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

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 \u27un-modeled dynamics\u27) 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

Data-Driven Identification of Dynamic Quality Models in Drinking Water Networks

Traditional control and monitoring of water quality in drinking water distribution networks (WDN) rely on mostly model- or toolbox-driven approaches, where the network topology and parameters are assumed to be known. In contrast, system identification (SysID) algorithms for generic dynamic system models seek to approximate such models using only input-output data without relying on network parameters. The objective of this paper is to investigate SysID algorithms for water quality model approximation. This research problem is challenging due to (i) complex water quality and reaction dynamics and (ii) the mismatch between the requirements of SysID algorithms and the properties of water quality dynamics. In this paper, we present the first attempt to identify water quality models in WDNs using only input-output experimental data and classical SysID methods without knowing any WDN parameters. Properties of water quality models are introduced, the ensuing challenges caused by these properties when identifying water quality models are discussed, and remedial solutions are given. Through case studies, we demonstrate the applicability of SysID algorithms, show the corresponding performance in terms of accuracy and computational time, and explore the possible factors impacting water quality model identification

Robust data-driven neuro-adaptive observers with Lipschitz activation functions

International audienceWhile the use of neural networks for learning has gained traction in control and system identification problems, their use in data-driven estimator design is not as prevalent. Prior art on neuro-adaptive observers limit the type of activation functions to radial basis function networks and provide conservative bounds on the resulting observer estimation error because they leverage boundedness of the activation functions rather than exploiting their underlying structure. This paper proposes the use of Lipschitz activation functions in the neuro-adaptive observer: utilizing the Lipschitz constants of these activations simplifies the data-driven observer design procedure via recently discovered LMI conditions. Furthermore, in spite of measurement noise and approximation error, pre-computable robust stability guarantees are provided on the resulting state estimation error