Parameter adaptive control algorithms-A tutorial

Convergence and logarithm laws of self-tuning regulators

Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties

Brief paper: Stochastic adaptive control using a modified least squares algorithm

A recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation (ODE). The ODEs describing the motion of several common adaptive filters are examined in some simple settings, including the least mean square (LMS) algorithm and all three of its signed variants (the signed regressor, the signed error, and the sign-sign algorithms). Stability and instability results are presented in terms of the eigenvalues of a correlation-like matrix. This generalizes known results for LMS, signed regressor LMS, and signed error LMS, and gives new stability criteria for the sign-sign algorithm. The ability of the algorithms to track moving parameterizations can be analyzed in a similar manner, by relating the time varying system to a forced ODE. The asymptotic distribution about the forced ODE is an Ornstein-Uhlenbeck process, the properties of which can be described in a straightforward manner. >

/pdf/weak-convergence-and-local-stability-properties-of-fixed-3dwczij3hw.pdf

Weak convergence and local stability properties of fixed step size recursive algorithms

Weighted least squares, and related stochastic approximation algorithms are studied for parameter estimation, adaptive state estimation, adaptive N -step-ahead prediction, and adaptive control, in both white and colored noise environments. For the fundamental algorithm which is the basis for the various applications, the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator. The selection is guided by the convergence theory. In this way, strong global convergence of the parameter estimates, state estimates, and prediction or tracking errors is not only guaranteed under the appropriate noise, passivity, and stability or minimum phase conditions, but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme.

Convergence of adaptive minimum variance algorithms via weighting coefficient selection

In adaptive equalization, there is a tradeoff between convergence rate of the equalizer tap coefficients, the computational speed for each adjustment, the implementation complexity, and algorithm robustness. Parameter update schemes called quantized state (QS) schemes, and fast versions of these schemes termed fast quantized state (FQS) schemes developed within a related context, are here applied to achieve attractive tradeoff options not previously available for adaptive equalization. Three novel simplifications to the QS schemes are introduced and justified by their performance characteristics in adaptive equalization. One simplification is to abandon the likeness to the method of instrumental variables (IV), where the "instrumental variable" is the quantized state vector, and introduce more quantization. Another simplification is to replace asymptotically Toeplitz matrices, or their inverses, by Toeplitz matrices to take advantage of fast schemes for updating QS schemes or taking their inverses.

http://users.rsise.anu.edu.au/~john/papers/JOUR/061.PDF

Adaptive Equalization Via Fast Quantized-State Methods

Minimum Variance Control Harnessed for Non-Minimum-Phase Plants

Detection techniques in least squares identification

The paper is concerned with the almost sure convergence of the adaptive parameter estimation, N-step ahead prediction and control algorithms based upon standard least square algorithm. With the usual stability and passivity assumptions for the prediction problem, it is demonstrated that the state estimation and the N-step ahead prediction errors converge to the optimum such errors achievable with known plant parameters, in the Cesaro sense. An additional regularity assumption on the signal model establishes the result that the state estimation and prediction errors also converge in the strong sense at an asymptotically arithmetic rate. Under an additional persistency of excitation condition it is shown that the parameter estimation error converges to zero at a rate specified by the degree of excitation. With the regularity condition holding, the convergence is also established for the adaptive control algorithms.

Almost sure convergence of adaptive identification prediction and control algorithms

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