controllers (ENMPCs). The design involves (i) the estimation of a feasible region using Lyapunov stability methods and support vector machines; and (ii) within the estimated feasible region: constructing the ENMPC manifold using regression and interpolation techniques. The method leverages the scalability of low-discrepancy sampling, the effectiveness of support vector machines with sparse samples, and the simplicity of regression using tensored polynomials to provide a computationally tractable, safe and efficient ENMPC construction scheme for a general class of nonlinear systems and specifically, biomedical applications. Since full system state information is rarely available in biological applications, we also develop observers for a wide class of nonlinear systems in the presence of unknown exogenous inputs (disturbances in the state and output vector fields). The nonlinearities are characterized using incremental multiplier matrices, which allow us to design the observer gains by solving a set of linear matrix inequalities. Additionally, we solve a generalized eigenvalue problem to prescribe guarantees on the state estimation error. For special cases, we demonstrate that these observers can be extended to estimate unknown but bounded exogenous inputs acting on the system. Next, the proposed observer is extended to a distributed setting for large-scale networks: that is, multiple local observers are constructed to estimate the state of the entire network by leveraging measurements taken from local subsystems. For specific configurations of the network graph, sufficient conditions are provided for simultaneous estimation of the state and exogenous input to an arbitrary degree. The distributed observer is tested on a gene regulatory network in E. coli. Estimates generated by the proposed observers inform the ENMPC in closed-loop, thereby enabling the ENMPC to regulate the system by mitigating the effect of the destabilizing exogenous inputs. The effectiveness of the proposed closed-loop control architecture is tested in-silico on a clinical model of the Hypothalamic-Pituitary-Adrenal (HPA) axis system: a neuro-endocrine system closely linked with post-traumatic-stress disorder. Synopsizing, we have developed systematic and efficient control and observer approaches that can be applied to a broad class of biomedical applications with guaranteed performance.

Degree

Ph.D.

Advisors

Rundell, Purdue University.

Subject Area

Applied Mathematics|Biomedical engineering|Electrical engineering

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