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Parameter identification methods for non-linear discrete-time systems

This paper presents three techniques for parameter identification for non-linear, discrete-time systems. The methods presented are intended to improve the performance of adaptive control systems. The first two methods rely on system excitation and a regressor matrix, 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 to define a parameter uncertainty set. The uncertainty set is periodically updated to shrink around the true parameters. Each method guarantees convergence of the parameter estimation error, provided an appropriate persistence of excitation condition is met. Each method is subsequently demonstrated using a simulation example, displaying convergence of the parameter error estimation error.