Guaranteed Exponential Convergence without Persistent Excitation in Adaptive Control

In this paper, a new adaptive control framework for linear systems in which the matched uncertainty can be linearly parameterized is introduced to guarantee the global exponential stability of reference tracking error and parameter convergence error without requiring restrictive persistent excitation condition. The framework uses time histories of control input and system signals to construct least-squares problem based on recorded data. Then, unique solution to least-squares problem is computed, and assigned as pre-selected value in well-known sigma-modification term. Such indirect use of recorded data matrices results in globally exponential convergence of tracking error and parameter convergence error provided that the recorded matrix satisfies the simple rank condition. The proofs are given by Lyapunov stability theorem, and the results are illustrated with simulations.


Sarsilmaz, S. Burak; Kutay, Ali Türker; Yucelen, Tansel (2017-11-09)
In this paper, we study the robustness characteristics of a recently developed concurrent learning model reference adaptive control approach to time-varying disturbances and system uncertainties. Specifically, the commonly-used constant (or slowly time-varying) assumption on disturbances and system uncertainties for this particular adaptive control approach is replaced with its bounded counterpart with piecewise continuous and bounded derivatives. Based on the Lyapunov's direct method, we then show that the...
Adaptive Control Algorithm for Linear Systems with Matched and Unmatched Uncertainties
Yayla, Metehan; Kutay, Ali Türker (2016-12-14)
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Markov chain Monte Carlo methods (MCMC) are iterative algorithms that are used in many Bayesian simulation studies, where the inference cannot be easily obtained directly through the defined model. Reversible jump MCMC methods belong to a special type of MCMC methods, in which the dimension of parameters can change in each iteration. In this study, we suggest Gibbs sampling in place of RJMCMC, to decrease the computational demand of the calculation of high dimensional systems. We evaluate the performance of...
Convergence Error Estimation and Convergence Acceleration in Iteratively Solved Problems
Eyi, Sinan (null; 2012-07-09)
New methods are developed for convergence error estimation and convergence acceleration in iteratively solved problems. The convergence error estimation method is based on the eigenvalue analysis of linear systems, but it can also be used for nonlinear systems. The convergence of iterative method is accelerated by subtracting convergence error from the iteratively calculated solutions. The performances of these methods are demonstrated for the Laplace, Euler and NavierStokes equations.
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Fritsche, Carsten; Orguner, Umut; Özkan, Emre; Gustafsson, Fredrik (2014-04-24)
Cram´er-Rao lower bounds (CRLBs) are proposed for deterministic parameter estimation under model mismatch conditions where the assumed data model used in the design of the estimators differs from the true data model. The proposed CRLBs are defined for the family of estimators that may have a specified bias (gradient) with respect to the assumed model. The resulting CRLBs are calculated for a linear Gaussian measurement model and compared to the performance of the maximum likelihood estimator for the corresp...
Citation Formats
M. Yayla and A. T. Kutay, “Guaranteed Exponential Convergence without Persistent Excitation in Adaptive Control,” 2016, Accessed: 00, 2020. [Online]. Available: