Electrical and Electronic Engineering - Theses
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ItemParameter and state estimation of nonlinear systems with applications in neuroscience( 2013)The focus of this work is deterministic parameter and state estimation of nonlinear systems with applications to neuroscience. Estimation in neuroscience typically involves the reconstruction of unmeasured neural activity from measurements of the human brain. We envisage that estimation plays a crucial role in neuroscience because of the possibility of creating new avenues for neuroscienti_c studies and for the development of diagnostic, management and treatment tools for diseases such as Epilepsy and Parkinsons disease. One of the most used measurements is the electroencephalogram (EEG). To this end, we consider lumped-parameter nonlinear models with EEG as the output, known as neural mass models. Four observers are proposed in this thesis: (1) a nonlinear observer, (2) robust circle criterion observers, (3) an adaptive observer and (4) the supervisory observer. These observers are synthesised for classes of nonlinear systems, that cover some of the commonly used neural mass models. Two state observers are shown and designed respectively, in Part I, to be robust towards input and measurement noise, as well as small perturbations in parameters. In the absence of noise and perturbations, the estimates converge exponentially to the true values. The convergence of estimates to their true values is with some error in the presence of noise and perturbations. Chapter 3 presents a nonlinear observer speci_c to the class of neural mass models considered. In Chapter 4, we propose robust circle criterion observers for a class of systems, that covers all our examples. We extended available results in the literature such that they can be synthesised for the neural mass models. The robustness of the designed state observers towards parameter uncertainty motivates the estimation of both parameters and states in Part II. In Chapter 5, we design an adaptive observer for a class of interconnected neural mass models. The convergence of the estimates is asymptotic. Finally, in Chapter 6, we present an alternative method using a multiple-model architecture, known in the literature as the supervisory framework. Under non-restrictive conditions, we guarantee the practical convergence of parameters and states.