Adaptive Identification of Nonlinear Systems
Lehrer, Devon Harold
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This work presents three techniques for parameter identification for nonlinear systems. The methods presented are expanded from those presented in Adetola and Guay [3, 4, 5] and are intended to improve the performance of existing adaptive control systems. The first two methods exactly recover open-loop system parameters once a defined convergence condition is met. In either case, the true parameters are identified when the regressor matrix is of full rank and can be inverted. The third case uses a novel method developed in Adetola and Guay  to define a parameter uncertainty set. The uncertainty set is periodically updated to shrink around the true value of the parameters. Each method is shown to be applicable to a large class of linearly parameterized nonlinear discrete-time system. In each case, parameter convergence is guaranteed subject to an appropriate convergence condition, which has been related to a classical persistence of excitation condition. The effectiveness of the methods is demonstrated using a simulation example. The application of the uncertainty set technique to nonlinearly parameterized systems constitutes the main contribution of the thesis. The parameter uncertainty set method is generalized to the problem of adaptive estimation in nonlinearly parameterized systems, for both continuous-time and discrete-time cases. The method is demonstrated to perform well in simulation for a simplified model of a bioreactor operating under Monod kinetics.