Internal models and adaptive controls are empirical and mathematical paradigms that have evolved separately to describe learning control processes in brain systems and engineering systems, respectively. This paper presents a comprehensive appraisal of the correlation between these paradigms with a view to forging a unified theoretical framework that may benefit both disciplines. It is suggested that the classic equilibrium-point theory of impedance control of arm movement is analogous to continuous gain-scheduling or high-gain adaptive control within or across movement trials, respectively, and that the recently proposed inverse internal model is akin to adaptive sliding control originally for robotic manipulator applications. Modular internal models' architecture for multiple motor tasks is a form of multi-model adaptive control. Stochastic methods, such as generalized predictive control, reinforcement learning, Bayesian learning and Hebbian feedback covariance learning, are reviewed and their possible relevance to motor control is discussed. Possible applicability of a Luenberger observer and an extended Kalman filter to state estimation problems—such as sensorimotor prediction or the resolution of vestibular sensory ambiguity—is also discussed. The important role played by vestibular system identification in postural control suggests an indirect adaptive control scheme whereby system states or parameters are explicitly estimated prior to the implementation of control. This interdisciplinary framework should facilitate the experimental elucidation of the mechanisms of internal models in sensorimotor systems and the reverse engineering of such neural mechanisms into novel brain-inspired adaptive control paradigms in future.

https://robots.iopscience.iop.org/article/10.1088/1741-2560/2/3/S01/pdf

Internal models in sensorimotor integration: perspectives from adaptive control theory.

This paper deals with the estimation of the noise covariance matrices of systems described by state-space models. Stress is laid on the systematic survey and classification of both the recursive an...

Noise covariance matrices in state-space models: A survey and comparison of estimation methods—Part I

SUMMARY
Unscented Kalman filter (UKF) is a filtering algorithm that gives sufficiently good estimation results for the estimation problems of nonlinear systems even when high nonlinearity is in question. However, in case of system uncertainty or measurement malfunctions, the UKF becomes inaccurate and diverges by time. This study introduces a fault-tolerant attitude estimation algorithm for pico satellites. The algorithm uses a robust adaptive UKF, which performs correction for the process noise covariance (Q-adaptation) or measurement noise covariance (R-adaptation) depending on the type of the fault. By the use of a newly proposed adaptation scheme for the conventional UKF algorithm, the fault is detected and isolated, and the essential adaptation procedure is followed in accordance with the fault type. The proposed algorithm is tested as a part of the attitude estimation algorithm of a pico satellite. Copyright © 2013 John Wiley & Sons, Ltd.

Robust adaptive unscented Kalman filter for attitude estimation of pico satellites

Robust Kalman filtering for small satellite attitude estimation in the presence of measurement faults

http://atestace.utia.cas.cz/DAR/en/download87b1.pdf?bd=626

Methods for Estimating State and Measurement Noise Covariance Matrices: Aspects and Comparison

A recursive algorithm called 3-OM is presented to estimate parameters and noise variances for discrete-time linear stochastic systems. The unprojected version of 3-OM is globally convergent with probability 1 to minima of the asymptotic negative log-likelihood function. 3-OM approximates the quick convergence attained by the optimal nonlinear filter used as a parameter estimator. The state-space form of 3-OM permits application to time-varying linear systems and to online tuning of a Kalman filter.

An online parameter estimator for quick convergence and time-varying linear systems

Towards a Useful Approximation of the Optimal Recursive Parameter Estimator

A counterexample of convergence of a parameter estimator, the recursive prediction error method (RPEM), is presented. Here, a case where the RPEM fails to reach a minimum of the negative log likelihood function is examined. The cause of the failure of asymptotic averaging is disclosed and shown to be generic for any proof of convergence using asymptotic averaging techniques. The assumptions made in the asymptotic averaging theory proof of convergence are strengthened to assure convergence wp1 to a minimum of the asymptotic negative log likelihood function. This is illustrated by means of a simple example. >

T.D. Powell

Papers

An online parameter estimator for quick convergence and time-varying linear systems

Towards a Useful Approximation of the Optimal Recursive Parameter Estimator

A counterexample of proof of convergence using asymptotic averaging