Adaptive control with selective memory

Abstract

Adaptive control with selective memory updates the parameter estimates only when there is new information present. The information content increases and the estimator eventually stops. In this paper we use the Fisher information matrix and a variance estimator to measure the information content. The parameter estimates are updated only when the Information Matrix and/or the estimated variance of the prediction error increases. This gives an algorithm for adaptive control which converges to a linear time invariant controller. The resulting controller is robust with respect to bounded disturbances and small model/plant mismatch. Knowledge about overbounding sets for the parameter estimates or the disturbances are not needed. Simulation results using theoretical test cases illustrate near optimal performance for the converged parameters.

Stability of supervised adaptive control

“…Therefore by demonstrating convergence and boundedness of x(t) one proves stability of the closedloop adaptive system. 1 Now define the types of control laws and classes of model mismatch (unmeasured dynamics) handled by the adaptive approach.…”

“…Proof: Given in [1]. Next we develop the relationship between x(t), e C (t) and the Switching Lemma.…”

“…However, the estimator never stops, which means that although the drifting behavior may be suppressed, the probability of introducing bursting remains. The deadzone approach stops parameter estimation once a metric, typically the prediction error, gets below a certain threshold [1], [9]. In this method the estimated parameters are deliberately forced to converge thereby eradicating infinite drift and bursting.…”

“…It is well known that two important types of instabilities arise in adaptive control due to un-modeled dynamics [1]. On the one hand, the estimated parameters drift without anticipated convergence.…”